4 hdd2 by Nakhon Pathom Rajabhat University

ISBN 974-229-997-2

ราคา 220 บาท

Strengthening The Hard Disk Industry in Thailand National Electornics and Computer Technology Center National Science and Technology Development Agency Ministry of Science and Technology 112 Thailand Science Park, Phahon Yothin Road, Klong Luang, Pathumthani 12120, THAILAND. Tel. +66(0)2-564-6900 Fax. +66(0)2-564-6901..2

การประมวลผลสัญญาณสำหรับการจัดเก็บข้อมูลดิจทิ ลั เล่ม 2 : การออกแบบวงจรภาครับ

โครงการเสริมสร้างความแข็งแกร่งให้กบั อุตสาหกรรมฮาร์ดดิสก์ไดรฟ์ในประเทศไทย ศูนย์เทคโนโลยีอเิ ล็กทรอนิกส์และคอมพิวเตอร์แห่งชาติ สำนักงานพัฒนาวิทยาศาสตร์และเทคโนโลยีแห่งชาติ กระทรวงวิทยาศาสตร์และเทคโนโลยี 112 อุทยานวิทยาศาสตร์ประเทศไทย ถนนพหลโยธิน ตำบลคลองหนึง่ อำเภอคลองหลวง จังหวัดปทุมธานี 12120 โทรศัพท์ 02-564-6900 โทรสาร 02-564-6901..2

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ãËé ¼ÙéÍèÒ¹ÈÖ¡ÉÒË¹Ñ§Ê×Í àÅèÁ ·Õ 1 ãËé à¢éÒã¨¡èÍ¹·Õ ¨ÐÈÖ¡ÉÒË¹Ñ§Ê×Í àÅèÁ ¹Õ à¾× Í·Õ ¨Ðä´é à¢éÒã¨ã¹º·àÃÕÂ¹ ÁÒ¡ÂÔ § ¢Ö ¹ â´Âã¹Ë¹Ñ§Ê×Í àÅèÁ¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ËÅÑ¡¡ÒÃÍÍ¡áººÇ§¨ÃÀÒ¤ÃÑº ¢Í§ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼Å ÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ã¹ÃÙ»áºº·Õ §èÒÂµèÍ ¡ÒÃà¢éÒã¨áÅÐÈÖ¡ÉÒ´éÇÂµ¹àÍ§ ¹Í¡¨Ò¡¹Õ ¼Ùéà¢ÕÂ¹ ÂÑ§ ä´é ãªé Ë¹Ñ§Ê×Í àÅèÁ ¹Õ »ÃÐ¡Íº¡ÒÃÊÍ¹ÇÔªÒ ¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ÊÓËÃÑº ¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ ´Ô¨Ô·ÑÅ (signal processing for digital data storage) «Ö §ã¹¢³Ð¹Õ ä´éà» ´ÊÍ¹ã¹ËÅÑ¡ÊÙµÃÇÔÈÇ¡ÃÃÁÈÒÊµÃ ºÑ³±Ôµ ªÑ ¹» ·Õ 4 ¢Í§ÁËÒÇÔ·ÂÒÅÑÂ ÃÒªÀÑ¯ ¹¤Ã»°Á áÅÐÊ¶ÒºÑ¹ à·¤â¹âÅÂÕ ¾ÃÐ¨ÍÁà¡ÅéÒ ¾ÃÐ¹¤Ã àË¹×Í

¢éÒ¾à¨éÒä´éà¢ÕÂ¹Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ¢Ö ¹ÁÒâ´ÂÍÒÈÑÂ»ÃÐÊº¡ÒÃ³ì·Ñ §ËÁ´·Õ ä´éÃÑºµÑ §áµèàÃÔ Á¡ÒÃÈÖ¡ÉÒÃÐ´Ñº ªÑ ¹»ÃÔÒàÍ¡·Õ Georgia Institute of Technology »ÃÐà·ÈÊËÃÑ°ÍàÁÃÔ¡Ò ¹Í¡¨Ò¡¹Õ ¢éÒ¾à¨éÒÂÑ§à¤Â ·Ó§Ò¹ÇÔ¨ÑÂ ·Ò§´éÒ¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ³ ÈÙ¹ÂìÇÔ¨ÑÂ ¢Í§«Õà¡· (Sea gate research center) ·Õ àÁ×Í§ Pittsburgh »ÃÐà·ÈÊËÃÑ°ÍàÁÃÔ¡Ò à» ¹ ÃÐÂÐàÇÅÒ 1 » ·ÓãËé ¢éÒ¾à¨éÒ ÁÕ ¤ÇÒÁÃÙé áÅÐ¤ÇÒÁªÓ¹Ò·Ò§´éÒ¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì â´Âã¹º··Õ 1 ¨Ð¡ÅèÒÇ¶Ö§ ¾× ¹°Ò¹·Ñ Çä»¢Í§¡ÒÃºÑ¹·Ö¡ ÃÐººààÁè àËÅç¡ ààºº´Ô¨Ô·ÑÅ, ¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹áÅÐÍèÒ¹¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì, áÅÐààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ ÃÐººààÁè àËÅç¡ «Ö § ¨Ð¶Ù¡ ¹Óä»ãªé ã¹¡ÒÃ ÍÍ¡áººÇ§¨ÃÀÒ¤ÃÑº ¢Í§ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì º··Õ 2 ¨ÐÍ¸ÔºÒÂ¶Ö§ ¤ÇÒÁÊÓ¤Ñ, ËÅÑ¡¡ÒÃ·Ó§Ò¹, áÅÐ¡ÒÃÍÍ¡áºº ¢Í§ÃÐººä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ (timing recovery) º· ·Õ 3 ¨Ð¡ÅèÒÇ¶Ö§ ¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ (target) ààÅÐÍÕ¤ÇÍäÅà«ÍÃì (equalizer) ·Õ ãªé ã¹ªÔ» ªèÍ§ÊÑÒ³ÍèÒ¹ (read channel chip) º··Õ 4 ¨ÐÍ¸ÔºÒÂ¶Ö§ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML (partial response maximum likelihood) º··Õ 5 ¨Ð¡ÅèÒÇ¶Ö§¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ (er ror event) à¾× Í·Õ ¨Ð¹Ó¼ÅÅÑ¾¸ì ·Õ ä´é ÁÒãªé »ÃÑº»ÃØ§ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ ÎÒÃì´´ÔÊ¡ì ä´Ã¿ì º··Õ 6 áÅÐº··Õ 7 ¨ÐÍ¸ÔºÒÂ¶Ö§ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML (noise predictive maximum likelihood) áÅÐÇ§¨ÃµÃÇ¨ËÒ PDNP (pattern dependent noise predictive) µÒÁÅÓ´Ñº «Ö §à» ¹Ç§¨ÃµÃÇ¨ËÒ·Ñ §ÊÍ§áºº¹Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML â´Âà©¾ÒÐ ÍÂèÒ§ÂÔ § àÁ× Í ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÁÕ ¤ÇÒÁ¨Ø ÁÒ¡ áÅÐº··Õ 8 «Ö § à» ¹ º·ÊØ´·éÒÂ¢Í§Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨ÐáÊ´§

¢Ñ ¹µÍ¹¡ÒÃÍÍ¡ààººÃËÑÊ RLL (run length limited) «Ö § à» ¹ ÃËÑÊ ÁÍ´Ù àÅªÑ¹ ·Õ ¹ÔÂÁãªé ã¹ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ¨ÐäÁèÊÒÁÒÃ¶·ÓãËéÊÓàÃç¨¢Ö ¹ÁÒä´éàÅÂ¶éÒËÒ¡¢Ò´ºØ¤¤ÅµèÒ§æ ·Õ ¤ÍÂãËé¤ÇÒÁªèÇÂàËÅ×Í áÅÐà» ¹¡ÓÅÑ§ã¨ãËé¢éÒ¾à¨éÒµÅÍ´ÁÒ

»ÃÖ¡ÉÒµÅÍ´ÃÐÂÐàÇÅÒ¡ÒÃÈÖ¡ÉÒ â´Âà©¾ÒÐÍÂèÒ§ÂÔ § Prof. John R. Barry áÅÐ Prof. Steve W. McLaughlin ÃÇÁ·Ñ §¹Ñ¡ÇÔ¨ÑÂ¨Ò¡ÈÙ¹ÂìÇÔ¨ÑÂ¢Í§«Õà¡· àªè¹ Dr. Erozan M. Kurtas, Dr. M. Fatih Er den, áÅÐ Dr. Inci Ozgunes ·Õ ãËéâÍ¡ÒÊ¢éÒ¾à¨éÒä´é·Ó§Ò¹ÇÔ¨ÑÂ·Ò§´éÒ¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì áÅÐ·Õ äÁè ÊÒÁÒÃ¶¨ÐÅ×Á ä´é ¡ç ¤×Í ·Ø¡æ ¤¹ã¹¤ÃÍº¤ÃÑÇ ¢Í§¢éÒ¾à¨éÒ ä´éá¡è ¤Ø³ à¡ÕÂÃµÔ â¤ÇÔ¹·ì·ÇÕÇÑ²¹ì, ¤Ø³¾ÃÃ³Õ â¤ÇÔ¹·ì·ÇÕÇÑ²¹ì, ¤Ø³ÃÑª¹ÔÈ âÃ¨¹¡Ô¨, ¤Ø³Í¹Ø·ÑÈ¹ì âÃ¨¹¡Ô¨, ¤Ø³ ©ÑµÃªÑÂ â¤ÇÔ¹·ì·ÇÕÇÑ²¹ì, ¤Ø³¡ÔµµÔÈÑ¡´Ô â¤ÇÔ¹·ì·ÇÕÇÑ²¹ì, áÅÐ¤Ø³ÈÔÃÊØ´Ò âÊÁ¹ÑÊ ¹Í¡¨Ò¡¹Õ ¢éÒ¾à¨éÒ¢Í ¢Íº¤Ø³ ÁËÒÇÔ·ÂÒÅÑÂ ÃÒªÀÑ¯ ¹¤Ã»°Á·Õ ãËé¡ÒÃÊ¹ÑºÊ¹Ø¹ áÅÐãËé ¤ÇÒÁÊÐ´Ç¡¢éÒ¾à¨éÒ µÅÍ´ÃÐÂÐàÇÅÒ ã¹¡ÒÃà¢ÕÂ¹Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ·éÒÂÊØ´¹Õ ¢éÒ¾à¨éÒä´é¾ÂÒÂÒÁÍÂèÒ§ÂÔ §ã¹¡ÒÃ·Õ ¨Ð·ÓãËéË¹Ñ§Ê×ÍàÅèÁ¹Õ §èÒÂµèÍ¡ÒÃàÃÕÂ¹ÃÙé à¾× ÍãËé¼ÙéÍèÒ¹ ÊÒÁÒÃ¶·Ó¤ÇÒÁà¢éÒã¨ä´é ´éÇÂµ¹àÍ§ÍÂèÒ§ÃÇ´àÃçÇ áÅÐÁÕ »ÃÐÊÔ·¸Ô¼Å ËÒ¡Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ÁÕ ¢éÍº¡¾ÃèÍ§ »ÃÐ¡ÒÃã´ ¢éÒ¾à¨éÒ ÁÕ ¤ÇÒÁÂÔ¹´Õ áÅÐ¨Ñ¡ ¢Íº¾ÃÐ¤Ø³ ÂÔ § ËÒ¡·èÒ¹¼Ùéãªé Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨ÐÊè§ ¢éÍ¤Ô´àËç¹ áÅÐ ¤Óá¹Ð¹Ó·Õ à» ¹»ÃÐâÂª¹ìÊÓËÃÑº¡ÒÃ»ÃÑº»ÃØ§Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ÁÒ·Õ ÍÕàÁÅì piya@npru.ac.th à¾× Í·Õ ¢éÒ¾à¨éÒ ¨Ðä´é ´Óà¹Ô¹¡ÒÃ»ÃÑº»ÃØ§ áÅÐá¡éä¢ã¹¡ÒÃ¾ÔÁ¾ì ¤ÃÑ § µèÍä» ÊÓËÃÑº ¢éÍÁÙÅ ¢èÒÇÊÒÃµèÒ§æ à¡Õ ÂÇ¡Ñº Ë¹Ñ§Ê×Í àÅèÁ¹Õ áÅÐÍ× ¹æ ÊÒÁÒÃ¶µÔ´µÒÁä´é·Õ àÇçºä«µì http://home.npru.ac.th/∼t3058

´Ã.» ÂÐ â¤ÇÔ¹·ì·ÇÕÇÑ²¹ì â»Ãá¡ÃÁÇÔÈÇ¡ÃÃÁâ·Ã¤Á¹Ò¤Á ÁËÒÇÔ·ÂÒÅÑÂÃÒªÀÑ¯¹¤Ã»°Á Á¡ÃÒ¤Á 2550

ÊÒÃºÑ

º·¹Ó

1.1

¾× ¹°Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡ààºº´Ô¨Ô·ÑÅ . . . . . . . . . . . . . . . . . . .

1.2

ààºº¨ÓÅÍ§¢Í§ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì . . . . . . . . . . . .

1.3

¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

¡ÃÐºÇ¹¡ÒÃÍèÒ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.5

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡ . . . . . . . . . . . . . . . . . .

1.5.1

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§

. . . . . . . . . . . . . . . . . . . .

1.5.2

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

. . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6

ÊÃØ»·éÒÂº·

1.7

ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ

2.1

º·¹Ó

2.2

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

2.3

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

2.4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

2.3.1

¡ÒÃÇÔà¤ÃÒÐËìàªÔ§àÊé¹¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö § . . . . . . . . . . . . . .

2.3.2

¡ÒÃÇÔà¤ÃÒÐËìàªÔ§àÊé¹¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§

. . . . . . . . . . . . . .

2.3.3

¡ÒÃËÒàÊé¹â¤é§ÃÙ»µÑÇàÍÊ

. . . . . . . . . . . . . . . . . . . . . . . . . .

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä» . . . . . . . . . . . . . . . . .

2.5

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº´Ô¨Ô·ÑÅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.6

àà¹Çâ¹éÁ¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕã¹Í¹Ò¤µ . . . . . . . . . . . . . . . . . . . .

2.7

ÊÃØ»·éÒÂº·

2.8

ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµààÅÐÍÕ¤ÇÍäÅà«ÍÃì

3.1

º·¹Ó

3.2

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1

à§× Í¹ä¢ºÑ§¤ÑºààººâÁ¹Ô¡ (h0

3.2.2

à§× Í¹ä¢ºÑ§¤Ñºààºº

3.2.3

à§× Í¹ä¢ºÑ§¤Ñºààºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ (H

. . . . . . . . . . . .

3.2.4

à§× Í¹ä¢ºÑ§¤Ñºààºº·ÒÃìà¡çµà©¾ÒÐ . . . . . . . . . . . . . . . . . . . . . .

3.3

¼Å¡ÒÃ·´ÅÍ§

3.4

ÊÃØ»·éÒÂº·

3.5

ààºº½ ¡ËÑ´·éÒÂº·

h1 = 1

= 1)

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .

= 1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ç§¨ÃµÃÇ¨ËÒ PRML

4.1

º·¹Ó

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

ÍÕ¤ÇÍäÅà«ÍÃì . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2.1

ÍÕ¤ÇÍäÅà«ÍÃìààºº¼ÅµÍºÊ¹Í§àµçÁ

. . . . . . . . . . . . . . . . . . . .

4.2.2

ÍÕ¤ÇÍäÅà«ÍÃìààºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹ . . . . . . . . . . . . . . . . . .

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2

àà¼¹ÀÒ¾à·ÃÅÅÔÊ

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.3

ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.4

¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ . . . . . . . . . . . . . . . . . . .

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ . . . . . . . . . . . . . . . . . . . . . . .

4.3

4.4

4.4.1

ÊÃØ»Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

ÊÃØ»·éÒÂº·

4.6

ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

5.1

º·¹Ó

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

¤ÇÒÁËÁÒÂ¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ . . . . . . . . . . . . . . . . . . . . . . . .

5.3

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5

¼Å¡ÒÃ·´ÅÍ§

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.5.1

¡ÒÃÇÔà¤ÃÒÐËìÃÐÂÐ·Ò§·Õ ¹éÍÂÊØ´ . . . . . . . . . . . . . . . . . . . . . . . 104

5.5.2

¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§

5.6

ÊÃØ»·éÒÂº·

5.7

ààºº½ ¡ËÑ´·éÒÂº·

SNReff

ààÅÐ BER

. . . . . . . . . . . . . . . . . 107

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Ç§¨ÃµÃÇ¨ËÒ NPML

115

6.1

º·¹Ó

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.2

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ . . . . . . . . . . . . . . . . . . . . . 117

6.3

¡ÒÃËÒ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

6.4

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML . . . . . . . . . . . . . . . . . . . . . . 120

6.5

¼Å¡ÒÃ·´ÅÍ§

6.6

ÊÃØ»·éÒÂº·

6.7

ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . 118

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Ç§¨ÃµÃÇ¨ËÒ PDNP

137

7.1

º·¹Ó

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.2

¡ÒÃ¢Ö ¹ÍÂÙè¡Ñºààºº¢éÍÁÙÅ¢Í§ÊÑÒ³Ãº¡Ç¹

7.3

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP

. . . . . . . . . . . . . . . . . . . . 138

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.4

ÍÑÅ¡ÍÃÔ·ÖÁ PS PDNP

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.5

¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP

7.6

¼Å¡ÒÃ·´ÅÍ§

7.7

ÊÃØ»·éÒÂº·

7.8

ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

¡ÒÃÍÍ¡ààººÃËÑÊ RLL

151

. . . . . . . . . . . . . . . . . . . . . . . 146

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.1

º·¹Ó

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

8.2

8.3

¤ÇÒÁ¨Ø¢Í§ÃËÑÊ RLL ààºº

(d, k)

. . . . . . . . . . . 153

. . . . . . . . . . . . . . . . . . . . . . . . . 154

(d, k)

8.3.1

ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº¢Í§ÃËÑÊ RLL ààºº

. . . . . . . . . . . 155

8.3.2

ÍÑµÃÒ¤ÇÒÁË¹Òàà¹è¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

8.4

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL . . . . . . . . . . . . . . . . . . . . . . . . . . 156

8.5

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

8.5.1

¡ÒÃËÒÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº . . . . . . . . . . . . . . . . . . . . . . 160

8.5.2

(d, k)

. . 160

8.6

¢Ñ ¹µÍ¹¡ÒÃÍÍ¡ààººÃËÑÊ RLL . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

8.7

µÑÇÍÂèÒ§ÃËÑÊ RLL ààººµèÒ§æ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

8.8

ÃËÑÊ

8.9

ÊÃØ»·éÒÂº·

(0, G/I)

ÊÓËÃÑºªèÍ§ÊÑÒ³ PRML

. . . . . . . . . . . . . . . . . . . . 166

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

8.10 ààºº½ ¡ËÑ´·éÒÂº·

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

µÒÃÒ§¿ §¡ìªÑ¹

ÊÙµÃ¤³ÔµÈÒÊµÃì·Õ ÊÓ¤Ñ

171

175

¢.1

µÃÕâ¡³ÁÔµÔ (Trigonometric)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

¢.2

»ÃÔ¾Ñ¹¸ìäÁè¨Ó¡Ñ´à¢µ (Inde nite Integral) . . . . . . . . . . . . . . . . . . . . . . 176

¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì¢Í§àÇ¡àµÍÃìààÅÐàÁ·ÃÔ¡«ì

177

¤ÓÈÑ¾·ìà·¤¹Ô¤

179

ºÃÃ³Ò¹Ø¡ÃÁ

191

´ÃÃª¹Õ

199

ÊÒÃºÑÃÙ»

1.1

ËÅÑ¡¡ÒÃ¾× ¹°Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡ . . . . . . . . . . . . . . . . . . . .

1.2

áºº¨ÓÅÍ§·Ñ Çä»¢Í§ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì [6] . . . . . . .

1.3

ÊÑÒ³¾ÑÅÊì à»ÅÕ Â¹Ê¶Ò¹Ð ÊÓËÃÑº ¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áºº á¹ÇµÑ § . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

¼ÅµÍºÊ¹Í§ä´ºÔµ ÊÓËÃÑº¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ § . . .

1.5

¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³¾ÑÅÊìä´ºÔµ ÊÓËÃÑº ¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç ¹Í¹ áÅÐ (b) áººá¹ÇµÑ § . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§ . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

1.8

¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ áººµèÒ§æ ÊÓËÃÑº ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ (a)

. . . . . . . . . . . . . . . . . . . . . . . . . .

áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

. . . . . . . . . . . . . . . . . . . . . . . .

2.1

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº¹ÔÃ¹ÑÂ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ ¾ÃéÍÁ¡Ñºä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººÍØ»¹ÑÂ . . . . . . . .

2.3

¤èÒÁÒ¡ÊØ´¢Í§

2.4

(a) ¤èÒ

αC

áµèÅÐ

2.5

·Õ ÂÑ§¤§·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ ÊÓËÃÑºáµèÅÐ¤èÒ

·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾áÅÐÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒÀÒÂã¹

14T

áÅÐ¤èÒ

µèÒ§æ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

ºÔµ ÊÓËÃÑº

30T

ÊÓËÃÑº¤èÒ

. . . . . .

¨Ò¡ 0 ¶Ö§

áÅÐ (b) ¼ÅµÍºÊ¹Í§¢Í§ÃÐººàÁ× Íãªé

α100

E(z)

ºÔµ àÁ× Íãªé

d = 14

áÅÐ

αC

¢¹Ò´ÁÒ¡ÊØ´¢Í§

2.7

áºº¨ÓÅÍ§ÊÓËÃÑº¡ÒÃËÒàÊé¹â¤é§ÃÙ»µÑÇàÍÊ

2.8

àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ¢Í§Ç§¨Ã M&M TED ÊÓËÃÑº ªèÍ§ÊÑÒ³ PR4 ·Õ ãªé ä·ÁÁÔ §

2.9

ËÅÑ§¨Ò¡·Õ ¢éÍÁÙÅ¼èÒ¹ä»

2.6

. .

. . . . . . . . . . . . . . . . . . . . .

ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

µÑÇÍÂèÒ§ÅÑ¡É³Ð¢Í§ä«à¤ÔÅÊÅÔ» . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.10 (a) ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒáºº RMS

σ² /T

ªèÍ§ÊÑÒ³ÍØ´Á¤µÔáºº PR4 ·Õ ÁÕ¤èÒ ¤ÇÒÁ¶Õ )

áÅÐ (b) »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ BER ÊÓËÃÑº

σw /T

µèÒ§æ ¡Ñ¹ (àÁ× ÍÃÐººäÁèÁÕÍÍ¿à«µ·Ò§

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.11 »ÃÐÊÔ·¸ÔÀÒ¾ BER ¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»¢Í§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ áºº PR4 ÊÓËÃÑº

σw /T = 0.5%

áÅÐÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ 0.2%

. . . . . . . . .

2.12 â¤Ã§ÊÃéÒ§¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº»ÃÐÁÒ³¤èÒã¹ªèÇ§ . . . . . . . . . . . . . . . .

2.13 »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ ¢Í§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔáºº PR4 . . .

2.14 ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ àÁ× Íãªé

3.1

α50

·Õ

Eb /N0 = 10

. . .

¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ áººµèÒ§æ ÊÓËÃÑº ÃÐºººÑ¹·Ö¡ (a) áººá¹Ç ¹Í¹ áÅÐ (b) áººá¹ÇµÑ § . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

áºº¨ÓÅÍ§ÊÓËÃÑº¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE . . . . . . . . . . . . .

3.3

»ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» BER ¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµµèÒ§æ ÊÓËÃÑº ND = 2

. . . . . . .

3.4

»ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» BER ¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµµèÒ§æ ·Õ ND = 2.5 . . . . . . . . .

3.5

¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµáººµèÒ§æ à·ÕÂº¡ÑºªèÍ§ÊÑÒ³·Õ ND = 2.5

3.6

ÍÑµÊËÊÑÁ¾Ñ¹¸ì¢Í§ÅÓ´Ñº¢éÍÁÙÅ

3.7

(a) ¡ÃÒ¿ÃÐËÇèÒ§ SNR ·Õ µéÍ§¡ÒÃ áÅÐ ND àÁ× Í SNR ·Õ µéÍ§¡ÒÃ áÅÐ

σj

{wk }

ÊÓËÃÑºÃÐºº·Õ ·ÒÃìà¡çµáººµèÒ§æ ·Õ ND = 2.5

σj = 0%

áÅÐ (b) ¡ÃÒ¿ÃÐËÇèÒ§

·Õ ND = 2.5 . . . . . . . . . . . . . . . . . . . . . . .

4.1

ËÅÑ¡¡ÒÃ¾× ¹°Ò¹¢Í§à·¤¹Ô¤ PRML

. . . . . . . . . . . . . . . . . . . . . . . .

4.2

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ

4.3

µÑÇÍÂèÒ§áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅÅÑ¡É³ÐµèÒ§æ

. . . . . . . . . . . . . . . . .

66 66 70

H(D) = 1 + D

4.4

á¼¹ÀÒ¾ªèÍ§ÊÑÒ³áºº PR1,

4.5

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ªèÍ§ÊÑÒ³ PR1,

4.6

á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ PR1,

4.7

á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ EPR4,

4.8

(a) á¼¹ÀÒ¾ºÅçÍ¡, (b) à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, áÅÐ (c) á¼¹ÀÒ¾à·ÃÅÅÔÊ ¢Í§ªèÍ§ ÊÑÒ³

4.9

H(D) = 1 − D2

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³

. . . . . . . . . . . . . . . . .

H(D) = 1 + D

. . . . . . . . . . . .

. . . . . . . . . . . . .

H(D) = 1 + D − D2 − D3

. . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

H(D)

¾ÃéÍÁÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

. . . . . . . . . . . .

4.10 ¤ÓÍ¸ÔºÒÂá¼¹ÀÒ¾à·ÃÅÅÔÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.11 á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ PR4,

H(D) = 1 − D2

. . . . . . . . . . . .

4.12 ¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ . . . . . . . . . . . . . . . . . . . . . .

4.13 á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³

H(D) = 1 + 0.5D

. . . . . . . . . . . . . .

4.14 á¼¹ÀÒ¾Í¸ÔºÒÂ¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔã¹áµèÅÐªèÇ§àÇÅÒ . . . . . . . .

4.15 (a) á¼¹ÀÒ¾ºÅçÍ¡, (b) à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, áÅÐ (c) á¼¹ÀÒ¾à·ÃÅÅÔÊ ¢Í§ªèÍ§ ÊÑÒ³

H(D) = 1 − D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.16 á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ . . . . . . . . . . . . . .

5.1

µÑÇÍÂèÒ§¡ÒÃ·Ó§Ò¹ÀÒÂã¹à·ÃÅÅÔÊ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ . . . . . . . . . . . . .

5.2

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ GPR áººÊÁÁÙÅ

. . . . . . . . . . . . . . . . . . . . .

5.3

µÑÇÍÂèÒ§¡ÒÃ¤Ó¹Ç³ËÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

. . . . . . . . . . . . . . . . . . . . . .

5.4

5.5

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººã¹ÃÙ» (a) BER áÅÐ (b)

5.6

(a) ¡ÃÒ¿ BER áÅÐ

SNReff ,

SNReff

. . . . . .

¢Í§·ÒÃìà¡çµáºº GPR5 . . 109

(b) ¡ÃÒ¿ BER áÅÐ SNR ¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ

áººµèÒ§æ ³ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡·Õ à¢ÕÂ¹ÇèÒ jitter µèÒ§æ ·Õ ND = 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.1

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ

6.2

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¾ÃéÍÁÇ§¨ÃµÃÇ¨ËÒ NPML

. . . . . . . . . . . . . . 116

. . . . . . . . . . . . . . . . 117

6.3

áºº¨ÓÅÍ§¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ

6.4

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR4

6.5

â¤Ã§ÊÃéÒ§¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ·Õ ãªé ¡Ñº §Ò¹»ÃÐÂØ¡µì ·Õ µéÍ§¡ÒÃ¤ÇÒÁàÃçÇ ã¹¡ÒÃ »ÃÐÁÇÅ¼ÅÊÙ§

. . . . . . . . . . . 118

. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.6

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³áººÊÁÁÙÅ ¾ÃéÍÁ·Ñ §Ç§¨ÃµÃÇ¨ËÒ NPML áÅÐ PRML

6.7

á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ (a) ·ÒÃìà¡çµ

Heff (D)

H(D)

1 − 0.247D − 0.753D2

1−D

. . 126

áÅÐ (b) ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

·Õ ãªéã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ¢Í§ÃÐºº PRML

áÅÐ NPML µÒÁÅÓ´Ñº . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.8

á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÓËÃÑºÃÐºº PRML

. . . 128

6.9

á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÓËÃÑºÃÐºº NPML . . . 129

6.10 áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áÁèàËÅç¡ . . . . . . . . . . . . . . . . 130 6.11 »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2

. . . . . . . . . . . . . . . . . . . . . . 131

6.12 »ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ·Õ ãªé¨Ó¹Ç¹á·ç»µèÒ§¡Ñ¹ ·Õ SNR = 17 dB . . . . 132 6.13 »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2.5

. . . . . . . . . . . . . . . . . . . . . 133

6.14 ¼Å¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2.5 . . . . . . . . . . . . 134

7.1

áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.2

¡ÓÅÑ§ÊÑÒ³Ãº¡Ç¹·Õ ¢Ö ¹¡Ñºáºº¢éÍÁÙÅ ³ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃì·Õ ¶Ù¡ÍÍ¡áºº ÊÓËÃÑº·ÒÃìà¡çµ EEPR2 [1 4 6 4 1] ¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ·Õ ND = 2.5, SNR = 30 dB, áÅÐ

7.3

σj /T = 10%

. . . . . . . . . . . . . . . . . . . . . . . . 140

(a) á¼¹ÀÒ¾à·ÃÅÅÔÊÊÓËÃÑº·ÒÃìà¡çµáºº PR4 áÅÐ (b) ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ ´éÇÂá¼¹ÀÒ¾à·ÃÅÅÔÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.4

»ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» ¢Í§ BER ¢Í§Ç§¨ÃµÃÇ¨ËÒµèÒ§æ ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ § ·Õ ND = 2.5 áÅÐ

σj /T = 10%

. . . . . . . 149

8.1

áºº¨ÓÅÍ§¡ÒÃà¢éÒÃËÑÊ RLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.2

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(d, k)

. . . . . . . . . . . . . . . . . . . 157

8.3

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(1, 3)

. . . . . . . . . . . . . . . . . . . 158

8.4

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(0, 3)

. . . . . . . . . . . . . . . . . . . 160

8.5

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(0, 2)

. . . . . . . . . . . . . . . . . . . 161

8.6

µÑÇÍÂèÒ§ÃËÑÊ RLL áººµèÒ§æ ·Õ ãªéã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì . . . . . . . . . . . . . . . . 165

ÊÒÃºÑµÒÃÒ§

3.1

µÑÇÍÂèÒ§·ÒÃìà¡çµáºº PR ·Õ à» ¹·Õ ÂÍÁÃÑº¡Ñ¹ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

4.1

¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§

4.2

5.1

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§

áÅÐ

5.2

. . .

71 88

εa (D) ¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáºº GPR3 ·Õ ND = 2.5

εa (D)

¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áºº PR2 ·Õ ND=2.5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ ÃÐººÁÕ BER =

. . . . . . .

d2 {εa (D)}, ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§ d2eff {εa (D)},

áÅÐÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

5.3

H(D) = 1 + D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§

áÅÐ SNR=22 dB

¢Í§ªèÍ§ÊÑÒ³

d2 {εa (D)}, ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§ d2eff {εa (D)},

áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ áÅÐ SNR = 22 dB

. . . . . . . . . . .

10−4

εa (D)

¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáÅÐ

σj /T

áººµèÒ§æ ³ ¨Ø´

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.1

¨Ó¹Ç¹¢Í§µÑÇ´Óà¹Ô¹¡ÒÃ·Õ ãªéµèÍ¢éÍÁÙÅ 1 ºÔµ ¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP áÅÐ PS PDNP147

8.1

µÑÇÍÂèÒ§¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Ñ §ËÁ´ ºÑ§¤Ñº

(d, ∞)

Nd (L)

·Õ ÁÕ¤ÇÒÁÂÒÇ

·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

(d, k)

8.2

ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº¢Í§ÃËÑÊ RLL áºº

8.3

¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¤ÇÒÁ¨Ø

8.4

µÒÃÒ§¤é¹ËÒÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ RLL áºº

C(d, k)

µèÒ§æ

. . . . . . . . . . . . 156

áÅÐÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR . . . . . . . . . 157

xxi

(0, 2)

. . . . . . . . . . . . . 163

º··Õ 1

º·¹Ó

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ÀÒ¾ÃÇÁ¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅ¢Í§ÍØ»¡Ã³ìÎÒÃì´´ÔÊ¡ìä´Ã¿ì (hard disk drive) à¾× Í à» ¹ ¡ÒÃàµÃÕÂÁ¤ÇÒÁ¾ÃéÍÁãËé ¼ÙéÍèÒ¹à¢éÒã¨¶Ö§ ¾× ¹°Ò¹µèÒ§æ ·Õ à¡Õ ÂÇ¢éÍ§¡Ñº ÃÐºº¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ áºº´Ô¨Ô·ÑÅ ÃÇÁ·Ñ § ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹áÅÐ¡ÒÃÍèÒ¹¢éÍÁÙÅ ã¹ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ¡èÍ¹ ·Õ Í¸ÔºÒÂà¡Õ ÂÇ¡Ñº ¡ÒÃÇÔà¤ÃÒÐËì ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³áÅÐ¡ÒÃÍÍ¡áººÇ§¨ÃÀÒ¤ÃÑº ¢Í§ÎÒÃì´ ´ÔÊ¡ìä´Ã¿ìã¹º·µèÍä»

1.1

¾× ¹°Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡ààºº´Ô¨Ô·ÑÅ

¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡ (magnetic recording) ¤×Í ¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅºÔµãËéÍÂÙèã¹ÃÙ»¢Í§¡ÒÃà»ÅÕ Â¹ á»Å§ÃÐ´ÑºÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ (magnetization) ã¹Ê× ÍºÑ¹·Ö¡ «Ö §ÊÒÁÒÃ¶áºè§ÍÍ¡à» ¹ 2 áºº [1] ¤×Í áººáÍ¹ÐÅçÍ¡ (analog) áÅÐáºº´Ô¨Ô·ÑÅ (digital) ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐ¡ÒÃ ºÑ¹·Ö¡ ÃÐººáÁèàËÅç¡ áºº´Ô¨Ô·ÑÅ ·Õ ãªé ÊÓËÃÑº ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì à·èÒ¹Ñ ¹ â´Â·Õ ¡ÒÃºÑ¹·Ö¡ ÃÐººáÁèàËÅç¡ áºº´Ô¨Ô·ÑÅ¨Ðãªé»ÃÐâÂª¹ì¨Ò¡ÊÁºÑµÔ¢Í§¤ÇÒÁà» ¹áÁèàËÅç¡¢Í§ÇÑÊ´ØºÒ§ª¹Ô´ ·Õ àÁ× ÍÍÂÙèã¹Ê¶Ò¹ÐÍÔ ÁµÑÇ (saturated) áÅéÇ ¨Ð·ÓãËéÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ã¹Ê× ÍºÑ¹·Ö¡ÁÕ·ÔÈ·Ò§ªÕ ä»ã¹·ÔÈ·Ò§ã´·ÔÈ·Ò§Ë¹Ö § ËÃ×Í ã¹·ÔÈ·Ò§µÃ§¡Ñ¹¢éÒÁ «Ö § ÅÑ¡É³Ð¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ áºº¹Õ ¨ÐàËÁÒÐÊÓËÃÑº ¡ÒÃà¡çº ¢éÍÁÙÅ ´Ô¨Ô·ÑÅ ·Õ ÁÕ 2 Ê¶Ò¹Ð ¤×Í ºÔµ 1 áÅÐºÔµ 0 ËÃ×Í·Õ àÃÕÂ¡¡Ñ¹ÇèÒ ¢éÍÁÙÅäº¹ÒÃÕ (binary data) à¾ÃÒÐ©Ð¹Ñ ¹ 1

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

write signal

read-back signal write head

read head

medium disk motion

write current

read voltage

ÃÙ»·Õ 1.1: ËÅÑ¡¡ÒÃ¾× ¹°Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡

ÇÑÊ´Ø àËÅèÒ¹Õ ¨Ö§ ¶Ù¡ ¹ÓÁÒ·Óà» ¹ Ê× Í ºÑ¹·Ö¡ à¾× Í à¡çº ¢éÍÁÙÅ äº¹ÒÃÕ à¹× Í§¨Ò¡¢éÍÁÙÅ ã¹» ¨¨ØºÑ¹ ÊèÇ¹ÁÒ¡¨Ð ÍÂÙè ã¹ÃÙ» ¢Í§¢éÍÁÙÅ ´Ô¨Ô·ÑÅ àªè¹ ¢éÍÁÙÅ ã¹à¤Ã× Í§¤ÍÁ¾ÔÇàµÍÃì áÅÐ¢éÍÁÙÅ ·Õ ÃÑºÊè§ ¼èÒ¹à¤Ã×Í¢èÒÂÍÔ¹ à·ÍÃì à¹çµ à» ¹µé¹ ¹Í¡¨Ò¡¹Õ ¢éÍÁÙÅáÍ¹ÐÅçÍ¡¡çÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡á»Å§ãËéÍÂÙèã¹ÃÙ»¢Í§¢éÍÁÙÅ´Ô¨Ô·ÑÅä´éà¾× ÍãËé §èÒÂµèÍ ¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ â´Â¼èÒ¹¢Ñ ¹µÍ¹¡ÒÃ¡Å Ó ÃËÑÊ ¾ÑÅÊì (PCM: pulse code modulation) [2] à¾ÃÒÐ©Ð¹Ñ ¹ ¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡áºº´Ô¨Ô·ÑÅ¨Ö§àËÁÒÐÊÁ¡Ñº¡ÒÃà¡çº¢éÍÁÙÅã¹» ¨¨ØºÑ¹ ã¹» ¨¨ØºÑ¹¹Õ ¤ÇÒÁµéÍ§¡ÒÃà¹× Í·Õ ã¹¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ¢Í§ÍØ»¡Ã³ìÍÔàÅç¡·ÃÍ¹Ô¡ÊìµèÒ§æ ä´éá¡è ¤ÍÁ ¾ÔÇàµÍÃì, â·ÃÈÑ¾·ìà¤Å× Í¹·Õ , à¤Ã× Í§àÅè¹ à¾Å§áºº¾¡¾Ò, áÅÐ¡ÅéÍ§¶èÒÂÃÙ» ´Ô¨Ô·ÑÅ à» ¹µé¹ ÁÕ ÁÒ¡¢Ö ¹ àÃ× ÍÂæ à·¤â¹âÅÂÕ ¡ÒÃºÑ¹·Ö¡ ÃÐººáÁèàËÅç¡ áºº´Ô¨Ô·ÑÅ ¶×Í ä´é ÇèÒ à» ¹ ÇÔ¸Õ¡ÒÃËÅÑ¡ ·Õ ãªé ã¹¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ¢Í§§Ò¹»ÃÐÂØ¡µì (application) µèÒ§æ ÃÇÁä»¶Ö§ á¼è¹ºÑ¹·Ö¡áÁèàËÅç¡ (magnetic oppy disk), á¶ººÑ¹·Ö¡ áÁèàËÅç¡ (magnetic tape), ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì, á¼è¹ «Õ ´Õ (CD: compact disc), áÅÐá¼è¹ ´ÕÇÕ´Õ (DVD: digital versatile disc) à» ¹µé¹ ÍÂèÒ§äÃ¡çµÒÁ ·Ø¡§Ò¹»ÃÐÂØ¡µì¨ÐµÑ §ÍÂÙèº¹¾× ¹°Ò¹¢Í§ ËÅÑ¡¡ÒÃ·Ó§Ò¹à´ÕÂÇ¡Ñ¹«Ö §à¡Õ ÂÇ¢éÍ§¡Ñº ËÑÇÍèÒ¹ (read head), ËÑÇà¢ÕÂ¹ (write head), áÅÐÊ× ÍºÑ¹·Ö¡ áÁèàËÅç¡ (magnetic media) ´Ñ§áÊ´§ã¹ÃÙ»·Õ 1.1 àÁ× Í ËÑÇÍèÒ¹áÅÐËÑÇà¢ÕÂ¹áººÍÔ¹´Ñ¡·Õ¿ (inductive head) ¨Ð·ÓÁÒ¨Ò¡ÊÒÃáÁèàËÅç¡ÃÙ»à¡×Í¡ÁéÒ·Õ ÁÕ¤èÒÊÀÒ¾ÅºÅéÒ§áÁèàËÅç¡ (coercivity) µ Ó áÅÐ¤èÒÊÀÒ¾

1.2.

ãËé«ÖÁ¼èÒ¹ä´é (permeability) ÊÙ§ [1, 3] â´Â¨ÐÁÕ¢´ÅÇ´¾Ñ¹ÍÂÙèÃÍºæ áÅÐÊ× ÍºÑ¹·Ö¡¨Ð·ÓÁÒ¨Ò¡ÊÒÃ áÁèàËÅç¡·Õ ÁÕ¤èÒÊÀÒ¾ÅºÅéÒ§áÁèàËÅç¡ÊÙ§ ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨Ð¡ÅèÒÇ¶Ö§ à©¾ÒÐà·¤â¹âÅÂÕ ¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ 2 áºº ¤×Í ¡ÒÃºÑ¹·Ö¡ áººá¹Ç ¹Í¹ (longitudinal recording) áÅÐ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § (perpendicular recording) â´Â·Õ à·¤â¹ âÅÂÕ ¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹à» ¹ à·¤â¹âÅÂÕ ·Õ ãªé ã¹¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì µÑ §áµè Í´Õµ ¨¹ ¶Ö§ » ¨¨ØºÑ¹ ¹Ñ ¹¤×Í ÊÀÒ¾¤ÇÒÁà» ¹ áÁèàËÅç¡ ¢Í§Ê× Í ºÑ¹·Ö¡ ¨Ð¢¹Ò¹¡Ñº ÃÐ¹Òº¢Í§¨Ò¹ºÑ¹·Ö¡ áÁèàËÅç¡ (magnetic disk) ´Ñ§·Õ áÊ´§ã¹ÃÙ»·Õ 1.1 ã¹¢³Ð·Õ à·¤â¹âÅÂÕ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §ä´éàÃÔ Á·Õ ¨Ð¹ÓÁÒãªé ÊÓËÃÑº ¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ã¹» ¨¨ØºÑ¹ â´ÂÊÀÒ¾¤ÇÒÁà» ¹ áÁèàËÅç¡ ¢Í§Ê× Í ºÑ¹·Ö¡ ¨Ð µÑ §©Ò¡¡ÑºÃÐ¹Òº¢Í§¨Ò¹ºÑ¹·Ö¡áÁèàËÅç¡ «Ö §ã¹» ¨¨ØºÑ¹¹Õ §Ò¹ÇÔ¨ÑÂ·Ò§´éÒ¹à·¤â¹âÅÂÕ¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅ áººá¹ÇµÑ §ä´é´Óà¹Ô¹ä»ÍÂèÒ§ÃÇ´àÃçÇ à¾ÃÒÐÇèÒ à·¤â¹âÅÂÕ¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹à¢éÒã¡Åé ¢Õ´¨Ó¡Ñ´ «Ùà»ÍÃì¾ÒÃÒáÁ¡à¹µÔ¡ (superparamagnetic limit) [1, 3, 4, 10] ·ÓãËéäÁèÊÒÁÒÃ¶à¾Ô Á¤ÇÒÁ¨Ø¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ä´é ÁÒ¡¡ÇèÒ 1 à·ÃÐäºµì (TB: terabyte) ¹Í¡¨Ò¡¹Õ à·¤â¹âÅÂÕ ¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅ áººá¹ÇµÑ § ÊÒÁÒÃ¶ªèÇÂà¾Ô Á ¢¹Ò´¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ä´é ËÅÒÂÊÔº à·èÒ àÁ× Í à·ÕÂº¡Ñº ¡ÒÃ ãªéà·¤â¹âÅÂÕ¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅáººá¹Ç¹Í¹ [3, 5]

1.2

ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅ (digital data storage system) ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÒÁÒÃ¶·Õ ¨Ð¨ÓÅÍ§à» ¹ á¼¹ÀÒ¾·Ñ Çä»ä´é µÒÁÃÙ»·Õ 1.2 àÁ× Í ºÔµ¢èÒÇÊÒÃ (message bits) ¨Ð¶Ù¡·Ó¡ÒÃà¢éÒÃËÑÊâ´Â Ç§¨Ãà¢éÒ ÃËÑÊá¡éä¢¢éÍ¼Ô´¾ÅÒ´ (error correction code (ECC) encoder) â´Â·Õ ÃËÑÊ RS (Reed Solomon code) [7, 8] à» ¹ ÃËÑÊ ·Õ ¹ÔÂÁ¹ÓÁÒãªé ã¹¡ÒÃà¢éÒ ÃËÑÊ á¡éä¢¢éÍ¼Ô´¾ÅÒ´¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ã¹» ¨¨ØºÑ¹ ¨Ò¡¹Ñ ¹ ¢éÍÁÙÅ·Õ à¢éÒÃËÑÊáÅéÇ¡ç¨Ð¶Ù¡·Ó¡ÒÃà¢éÒÃËÑÊÍÕ¡¤ÃÑ §Ë¹Ö §´éÇÂ Ç§¨Ãà¢éÒÃËÑÊÁÍ´ÙàÅªÑ¹ (modu lation encoder) à¾× Í·ÓË¹éÒ·Õ ã¹¡ÒÃ»ÃÑº¤Ø³ÊÁºÑµÔ¢Í§¢éÍÁÙÅãËéàËÁÒÐÊÁ¡ÑºªèÍ§ÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ìä´Ã¿ì àªè¹ ·ÓãËéÅÓ´Ñº¢éÍÁÙÅ (data sequence) ÁÕÃÙ»áººµÒÁ·Õ µéÍ§¡ÒÃ ËÃ×Í·ÓãËéÅÓ´Ñº¢éÍÁÙÅäÁè ÁÕÊèÇ¹»ÃÐ¡Íºä¿¿ Ò¡ÃÐáÊµÃ§ (d.c. component) à» ¹µé¹ ÃËÑÊ·Õ ¹ÔÂÁãªéã¹Ç§¨Ãà¢éÒÃËÑÊÁÍ´ÙàÅªÑ¹ ¤×Í ÃËÑÊ RLL (run length limited code) [9] ¢éÍÁÙÅ àÍÒµì¾Øµ ·Õ ä´é ¨Ò¡Ç§¨Ãà¢éÒ ÃËÑÊ ÁÍ´ÙàÅªÑ¹ ¨Ð¶×Í ÇèÒ à» ¹ ¢éÍÁÙÅ ·Õ ¨Ð¶Ù¡ à¢ÕÂ¹à¢éÒ ä»ã¹Ê× Í ºÑ¹·Ö¡ «Ö § ¨ÐàÃÕÂ¡¡Ñ¹ ÇèÒ ºÔµ ·Õ ¨Ð¶Ù¡ ºÑ¹·Ö¡ (recorded bit)

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

message bits

ECC encoder

modulation encoder

(e.g., RS codes)

(e.g., RLL codes)

write current waveform

recorded bits

modulator

write head/medium/read head assembly estimated message bits

ECC decoder

modulation decoder

reproduced bits

read channel read-back voltage waveform

A ÃÙ»·Õ 1.2: áºº¨ÓÅÍ§·Ñ Çä»¢Í§ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì [6]

ËÅÑ§¨Ò¡¹Ñ ¹ ºÔµ ·Õ ¨Ð¶Ù¡ ºÑ¹·Ö¡ ¡ç ¨Ð¶Ù¡ Êè§ ä»ÂÑ§ Ç§¨ÃÁÍ´ÙàÅàµÍÃì (modulator) à¾× Í á»Å§¢éÍÁÙÅ ºÔµ ãËé ÍÂÙè ã¹ÃÙ» ¤Å× ¹ ¡ÃÐáÊä¿¿ Ò à¢ÕÂ¹ (write current waveform) ¨Ò¡¹Ñ ¹ ÃÙ» ¤Å× ¹ ¡ÃÐáÊä¿¿ Ò à¢ÕÂ¹¡ç ¨Ð¶Ù¡» Í¹ä»ÂÑ§ËÑÇà¢ÕÂ¹ à¾× Í·Ó¡ÒÃà¢ÕÂ¹¢éÍÁÙÅÅ§ä»ã¹Ê× ÍºÑ¹·Ö¡ ÊÓËÃÑº ¢Ñ ¹µÍ¹ã¹¡ÒÃÍèÒ¹¢éÍÁÙÅ ËÑÇÍèÒ¹¨Ð·Ó¡ÒÃÍèÒ¹¢éÍÁÙÅ ¨Ò¡Ê× Í ºÑ¹·Ö¡ àÁ× Í ËÑÇÍèÒ¹à¤Å× Í¹·Õ 1

ÁÒ¶Ö§ ºÃÔàÇ³·Õ ÁÕ ¡ÒÃà»ÅÕ Â¹á»Å§ÊÀÒ¾¤ÇÒÁà» ¹ áÁèàËÅç¡

(´Ù ÃÙ» ·Õ 1.1) ¨Ðä´é ¼ÅÅÑ¾¸ì ÍÍ¡ÁÒà» ¹

ÊÑÒ³ÃÙ»¤Å× ¹áÃ§´Ñ¹ä¿¿ Ò ·Õ àÃÕÂ¡¡Ñ¹ÇèÒ ÊÑÒ³ read back ¨Ò¡¹Ñ ¹ ÊÑÒ³ read back ¡ç¨Ð ¶Ù¡Êè§à¢éÒä»·Ó¡ÒÃ»ÃÐÁÇÅ¼Åã¹ªèÍ§ÊÑÒ³ÍèÒ¹ (read channel) «Ö §»ÃÐ¡Íºä»´éÇÂÊèÇ¹»ÃÐ¡Íº µèÒ§æ ä´éá¡è Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó (LPF: low pass lter), Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§ (sampler ËÃ×Í analog to digital converter), ÍÕ¤ÇÍäÅà«ÍÃì (equalizer), áÅÐÇ§¨ÃµÃÇ¨ËÒ (detector) à» ¹µé¹ â´Â¢éÍÁÙÅ àÍÒµì¾Øµ ·Õ ä´é ¡ç ¨Ð¶Ù¡ ·Ó¡ÒÃ¶Í´ÃËÑÊ ´éÇÂ Ç§¨Ã¶Í´ÃËÑÊ ÁÍ´ÙàÅªÑ¹ (modulation decoder) áÅÐÇ§¨Ã ¶Í´ÃËÑÊá¡éä¢¢éÍ¼Ô´¾ÅÒ´ (ECC decoder) à¾× ÍËÒ¤èÒ»ÃÐÁÒ³¢Í§ºÔµ¢èÒÇÊÒÃ·Õ Êè§ÁÒ¨Ò¡µé¹·Ò§ 1

ã¹·Ò§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ºÃÔàÇ³·Õ ÁÕ¡ÒÃà»ÅÕ Â¹á»Å§ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ ¨Ð¶Ù¡á·¹´éÇÂ¢éÍÁÙÅºÔµ 1 áÅÐºÃÔàÇ³

·Õ ÁÕäÁè¡ÒÃà»ÅÕ Â¹á»Å§ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ ¨Ð¶Ù¡á·¹´éÇÂ¢éÍÁÙÅºÔµ 0 â´Â·Õ ÃÙ»áºº¢éÍÁÙÅÅÑ¡É³Ð¹Õ ¨ÐàÃÕÂ¡¡Ñ¹ÇèÒ ÃÙ»áºº NRZI (non return to zero interleaved) àÁ× Í ¢éÍÁÙÅ ºÔµ 1 ËÁÒÂ¶Ö§ ÁÕ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð (transition) áÅÐ ¢éÍÁÙÅºÔµ 0 ËÁÒÂ¶Ö§ äÁèÁÕ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

1.3.

¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹

1.3

¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹

ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹¢éÍÁÙÅ [10] ¢éÍÁÙÅºÔµ¨Ð¶Ù¡á»Å§ãËéÍÂÙèã¹ÃÙ»¤Å× ¹¡ÃÐáÊä¿¿ ÒÃÙ»ÊÕ àËÅÕ ÂÁ (rectangular current waveform) ·Õ àÃÕÂ¡¡Ñ¹ ÇèÒ ¡ÃÐáÊä¿¿ Ò à¢ÕÂ¹ (write current) (´Ù ÃÙ» ·Õ 1.1) â´ÂÇ§¨ÃÁÍ´ÙàÅàµÍÃì (modulator) [1, 4] ¨Ò¡¹Ñ ¹ ¡ÃÐáÊä¿¿ Ò à¢ÕÂ¹¨Ð¶Ù¡ » Í¹ä»ÂÑ§ ¢´ÅÇ´¢Í§ËÑÇ à¢ÕÂ¹ (write head) ·ÓãËéà¡Ô´à» ¹Ê¹ÒÁà¢ÕÂ¹áÁèàËÅç¡ (magnetic write eld) ºÃÔàÇ³ªèÍ§ÇèÒ§ (gap) ÃÐËÇèÒ§ Ê× Í ºÑ¹·Ö¡ ¡Ñº ËÑÇ à¢ÕÂ¹ â´Â ·Ñ Çä» Ê¹ÒÁ à¢ÕÂ¹ áÁèàËÅç¡ ¨Ð µéÍ§ ÁÕ ¢¹Ò´ ËÃ×Í ¤ÇÒÁ à¢éÁ ÁÒ¡ ¡ÇèÒ ÊÀÒ¾ÅºÅéÒ§áÁèàËÅç¡¢Í§Ê× Í ºÑ¹·Ö¡ à¾× Í·Õ ¨Ðä´é ÊÒÁÒÃ¶·ÓãËé Ê× Í ºÑ¹·Ö¡ ³ ºÃÔàÇ³¹Ñ ¹ ÁÕ ÊÀÒ¾¤ÇÒÁ à» è¹ áÁèàËÅç¡ µÒÁ·ÔÈ·Ò§¢Í§Ê¹ÒÁà¢ÕÂ¹áÁèàËÅç¡ ·Õ » Í¹à¢éÒ ä» ¹Í¡¨Ò¡¹Õ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐÊÀÒ¾ ¤ÇÒÁà» ¹ áÁèàËÅç¡ (magnetization transition) ¢Í§Ê× Í ºÑ¹·Ö¡ ÊÒÁÒÃ¶·Óä´é â´Â¡ÒÃà»ÅÕ Â¹á»Å§ ·ÔÈ·Ò§¢Í§Ê¹ÒÁáÁèàËÅç¡ÊÓËÃÑºà¢ÕÂ¹ (ËÃ×Í·ÔÈ·Ò§¢Í§¡ÃÐáÊä¿¿ Òà¢ÕÂ¹) à¾× ÍãËéÊÍ´¤ÅéÍ§¡Ñº¡ÒÃ à¢ÕÂ¹¢éÍÁÙÅºÔµ 0 áÅÐºÔµ 1 ã¹·Ò§»¯ÔºÑµÔ ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì¨Ðãªé ¡ÒÃºÑ¹·Ö¡áººäº¹ÒÃÕ (bina 2

ry recording) ¹Ñ ¹¤×Í ÊÀÒ¾¤ÇÒÁà» ¹ áÁèàËÅç¡ ·Õ ÍÂÙè ã¹Ê× Í ºÑ¹·Ö¡ ¨ÐÁÕ à¾ÕÂ§ 2 ·ÔÈ·Ò§à·èÒ¹Ñ ¹

ËÃ×Í

¡ÅèÒÇÍÕ¡ ¹ÑÂ Ë¹Ö § ¤×Í ÃÐººÊÒÁÒÃ¶ºÑ¹·Ö¡ ¢éÍÁÙÅ ä´é à¾ÕÂ§ 2 ÃÐ´Ñº (ËÃ×Í 2 ¤èÒ) à·èÒ¹Ñ ¹ «Ö § µèÒ§¨Ò¡ ¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅ¢Í§´ÕÇÕ´Õ (DVD) ·Õ ÊÒÁÒÃ¶ºÑ¹·Ö¡¢éÍÁÙÅä´éËÅÒÂæ ÃÐ´Ñº ·Ñ §¹Õ à» ¹à¾ÃÒÐÇèÒ â´Â»¡µÔ ¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹¢éÍÁÙÅÁÕ¤ÇÒÁäÁèà» ¹àªÔ§àÊé¹ (nonlinearity) ÍÂÙè¾ÍÊÁ¤ÇÃ ´Ñ§¹Ñ ¹ ¶éÒ·Ó¡ÒÃºÑ¹·Ö¡ ¢éÍÁÙÅÁÒ¡¡ÇèÒ 2 ÃÐ´ÑºÅ§ä»ã¹Ê× ÍºÑ¹·Ö¡¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ¼Å¡ÃÐ·º·Õ à¡Ô´¨Ò¡¤ÇÒÁäÁèà» ¹àªÔ§àÊé¹ ¡ç¨ÐÂÔ §ÁÕ¤ÇÒÁÃØ¹áÃ§ÁÒ¡¢Ö ¹ «Ö §¨ÐÊè§¼Å·ÓãËé»ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐººáÂèÅ§ÁÒ¡ [4]

1.4

¡ÃÐºÇ¹¡ÒÃÍèÒ¹

ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃÍèÒ¹¢éÍÁÙÅ [10] ËÑÇÍèÒ¹¨Ð·Ó¡ÒÃµÃÇ¨¨Ñº¡ÒÃà»ÅÕ Â¹á»Å§¿ÅÑ¡«ìáÁèàËÅç¡ (mag netic ux) ³ µÓáË¹è§·Õ ÁÕ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ «Ö §à» ¹¼Å·ÓãËéà¡Ô´à» ¹ÊÑÒ³ ¾ÑÅÊì áÃ§´Ñ¹ä¿¿ Ò àË¹Õ ÂÇ¹Óã¹¢´ÅÇ´ µÒÁ¡®¢Í§¿ÒÃÒà´Âì (Faraday s law) ÊÓËÃÑº ºÃÔàÇ³·Õ ÁÕ ¡ÒÃ 2

¶éÒ ¾Ô¨ÒÃ³Ò·ÔÈ·Ò§¢Í§Ê¹ÒÁáÁèàËÅç¡ ¨Ò¡¢Ñ Ç àË¹×Í ä»¢Ñ Ç ãµé (ËÃ×Í ¨Ò¡¢Ñ ÇºÇ¡ä»¢Ñ ÇÅº) ¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹¨ÐÁÕ

ÅÑ¡É³Ðà» ¹áºº¢ÇÒä»«éÒÂ ËÃ×Í«éÒÂä»¢ÇÒ ã¹¢³Ð·Õ ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §¨Ðà» ¹áººº¹Å§ÅèÒ§ ËÃ×ÍÅèÒ§¢Ö ¹º¹ à·èÒ¹Ñ ¹

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

à»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È (isolated transition) ËÑÇÍèÒ¹¨ÐãËé ÊÑÒ³¾ÑÅÊì áÃ§´Ñ¹ä¿¿ Ò ·Õ àÃÕÂ¡¡Ñ¹ ÇèÒ ÊÑÒ³¾ÑÅÊì à»ÅÕ Â¹Ê¶Ò¹Ð (transition pulse)

g(t)

ËÃ×Í

−g(t)

â´Â¨Ð¢Ö ¹ ÍÂÙè ¡Ñº ·ÔÈ·Ò§¢Í§

ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ã¹Ê× ÍºÑ¹·Ö¡ (´ÙÃÙ»·Õ 1.1) ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð (ËÃ×Í ÊÑÒ³¾ÑÅÊì Lorent zian) ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìä´é ¤×Í [4]

g(t) =

³ 1+

PW50

àÁ× Í

¤×Í ¤ÇÒÁ¡ÇéÒ§¢Í§ÊÑÒ³¾ÑÅÊì

g(t)

1 2t PW50

´2

(1.1)

ÇÑ´ ³ µÓáË¹è§ ·Õ ÊÑÒ³¾ÑÅÊì ÁÕ ¤ÇÒÁÊÙ§ à» ¹

¤ÃÖ §Ë¹Ö § ¢Í§¤ÇÒÁÊÙ§ ÊÙ§ÊØ´ áÅÐÊÓËÃÑº ¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § ÊÑÒ³¾ÑÅÊì à»ÅÕ Â¹Ê¶Ò¹Ð¨ÐÁÕ ÃÙ» ÊÁ¡ÒÃ ¤×Í [11]

ln(·)

àÁ× Í

¤×Í ÅÍ¡ÒÃÔ·ÖÁ¸ÃÃÁªÒµÔ (natural logarithm),

tion) «Ö §¹ÔÂÒÁâ´Â ¢Í§

g(t)

Ã √ ! 2t ln 2 g(t) = erf PW50

erf(x) =

√2 π

Rx 0

−t2

erf(·)

dt, áÅÐ PW50

(1.2)

¤×Í ¿ §¡ìªÑ¹¢éÍ¼Ô´¾ÅÒ´ (error func

¤×Í ¤ÇÒÁ¡ÇéÒ§¢Í§¾ÑÅÊì

g 0 (t) ËÃ×Í Í¹Ø¾Ñ¹¸ì

ÇÑ´ ³ µÓáË¹è§·Õ ÊÑÒ³¾ÑÅÊìÁÕ¤ÇÒÁÊÙ§à» ¹¤ÃÖ §Ë¹Ö §¢Í§¤ÇÒÁÊÙ§ÊÙ§ÊØ´

ã¹ ÃÐºº ¡ÒÃ ºÑ¹·Ö¡ ¢éÍÁÙÅ ¢Í§ ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ¤ÇÒÁ Ë¹Òá¹è¹ ¢Í§ ¡ÒÃ ºÑ¹·Ö¡ áºº ¹ÍÃì ÁÍ ÅäÅ«ì (ND: normalized recording density) ËÃ×Í ¤ÇÒÁË¹Òá¹è¹¢Í§¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅ [4] ¨Ð¹ÔÂÒÁâ´Â

ND = àÁ× Í

(1.3)

¤×Í ¤ÒºàÇÅÒ¢Í§¢éÍÁÙÅË¹Ö §ºÔµ ËÃ×Í·Õ àÃÕÂ¡¡Ñ¹ÇèÒ ºÔµà«ÅÅì (bit cell) «Ö §¨Ðà» ¹µÑÇºè§ºÍ¡

ÇèÒ ºÃÔàÇ³ ¤èÒ

PW50 T

PW50

ÊÒÁÒÃ¶·Õ ¨Ð¨Ñ´à¡çº¢éÍÁÙÅä´é¨Ó¹Ç¹¡Õ ºÔµ ´Ñ§¹Ñ ¹ ¶éÒ¡ÓË¹´ãËé

à» ¹¤èÒ¤§·Õ àÁ× Í

ËÃ×Í ND à¾Ô Á ¢Ö ¹ ¡ç ËÁÒÂ¤ÇÒÁÇèÒ ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÊÒÁÒÃ¶¨Ø ¢éÍÁÙÅ ä´é ÁÒ¡¢Ö ¹ ÃÙ» ·Õ 1.3

áÊ´§¼ÅµÍºÊ¹Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐÊÓËÃÑº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹áÅÐáººá¹ÇµÑ § ³ ÃÐ´Ñº ND µèÒ§æ ¨ÐàËç¹ä´éÇèÒ ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð¢Í§·Ñ § 2 ÃÐºº¨Ð¤ÃÍº¤ÅØÁªèÇ§àÇÅÒËÅÒÂæ ºÔµà«ÅÅì â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í ND ÁÕ ¤èÒ à¾Ô Á ¢Ö ¹ ËÃ×Í ÍÒ¨¨Ð¡ÅèÒÇä´é ÇèÒ ¡ÒÃá·Ã¡ÊÍ´ÃÐËÇèÒ§ÊÑÅÑ¡É³ì (ISI: intersymbol interference) ã¹ÊÑÒ³ read back ¨ÐÁÕ ¤ÇÒÁÃØ¹áÃ§ÁÒ¡¢Ö ¹ àÁ× Í ND ÁÕ ¤èÒ

1.4.

¡ÃÐºÇ¹¡ÒÃÍèÒ¹

ND = 2

ND = 2.5 ND = 3

Amplitude

0.8

0.6

0.4

0.2

0 −5

(a) t/T 1 0.8

ND = 2 ND = 2.5 ND = 3

0.6

Amplitude

0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −5

(b) t/T

ÃÙ»·Õ 1.3: ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð ÊÓËÃÑº¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

à¾Ô Á¢Ö ¹ à¹× Í§¨Ò¡ âÍ¡ÒÊ·Õ ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ÍÂÙèã¡Åé¡Ñ¹¨ÐÁÒ«éÍ¹àËÅ× ÍÁ (overlap) ¡Ñ¹ÁÕ ¤ÇÒÁà» ¹ä»ä´éÊÙ§ ã¹¡Ã³Õ·Õ ËÑÇÍèÒ¹à¤Å× Í¹·Õ ÁÒ¶Ö§ºÃÔàÇ³·Õ ÁÕµÓáË¹è§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐµÔ´¡Ñ¹ 2 ¤ÃÑ § ÊÑÒ³¾ÑÅÊì

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊØ·¸Ô ·Õ ä´é ¨ÐàÃÕÂ¡¡Ñ¹ ÇèÒ ÊÑÒ³¾ÑÅÊìä´ºÔµ (dibit pulse) ËÃ×Í ¼ÅµÍºÊ¹Í§ä´ºÔµ (dibit re sponse) [4] «Ö §ÁÕ¤èÒà·èÒ¡Ñº

m(t) = g(t) − g(t − T )

(1.4)

´Ñ§áÊ´§ã¹ÃÙ»·Õ 1.4 ¶éÒãªé¡ÒÃá»Å§¿ÙàÃÕÂÃì·Õ µèÍà¹× Í§·Ò§àÇÅÒ (continuous time Fourier transform) [12] ¡ÑºÊÑÒ³

m(t)

ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡

M (Ω) = exp{−π|Ω|ND} (1 − exp{−j2πΩ})

(1.5)

¨Ðä´é ÇèÒ ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ (frequency response) ¢Í§

áººá¹Ç¹Í¹ ¤×Í

àÁ× Í

exp{·}

m(t)

¤×Í ¿ §¡ìªÑ¹àÅ¢ªÕ ¡ÓÅÑ§ (exponential function) ã¹¢³Ð·Õ ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§

ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ¤×Í

½ 2 2 ¾ π Ω ND2 T exp − (1 − exp{−j2πΩ}) M (Ω) = jπΩ ln(16) àÁ× Í

Ω = fT

(1.6)

f ¤×Í ¤ÇÒÁ¶Õ ÁÕË¹èÇÂà» ¹ √ j = −1 ¤×Í Ë¹èÇÂ¨Ô¹µÀÒ¾

¤×Í ¤ÇÒÁ¶Õ áºº¹ÍÃìÁÍÅäÅ«ì (normalized frequency),

àÎÔÃµ«ì (Hertz),

|x|

¤×Í ¤èÒÊÑÁºÙÃ³ì (absolute value) ¢Í§

áÅÐ

(imadinary unit) ÃÙ»·Õ 1.5 áÊ´§¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³¾ÑÅÊìä´ºÔµ ¨ÐàËç¹ä´éÇèÒ àÁ× Í ND à¾Ô Á ¢Ö ¹ ÃÙ»ÃèÒ§¢Í§¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³¾ÑÅÊìä´ºÔµ ·Ñ § 2 áºº¨Ð¶Ù¡ ºÕº ãËé ÁÒ ÍÂÙè ³ ºÃÔàÇ³¤ÇÒÁ¶Õ µ Ó ¹Í¡¨Ò¡¹Õ ªèÍ§ÊÑÒ³¢Í§¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹¨ÐÁÕÊà»¡µÃÑÁ¤èÒÈÙ¹Âì (spectral null) ³ µÓáË¹è§·Õ ¤ÇÒÁ¶Õ

f = 0 «Ö §ËÁÒÂ¶Ö§ äÁèÁÕÊèÇ¹»ÃÐ¡Íºä¿¿ Ò¡ÃÐáÊµÃ§ ã¹¢³Ð·Õ

ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨Ðãªé â»Ãá¡ÃÁ SCILAB

[14] ã¹¡ÒÃÇÒ´ÃÙ» ¡ÃÒ¿¢Í§ÊÑÒ³µèÒ§æ

ÃÇÁ·Ñ § ¼Å¡ÒÃ·´ÅÍ§·Õ ä´é ¨Ò¡¡ÒÃ·Ó¡ÒÃ¨ÓÅÍ§ (simulation) ÃÐºº ¼ÙéÍèÒ¹¤ÇÃ·Õ ¨Ð¾ÂÒÂÒÁ·´ÅÍ§ ÇÒ´ÃÙ»¡ÃÒ¿µèÒ§æ ã¹Ë¹Ñ§Ê×ÍàÅèÁ¹Õ à¾× Í·Õ ¨Ðä´éªèÇÂ·ÓãËéà¢éÒã¨ã¹º·àÃÕÂ¹ÁÒ¡ÂÔ §¢Ö ¹ 3

â»Ãá¡ÃÁ SCILAB à» ¹â»Ãá¡ÃÁ·Õ ÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ã¡Åéà¤ÕÂ§¡Ñºâ»Ãá¡ÃÁ MATLAB [13] «Ö §

¤èÒÅÔ¢ÊÔ·¸Ô «Í¿µìáÇÃì ¢Í§â»Ãá¡ÃÁ MATLAB ÁÕ ÃÒ¤Òá¾§ÁÒ¡ áµè â»Ãá¡ÃÁ SCILAB à» ¹ â»Ãá¡ÃÁ·Õ ãËé¿ÃÕ (freeware) ¼ÙéÍèÒ¹ÊÒÁÒÃ¶´ÒÇ¹ìâËÅ´µÑÇâ»Ãá¡ÃÁä´é¨Ò¡ http//www.scilab.org ËÃ×Í http://home.npru.ac.th/∼t3058/Scilab.html

1.5.

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡

0.5

ND = 2 ND = 2.5

0.4

ND = 3 0.3

Amplitude

0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 −0.5 −5

(a) t/T 1 ND = 2

0.9

ND = 2.5 0.8

ND = 3

Amplitude

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −5

(b) t/T

ÃÙ»·Õ 1.4: ¼ÅµÍºÊ¹Í§ä´ºÔµ ÊÓËÃÑº¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

1.5

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡

â´Â·Ñ Çä» ªèÍ§ÊÑÒ³¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áÁèàËÅç¡ ÊÒÁÒÃ¶¨ÓÅÍ§ä´é à» ¹ 2 áºº ¤×Í áºº¨ÓÅÍ§ ªèÍ§ÊÑÒ³ àÊÁ×Í¹ ¨ÃÔ§ (realistic channel model) áÅÐ áºº¨ÓÅÍ§ ªèÍ§ÊÑÒ³ ÍØ´Á¤µÔ (ideal

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ND = 2

Normalized magnitude

ND = 2.5 ND = 3 0.8

0.6

0.4

0.2

0.1

0.2

0.3

0.4

0.5

(a) Normalized frequency (fT)

ND = 2

ND = 2.5

Normalized magnitude

ND = 3 0.8

0.6

0.4

0.2

0.1

0.2

0.3

0.4

0.5

(b) Normalized frequency (fT)

ÃÙ»·Õ 1.5: ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³¾ÑÅÊìä´ºÔµ ÊÓËÃÑº¡ÒÃºÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

1.5.

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡

n(t)

1–D

p(t)

g(t)

LPF

symbol detector

equalizer

â k

m(t) timing recovery target response H(D) ÃÙ»·Õ 1.6: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§

channel model) â´Â·Õ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§ [10] ¨ÐÁÕÅÑ¡É³Ð¡ÒÃ·Ó§Ò¹ã¡Åéà¤ÕÂ§¡Ñº ÃÐºº¨ÃÔ§ à¹× Í§¨Ò¡»ÃÐ¡Íºä»´éÇÂ·Ø¡ ÊèÇ¹»ÃÐ¡Íº·Õ ÊÓ¤Ñ ·Õ ÁÕ ÍÂÙè ã¹ Ê¶Ò» µÂ¡ÃÃÁªèÍ§ÊÑÒ³ ÍèÒ¹ (read channel architecture) [8, 10] ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ã¹¢³Ð·Õ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ ÍØ´Á¤µÔÁÑ¡¨Ð¹ÔÂÁãªéã¹¡ÒÃÈÖ¡ÉÒ áÅÐÇÔà¤ÃÒÐËì¾× ¹°Ò¹¡ÒÃ·Ó§Ò¹¢Í§ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì à¹× Í§¨Ò¡ à» ¹áºº¨ÓÅÍ§·Õ äÁè«Ñº«éÍ¹áÅÐ§èÒÂµèÍ¡ÒÃ·Ó¤ÇÒÁà¢éÒã¨

1.5.1

ÊèÇ¹

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§

ã¹ÃÙ»·Õ 1.2 ÊÒÁÒÃ¶·Õ ¨ÐáÊ´§ãËéÍÂÙèã¹ÃÙ»¢Í§áºº¨ÓÅÍ§·Ò§¤³ÔµÈÒÊµÃìä´é µÒÁÃÙ»·Õ 1.6

¡ÅèÒÇ¤×Í ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ áººäº¹ÒÃÕ

ak ∈ {0, 1}

·Õ ÁÕ ¤ÒºàÇÅÒ¢Í§ºÔµ (bit period) à·èÒ ¡Ñº

¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§Ç§¨ÃËÒÍ¹Ø¾Ñ¹¸ìÍØ´Á¤µÔ (ideal di erentiator) Ë¹èÇ§àÇÅÒ

Ë¹èÇÂ ·ÓãËéä´éà» ¹ÅÓ´Ñº¢éÍÁÙÅà»ÅÕ Â¹Ê¶Ò¹Ð

1−D

àÁ× Í

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ

bk ∈ {−1, 0, 1} àÁ× Í bk = ±1 ËÁÒÂ¶Ö§

¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐáºººÇ¡ (positive transition) ËÃ×Í áººÅº (negative transition) áÅÐ ËÁÒÂ¶Ö§ äÁèÁÕ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð ÅÓ´Ñº¢éÍÁÙÅà»ÅÕ Â¹Ê¶Ò¹Ð á·¹´éÇÂ¼ÅµÍºÊ¹Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð read back,

p(t),

g(t)

bk = 0

¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§ªèÍ§ÊÑÒ³·Õ ¶Ù¡

áÅÐ¶Ù¡ Ãº¡Ç¹´éÇÂÊÑÒ³Ãº¡Ç¹

n(t)

ÊÑÒ³

¤ÇÒÁ¶Õ (out of band noise) ¨Ò¡¹Ñ ¹ ¡ç ¨Ð¶Ù¡ ·Ó¡ÒÃªÑ¡ µÑÇÍÂèÒ§ (sampling) ³ àÇÅÒ·Õ ¶Ù¡ ¤Çº¤ØÁ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

â´ÂÃÐººä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ (timing recovery) ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§¨Ð¶Ù¡ Êè§ ¼èÒ¹ä»ÂÑ§ ÍÕ¤ÇÍäÅà«ÍÃì áÅÐÇ§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì (symbol detector) à¾× ÍËÒÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ à» ¹ä»ä´é ÁÒ¡·Õ ÊØ´ (most likely input sequence) ¹Ñ ¹¤×Í ËÒ¤èÒ»ÃÐÁÒ³¢Í§

ËÃ×Í

âk

Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì·Õ ¹ÔÂÁãªéã¹ÃÐºº¡ÒÃºÑ¹·Ö¡áÁèàËÅç¡ ¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ (Viter bi detector) [15] ÍÂèÒ§äÃ¡çµÒÁ à¹× Í§¨Ò¡ ¤ÇÒÁ«Ñº«éÍ¹ (complexity) ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ðà¾Ô Á ¢Ö ¹ áººàÅ¢ªÕ ¡ÓÅÑ§ µÒÁ¨Ó¹Ç¹Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³ (channel memory) ´Ñ§¹Ñ ¹ ÍÕ¤ÇÍäÅà«ÍÃì¨Ö§ à» ¹ ÊÔ § ¨Óà» ¹ ·Õ ¨ÐµéÍ§¶Ù¡ ¹ÓÁÒãªé §Ò¹ à¾× Í ·ÓË¹éÒ·Õ ã¹¡ÒÃ»ÃÑº ÃÙ»ÃèÒ§¼ÅµÍºÊ¹Í§ 4

ÃÇÁ¢Í§·Ñ § ÃÐººãËé à» ¹ ¼ÅµÍºÊ¹Í§·Õ µéÍ§¡ÒÃ ·Õ àÃÕÂ¡¡Ñ¹ ÇèÒ ¼ÅµÍºÊ¹Í§·ÒÃìà¡çµ sponse)

(target re

H(D) [4] áÅÐªèÇÂ·ÓãËé¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÅ´Å§ä´é (ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´

à¾Ô ÁàµÔÁä´éã¹º··Õ 3)

1.5.2

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

¶éÒÊÁÁØµÔãËé ÃÐººÁÕ¡ÃÐºÇ¹¡ÒÃÍÕ¤ÇÍäÅà«ªÑ¹áººÊÁºÙÃ³ì (perfect equalization) áºº¨ÓÅÍ§ã¹ÃÙ» ·Õ 1.6 ¨ÐÊÒÁÒÃ¶Å´ÃÙ» ä´é à» ¹ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ ´Ñ§ áÊ´§ã¹ÃÙ» ·Õ 1.7 â´Â·Õ ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ áººäº¹ÒÃÕ

·Õ ÁÕ ¤ÒºàÇÅÒ¢Í§ºÔµ à·èÒ ¡Ñº

ÊÑÒ³¾ÑÅÊì ä¹¤ÇÔµÊì ÍØ´Á¤µÔ (ideal Nyquist pulse) Ãº¡Ç¹´éÇÂÊÑÒ³Ãº¡Ç¹

n(t)

q(t)

¨Ð¶Ù¡ ¡Å Ó ÊÑÒ³ (modulate) ¡Ñº =

sin(πt/T )/(πt/T )

ÊÑÒ³·Õ Ç§¨ÃÀÒ¤ÃÑº ä´é ÃÑº

p(t)

[16] áÅÐ¶Ù¡

¨Ð¶Ù¡ Êè§ ¼èÒ¹ä»ÂÑ§ Ç§¨Ã¡ÃÍ§

¼èÒ¹µ Ó à¾× Í¡Ó¨Ñ´ÊÑÒ³Ãº¡Ç¹·Õ ÍÂÙè¹Í¡á¶º¤ÇÒÁ¶Õ ¨Ò¡¹Ñ ¹ ¡ç¨Ð¶Ù¡·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§ ³ àÇÅÒ·Õ ¶Ù¡¤Çº¤ØÁâ´ÂÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ ¨Ò¡¹Ñ ¹ ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§Ç§¨ÃªÑ¡µÑÇÍÂèÒ§¡ç¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§ Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì à¾× Í·Ó¡ÒÃËÒÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ à» ¹ä»ä´éÁÒ¡·Õ ÊØ´ ·ÒÃìà¡çµáºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹ ËÃ×Í ·Õ àÃÕÂ¡ÇèÒ ·ÒÃìà¡çµáºº PR (partial response) [17] ·Õ à» ¹·Õ ÂÍÁÃÑºã¹¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ ¨ÐÁÕÃÙ»ÊÁ¡ÒÃà» ¹ [4]

H(D) = (1 − D)(1 + D)n 4

(1.7)

1.5.

ààºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ÃÐººààÁèàËÅç¡

n(t)

H(D)

p(t)

q(t)

âk

symbol detector

LPF

timing recovery

ÃÙ»·Õ 1.7: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

ã¹¢³Ð·Õ ·ÒÃìà¡çµáºº PR ·Õ à» ¹·Õ ÂÍÁÃÑºã¹¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ¨ÐÍÂÙèã¹ÃÙ»¢Í§ [18]

H(D) = (1 + D)n

àÁ× Í

(1.8)

¤×Í àÅ¢¨Ó¹Ç¹àµçÁ ºÇ¡ ¨Ò¡ÊÁ¡ÒÃ (1.8) ¨Ð¾ºÇèÒ ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § ¨ÐäÁè ÁÕ ¾¨¹ì

(1 − D)

·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § ÁÕ ÊèÇ¹»ÃÐ¡Íºä¿¿ Ò¡ÃÐáÊµÃ§ (´Ù

ÃÙ» ·Õ 1.5) ÃÙ» ·Õ 1.8 à»ÃÕÂºà·ÕÂº¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ áººµèÒ§æ â´Â·Õ µÑÇàÅ¢·Õ ÍÂÙè ã¹à¤Ã× Í§ËÁÒÂÇ§àÅçº ÊÕ àËÅÕ ÂÁ

[1 0 − 1]

áÊ´§¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô áµèÅÐá·ç» ¢Í§·ÒÃìà¡çµ µÑÇÍÂèÒ§àªè¹ PR4

ËÁÒÂ¶Ö§ ·ÒÃìà¡çµ áºº PR4 (PR class IV) ·Õ ÁÕ ¿ §¡ìªÑ¹ ¶èÒÂâÍ¹ã¹â´àÁ¹

H(D) = 1 − D2 ã¹â´àÁ¹

[. . .]

¤×Í

ËÃ×Í EEPR2

[1 4 6 4 1]

[10] ¤×Í

ËÁÒÂ¶Ö§ ·ÒÃìà¡çµáºº EEPR2 ·Õ ÁÕ¿ §¡ìªÑ¹¶èÒÂâÍ¹

H(D) = 1 + 4D + 6D2 + 4D3 + D4

à» ¹µé¹

¨Ò¡ÃÙ» ·Õ 1.8 ¨Ð¾ºÇèÒ àÁ× Í ªèÍ§ÊÑÒ³ÁÕ ¤èÒ ND à¾Ô Á ¢Ö ¹ ·ÒÃìà¡çµ·Õ ãªé ¡ç ¤ÇÃ·Õ ¨ÐÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡¢Ö ¹ (ÁÕ ¤èÒ

¢Í§ ªèÍ§ÊÑÒ³ ãËé ÁÒ¡ ·Õ ÊØ´ «Ö § ¨Ð Êè§ ¼Å ·Ó ãËé Ç§¨Ã µÃÇ¨ËÒ ÇÕà·ÍÃìºÔ ·Ó§Ò¹ ä´é ÍÂèÒ§ ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ ÁÒ¡¢Ö ¹ (ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´à¾Ô ÁàµÔÁ ä´é ã¹º··Õ 3) ¹Í¡¨Ò¡¹Õ ¨Ò¡ÊÁ¡ÒÃ (1.7) áÅÐ (1.8) ¨Ð¾º ÇèÒ ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§·ÒÃìà¡çµ áºº PR ·Ø¡ µÑÇ ¨Ðà» ¹ àÅ¢¨Ó¹Ç¹àµçÁ ÍÂèÒ§äÃ¡çµÒÁ ¶éÒ ãªé ·ÒÃìà¡çµ ·Õ ÁÕ ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô à» ¹àÅ¢¨Ó¹Ç¹¨ÃÔ§ «Ö §¨ÐàÃÕÂ¡ÇèÒ ·ÒÃìà¡çµáºº GPR (generalized partial response target) »ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐºº·Õ ä´é¨ÐÁÕÁÒ¡¡ÇèÒ¡ÒÃãªé·ÒÃìà¡çµáºº PR [18, 19]

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Normalized magnitude

0.8

0.6

0.4

Channel response (ND = 2) Channel response (ND = 2.5) PR4 [1 0 −1] (n = 1)

0.2

EPR4 [1 1 −1 −1] (n = 2) EEPR4 [1 2 0 −2 1] (n = 3) 0

0.1

0.2

0.3

0.4

0.5

(a) Normalized frequency (fT)

Channel response (ND = 2)

Channel response (ND = 2.5)

Normalized magnitude

PR2 [1 2 1] (n = 2) EPR2 [1 3 3 1] (n = 3)

0.8

EEPR2 [1 4 6 4 1] (n = 4) 0.6

0.4

0.2

0.1

0.2

0.3

0.4

0.5

(b) Normalized frequency (fT)

ÃÙ»·Õ 1.8: ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ áººµèÒ§æ ÊÓËÃÑº ªèÍ§ÊÑÒ³¡ÒÃºÑ¹·Ö¡ (a) áºº á¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

1.6.

ÊÃØ»·éÒÂº·

1.6

ÊÃØ»·éÒÂº·

ã¹º·¹Õ ä´é¡ÅèÒÇ¶Ö§¾× ¹°Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡áºº´Ô¨Ô·ÑÅ ÃÇÁ·Ñ §ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§¡ÃÐºÇ¹ ¡ÒÃà¢ÕÂ¹áÅÐ¡ÒÃÍèÒ¹¢éÍÁÙÅã¹ÍØ»¡Ã³ìÎÒÃì´´ÔÊ¡ìä´Ã¿ì ¹Í¡¨Ò¡¹Õ ÂÑ§ä´éÍ¸ÔºÒÂ¶Ö§áºº¨ÓÅÍ§¡ÒÃ·Ó§Ò¹ ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ·Ñ §áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§ áÅÐáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ â´Â·Õ áºº¨ÓÅÍ§·Ñ §ÊÍ§¹Õ ¨Ð¶Ù¡¹ÓÁÒãªéã¹¡ÒÃ¨ÓÅÍ§ÃÐºº (system simulation) ã¹º·µèÍæ ä» à¹× Í§¨Ò¡ ¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì¨ÐÍÒÈÑÂ¾× ¹°Ò¹·Ò§¤³Ôµ ÈÒÊµÃì·Õ à¡Õ ÂÇ¢éÍ§¡Ñº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ áÅÐ¡ÒÃÊ× ÍÊÒÃ´Ô¨Ô·ÑÅ¤èÍ¹¢éÒ§ÁÒ¡ ´Ñ§¹Ñ ¹ ¼ÙéÍèÒ¹¤ÇÃ·Õ ¨Ð ·º·Ç¹¤ÇÒÁÃÙéàËÅèÒ¹Õ ãËéà¢éÒã¨¡èÍ¹·Õ ¨ÐÈÖ¡ÉÒË¹Ñ§Ê×ÍàÅèÁ¹Õ «Ö §¤ÇÒÁÃÙé¾× ¹°Ò¹·Ò§¤³ÔµÈÒÊµÃì´éÒ¹µèÒ§æ ·Õ à¡Õ ÂÇ¢éÍ§¡Ñº¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ÊÒÁÒÃ¶·Õ ¨ÐÈÖ¡ÉÒä´é¨Ò¡ Ë¹Ñ§Ê×Í ¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ÊÓËÃÑº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅ àÅèÁ 1: ¾× ¹°Ò¹ªèÍ§ÊÑÒ³ÍèÒ¹ à¢ÕÂ¹ [10]

1.7

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§Í¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡

3. ¨§Í¸ÔºÒÂËÅÑ¡¡ÒÃàº× Í§µé¹¢Í§¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹áÅÐ¡ÒÃÍèÒ¹¢éÍÁÙÅã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

5. ¨§Í¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

6. ¨§Â¡µÑÇÍÂèÒ§·ÒÃìà¡çµáºº PR ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ÁÒÍÂèÒ§¹éÍÂ 4 ·ÒÃìà¡çµ

7. ¨§Â¡µÑÇÍÂèÒ§·ÒÃìà¡çµáºº PR ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §ÁÒÍÂèÒ§¹éÍÂ 4 ·ÒÃìà¡çµ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

º··Õ 2

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ¤ÇÒÁÊÓ¤Ñ ¢Í§ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ (timing recovery) ¾ÃéÍÁ·Ñ § Í¸ÔºÒÂËÅÑ¡¡ÒÃ ·Ó§Ò¹¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» (conventional timing recovery) «Ö §ÍÂÙèº¹¾× ¹°Ò¹¢Í§ Ç§¨Ãà¿ÊÅçÍ¡ÅÙ» (PLL: phased lock loop) ¹Í¡¨Ò¡¹Õ ÂÑ§Í¸ÔºÒÂ¶Ö§ ÇÔ¸Õ¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ» â´Âãªéáºº¨ÓÅÍ§¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ»áººàªÔ§àÊé¹ (linearized PLL model) ÃÇÁ·Ñ §áÊ´§¼Å¡ÒÃ·´ÅÍ§à¾× ÍãËéàËç¹¶Ö§¤ÇÒÁÊÓ¤Ñ¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ

2.1

º·¹Ó

ã¹» ¨¨ØºÑ¹¹Õ ¤ÇÒÁà¨ÃÔ¡éÒÇË¹éÒ ·Ò§´éÒ¹à·¤â¹âÅÂÕ ¡ÒÃÊ× ÍÊÒÃ (communication) ä´é ¾Ñ²¹Òä»ÍÂèÒ§ ÃÇ´àÃçÇ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §¡ÒÃÊ× ÍÊÒÃ´Ô¨Ô·ÑÅ·Õ ãªéã¹ÃÐººµèÒ§æ àªè¹ ÃÐººâ·ÃÈÑ¾·ìà¤Å× Í¹·Õ áÅÐÃÐºº ¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³ÀÒÂã¹ÍØ»¡Ã³ìÎÒÃì´´ÔÊ¡ìä´Ã¿ì à» ¹µé¹ à¾ÃÒÐ©Ð¹Ñ ¹ ¤ÇÒÁµéÍ§¡ÒÃ·Õ ¨Ðà¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾â´ÂÃÇÁ¢Í§ÃÐºº¨Ö§ à» ¹ ÊÔ § ·Õ ¨Óà» ¹ ÁÒ¡ à¾ÃÒÐÇèÒ ¨Ðä´é ÊÒÁÒÃ¶ÃÑº áÅÐÊè§ ¢éÍÁÙÅ ä´é ÍÂèÒ§ ¹èÒàª× Í¶×ÍÁÒ¡ÂÔ §¢Ö ¹ ã¹ÃÐººÊ× ÍÊÒÃ´Ô¨Ô·ÑÅ (digital communication system) ¡ÒÃÊè§ÊÑÒ³¨Ò¡µé¹·Ò§ä»ÂÑ§»ÅÒÂ ·Ò§ ÍØ»¡Ã³ì µé¹·Ò§¨Ð·ÓË¹éÒ·Õ à»ÅÕ Â¹ÊÑÒ³´Ô¨Ô·ÑÅ (digital) ãËé à» ¹ ÊÑÒ³áÍ¹ÐÅçÍ¡ (ana log) ¡èÍ¹·Õ ¨Ð¶Ù¡Êè§ÍÍ¡ä»ÂÑ§»ÅÒÂ·Ò§ àÁ× ÍÊÑÒ³áÍ¹ÐÅçÍ¡ÁÒ¶Ö§·Õ ÍØ»¡Ã³ì»ÅÒÂ·Ò§ ¡ç¨Ð¶Ù¡Êè§ 17

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ä»ÂÑ§ Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§ (sampler) à¾× Í ·Ó¡ÒÃá»Å§ÊÑÒ³áÍ¹ÐÅçÍ¡ãËé ¡ÅÑº ä»à» ¹ ÊÑÒ³´Ô¨Ô·ÑÅ ã¹ÃÙ» ¢Í§ ¢éÍÁÙÅ ÇÔÂØµ (discrete data) ËÃ×Í ·Õ àÃÕÂ¡¡Ñ¹ ÇèÒ á«Áà» Å (sample) ¡ÒÃªÑ¡ µÑÇÍÂèÒ§ (sampling) ÊÑÒ³áÍ¹ÐÅçÍ¡·Õ ¼Ô´¨Ñ§ËÇÐ¨Ð·ÓãËéà¡Ô´¼ÅàÊÕÂËÒÂÍÂèÒ§ÁÒ¡¡Ñº»ÃÐÊÔ·¸ÔÀÒ¾â´ÂÃÇÁ ¢Í§ÃÐºº ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨Ð·ÓË¹éÒ·Õ ã¹¡ÒÃà¢éÒ¨Ñ§ËÇÐ (synchronize) Ç§¨ÃªÑ¡µÑÇÍÂèÒ§¡ÑºÊÑÒ³ áÍ¹ÐÅçÍ¡·Õ ä´é ÃÑº à¾× ÍãËé ä´é ¢éÍÁÙÅ á«Áà» Å ·Õ ´Õ ·Õ ÊØ´ ÍÍ¡ÁÒ ¡èÍ¹·Õ ¨Ð¹Ó¢éÍÁÙÅ á«Áà» Å àËÅèÒ¹Ñ ¹ ä»·Ó ¡ÒÃ»ÃÐÁÇÅ¼Å¢Ñ ¹ µèÍä» àªè¹ Êè§ µèÍä»ÂÑ§ ÍÕ¤ÇÍäÅà«ÍÃì (equalizer) áÅÐÇ§¨Ã¶Í´ÃËÑÊ (decoder) à» ¹µé¹ ´Ñ§¹Ñ ¹ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨Ö§¹Ñºä´éÇèÒà» ¹Í§¤ì»ÃÐ¡Íº·Õ ¤ÇÒÁÊÓ¤ÑÁÒ¡ÍÂèÒ§Ë¹Ö §ã¹ÃÐººÊ× ÍÊÒÃ ´Ô¨Ô·ÑÅ à¾ÃÒÐÇèÒ ¶éÒ Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§·Ó§Ò¹äÁè ´Õ ¡ç ¨ÐÊè§ ¼Å·ÓãËé ¢éÍÁÙÅ á«Áà» Å ·Õ ä´é äÁè ÁÕ ¤Ø³ÀÒ¾ËÃ×Í ÁÕ ¢éÍ¼Ô´¾ÅÒ´ÁÒ¡ áÅÐàÁ× Í Êè§ ¢éÍÁÙÅ á«Áà» Å àËÅèÒ¹Õ ä»ÂÑ§ ÍÕ¤ÇÍäÅà«ÍÃì áÅÐÇ§¨Ã¶Í´ÃËÑÊ ¡ç ¨Ð·ÓãËé ¼ÅÅÑ¾¸ì·Õ ä´éÁÕ¢éÍ¼Ô´¾ÅÒ´ÁÒ¡ ¹Ñ ¹¤×Í ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´ºÔµ (BER: bit error rate) ¢Í§ÃÐºº¨ÐÁÕ¤èÒ ÊÙ§ «Ö §à» ¹ÊÔ §·Õ ¤ÇÃ¨ÐËÅÕ¡àÅÕ Â§ â´Â·Ñ Çä»ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨Ð·Ó§Ò¹ÍÂÙèº¹¾× ¹°Ò¹¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ» (PLL) [4] «Ö §»ÃÐ¡Íºä» ´éÇÂ Ç§¨ÃµÃÇ¨ËÒ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ (TED: timing error detector), Ç§¨Ã¡ÃÍ§ÅÙ» (loop lter), áÅÐÇ§¨Ã VCO (voltage controlled oscillator) ã¹·Ò§»¯ÔºÑµÔ â¤Ã§ÊÃéÒ§¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨ÐÁÕÍÂÙè 2 ÃÙ»áºº ¤×Í áºº¹ÔÃ¹ÑÂ (deductive) áÅÐáººÍØ»¹ÑÂ (inductive) â´Â¨Ð¢Ö ¹ÍÂÙè¡ÑºÇèÒ ¢éÍÁÙÅ·Ò§àÇÅÒ ¶Ù¡ ´Ö§ ÍÍ¡ÁÒãªé ³ µÓáË¹è§ ¡èÍ¹ËÃ×Í ËÅÑ§ Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº¹ÔÃ¹ÑÂ (deductive timing recovery) ¨Ð´Ö§¢éÍÁÙÅ·Ò§àÇÅÒ ·Õ àÃÕÂ¡¡Ñ¹ÇèÒ timing tone [16] ¨Ò¡ÊÑÒ³áÍ¹ÐÅçÍ¡·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃªÑ¡µÑÇÍÂèÒ§ µÒÁÃÙ»·Õ 2.1 â´Â·Õ Ç§¨Ã PLL ¶Ù¡¹Óãªéà¾× ÍÅ´¼Å¡ÃÐ·º¢Í§ä·ÁÁÔ § 1

¨ÔµàµÍÃì

(timing jitter) ·Õ á½§ÍÂÙèã¹ÊÑÒ³áÍ¹ÐÅçÍ¡ ã¹¢³Ð·Õ ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººÍØ»¹ÑÂ (in

ductive timing recovery) ¨ÐãªéÇ§¨Ã PLL áºº» Í¹¡ÅÑº (feedback) à¾× Í·ÓË¹éÒ·Õ ã¹¡ÒÃ´Ö§¢éÍÁÙÅ ·Ò§àÇÅÒ¨Ò¡ÊÑÒ³áÍ¹ÐÅçÍ¡·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§ ´Ñ§·Õ áÊ´§ã¹ÃÙ» ·Õ 2.2 ¢éÍ´Õ ¢Í§ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áººÍØ»¹ÑÂ ¤×Í ·Ø¡ ÊèÇ¹»ÃÐ¡Íº¢Í§ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº¹Õ ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡ ÊÃéÒ§ãËé à» ¹áºº´Ô¨Ô·ÑÅä´é à¹× Í§¨Ò¡ ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººÍØ»¹ÑÂà» ¹·Õ ¹ÔÂÁãªé§Ò¹¡Ñ¹ÁÒ¡ ´Ñ§¹Ñ ¹ ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨ÐàÃÕÂ¡ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº¹Õ ÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä» (conventional timing

ä·ÁÁÔ § ¨Ôµ àµÍÃì ¤×Í ÊÑÒ³Ãº¡Ç¹ÀÒÂã¹Ç§¨ÃªÑ¡ µÑÇÍÂèÒ§

¤ÃÑ §à¡Ô´¤ÇÒÁ¤ÅÒ´à¤Å× Í¹ä»¨Ò¡µÓáË¹è§·Õ µéÍ§¡ÒÃ

«Ö § ¨Ð·ÓãËé ¨Ñ§ËÇÐ¢Í§àÇÅÒ·Õ ¨Ð·Ó¡ÒÃªÑ¡ µÑÇÍÂèÒ§áµèÅÐ

2.2.

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

received signal

y(t)

to data detection

t k = kT + τˆk timing tone detector

loop filter

TED

VCO

ÃÙ»·Õ 2.1: ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº¹ÔÃ¹ÑÂ

H(D)

q(t)

τk

n(t) p(t)

y(t) LPF

yk = y (kT + τˆk )

t k = kT + τˆk

Viterbi detector

âk

z − d symbol detector

VCO D 1− D

loop filter

α+

β εˆk 1− D

rˆk −d

yk − d TED

ÃÙ»·Õ 2.2: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ ¾ÃéÍÁ¡Ñºä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººÍØ»¹ÑÂ

recovery) ÊÓËÃÑºÃÒÂÅÐàÍÕÂ´à¡Õ ÂÇ¡Ñºä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº¹ÔÃ¹ÑÂÊÒÁÒÃ¶ÈÖ¡ÉÒà¾Ô ÁàµÔÁä´é¨Ò¡ [20]

2.2

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ (ideal channel model) ã¹ÃÙ» ·Õ 2.2 ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

ak ∈ {±1}

«Ö §ÁÕ¤ÒºàÇÅÒ¢Í§ºÔµ

¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô µÑÇ·Õ

¶Ù¡Êè§¼èÒ¹ä»ÂÑ§ªèÍ§ÊÑÒ³

¢Í§ªèÍ§ÊÑÒ³,

H(D) =

Pν

k=0 hk D

k â´Â·Õ

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃË¹èÇ§àÇÅÒ (delay operator), áÅÐ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¤×Í Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³ ´Ñ§¹Ñ ¹ ÊÑÒ³ read back ÊÒÁÒÃ¶à¢ÕÂ¹à» ¹ÊÁ¡ÒÃä´é ¤×Í

p(t) =

rk q(t − kT − τk ) + n(t)

(2.1)

k â´Â·Õ

rk =

i ak−i hi ¤×Í ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§ªèÍ§ÊÑÒ³·Õ »ÃÒÈ¨Ò¡ÊÑÒ³Ãº¡Ç¹,

sin(πt/T )/(πt/T )

q(t) =

¤×Í ¿ §¡ìªÑ¹«Ô§¡ì (sinc function) ËÃ×ÍÊÑÒ³¾ÑÅÊìä¹¤ÇÔµÊì (Nyquist pulse)

·Õ ÁÕ áº¹´ìÇÔ´·ì à¡Ô¹ à» ¹ ÈÙ¹Âì (zero excess bandwidth) [16], (unknown timing o set) µÑÇ ·Õ

áÅÐ

n(t)

τk

¤×Í ÍÍ¿à«µ·Ò§àÇÅÒ·Õ äÁè ·ÃÒº¤èÒ

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN:

additive white Gaussian noise) ·Õ ÁÕ ¤ÇÒÁË¹Òá¹è¹ Êà»¡µÃÑÁ ¡ÓÅÑ§ (power spectrum density) áººÊÍ§´éÒ¹à·èÒ ¡Ñº 2

à´Ô¹áººÊØèÁ

N0 /2

ã¹Ë¹Ñ§Ê×Í ¹Õ ÍÍ¿à«µ·Ò§àÇÅÒ

τk

¨Ð¶Ù¡ ¨ÓÅÍ§ãËé ÁÕ ÅÑ¡É³Ðà» ¹ ¡ÒÃ

(random walk) «Ö §¹ÔÂÒÁâ´Â [21]

τk+1 = τk + wk àÁ× Í

¤×Í µÑÇá»ÃÊØèÁà¡ÒÊìà«ÕÂ¹áºº

i.i.d. (independent and identically distributed) ·Õ ÁÕ¤èÒà©ÅÕ Â

(mean) à·èÒ¡Ñº¤èÒÈÙ¹Âì áÅÐÁÕ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹ (variance) à·èÒ¡Ñº

2) N (0, σw

â´Â¤èÒ

σw

(2.2)

2 σw

ËÃ×Íà¢ÕÂ¹á·¹ä´é´éÇÂ

¨Ðà» ¹µÑÇ¡ÓË¹´ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ä·ÁÁÔ §¨ÔµàµÍÃì 3

·Õ Ç§¨ÃÀÒ¤ÃÑº ÊÑÒ³ read back ¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó ÍÔÁ¾ÑÅÊìà·èÒ¡Ñº

q(t)/T

wk ∼

¹Ñ ¹¤×Í ÁÕ¤ÇÒÁ¶Õ µÑ´ (cut o frequency) à·èÒ¡Ñº

(LPF) ·Õ ÁÕ¼ÅµÍºÊ¹Í§

1/(2T )

à¾× Í·ÓË¹éÒ·Õ ¡Ó¨Ñ´

ÊÑÒ³Ãº¡Ç¹·Õ ÍÂÙè¹Í¡á¶º¤ÇÒÁ¶Õ (out of band noise) ¨Ò¡¹Ñ ¹ ¡ç¨Ð·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§ÊÑÒ³ read back ·Õ àÇÅÒ

kT + τ̂k

à¾× Í·ÓãËéä´éà» ¹¢éÍÁÙÅá«Áà» Å

yk = y(kT + τ̂k ) =

ri q(kT + τ̂k − iT − τi ) + nk

(2.3)

i 2

áºº¨ÓÅÍ§¡ÒÃà´Ô¹ áººÊØèÁ ¹Õ ¶Ù¡ ¹Óãªé à¾ÃÒÐÇèÒ à» ¹ áºº¨ÓÅÍ§·Õ §èÒÂ áÅÐÊÒÁÒÃ¶ãªé á·¹ÅÑ¡É³Ð¢Í§ªèÍ§ÊÑÒ³

µèÒ§æ ä´é§èÒÂ â´Â¡ÒÃà»ÅÕ Â¹á»Å§¤èÒ¾ÒÃÒÁÔàµÍÃì 3

2 σw

à¾ÕÂ§µÑÇà´ÕÂÇà·èÒ¹Ñ ¹

ÊÓËÃÑº ÃÐºº·Õ ÁÕ á¶º¤ÇÒÁ¶Õ ¨Ó¡Ñ´ (band limited system) ¹Ñ ¹¤×Í ¾ÅÑ§§Ò¹¢Í§ÊÑÒ³¨Ð¶Ù¡ ¨Ó¡Ñ´ ãËé ÍÂÙè ã¹ªèÇ§á¶º

¤ÇÒÁ¶Õ

|f | ≤ 1/(2T )

Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó ¨Ð·ÓãËé ¢éÍÁÙÅ àÍÒµì¾Øµ ·Õ ä´é ÁÕ ¤èÒ ·Ò§Ê¶ÔµÔ ·Õ ¾Íà¾ÕÂ§ (su cient statistic) [23]

àËÁ×Í¹¡Ñº¡ÒÃãªéÇ§¨Ã¡ÃÍ§àËÁÒÐÊØ´ (matched lter) [16]

2.2.

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

τ̂k

àÁ× Í

¤×Í ¤èÒ »ÃÐÁÒ³¢Í§

τk

ËÃ×Í ·Õ àÃÕÂ¡ÇèÒ ÍÍ¿à«µ·Ò§à¿Ê (phase o set) µÑÇ ·Õ

ªÑ¡ µÑÇÍÂèÒ§, áÅÐ

N0 /(2T )

nk ∼ N (0, σn2 )

¹Ñ ¹¤×Í

¢Í§¡ÒÃ

¤×Í AWGN ·Õ ÁÕ ¤èÒà©ÅÕ Â à·èÒ ¡Ñº ¤èÒ ÈÙ¹Âì áÅÐ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ ¡Ñº

σn2 =

Ç§¨Ã TED ¨Ð·ÓË¹éÒ·Õ ã¹¡ÒÃ¤Ó¹Ç³ËÒ¤èÒ»ÃÐÁÒ³¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ (timing error) =

τk − τ̂k

²k

¹ÒÌ ¡Ò¢Í§Ç§¨Ã PLL ã¹·Ò§»¯ÔºÑµÔ áÅéÇ Ç§¨Ã TED ÁÕ ËÅÒÂ»ÃÐàÀ· [4] â´Â¨Ð¢Ö ¹ ÍÂÙè ¡Ñº ÅÑ¡É³Ð ¡ÒÃ¹Ó¢éÍÁÙÅ·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨Ã TED ÁÒãªé§Ò¹ «Ö §â´Â·Ñ Çä»áÅéÇ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ ¨Ð¢Ö ¹ ÍÂÙè ¡Ñº ¤Ø³ÀÒ¾¢Í§Ç§¨Ã TED ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐÇ§¨Ã TED ·Õ ¹ÔÂÁãªé §Ò¹¡Ñ¹ ¹Ñ ¹¤×Í Ç§¨Ã TED áºº Mueller and Müller ËÃ×ÍàÃÕÂ¡ÊÑ ¹æ ÇèÒ M&M TED [24] «Ö §¨Ð¤Ó¹Ç³ ËÒ¤èÒ»ÃÐÁÒ³¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ ´Ñ§¹Õ

²̂k = KT {yk r̂k−1 − yk−1 r̂k } â´Â·Õ =

r̂k

¤×Í ¤èÒ»ÃÐÁÒ³¢Í§

rk , KT

(2.4)

¤×Í ¤èÒ¤§µÑÇ (constant) ·Õ ¶Ù¡ãªéà¾× Í·ÓãËéÁÑ ¹ã¨ä´éÇèÒ

E[²̂k |²]

àÁ× Í ÃÐ´Ñº ÍÑµÃÒÊèÇ¹¤èÒ ¡ÓÅÑ§ à©ÅÕ Â ¢Í§ÊÑÒ³·Õ µéÍ§¡ÒÃµèÍ ¤èÒ ¡ÓÅÑ§ à©ÅÕ Â ¢Í§ÊÑÒ³Ãº¡Ç¹

(SNR: signal to noise ratio) ÁÕ¤èÒÊÙ§ ËÃ×ÍÍÒ¨¨Ð¡ÅèÒÇä´éÇèÒ ¤èÒ

¶Ù¡¹ÓÁÒãªéà¾× Í·ÓãËé¤ÇÒÁªÑ¹

¢Í§àÊé¹â¤é§ÃÙ»µÑÇàÍÊ (S curve) [4] ÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § ³ ¨Ø´¡Óà¹Ô´, áÅÐ

E[·]

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ

¤èÒ ¤Ò´ËÁÒÂ (expectation operator) [10, 25, 26] ¨Ò¡ÊÁ¡ÒÃ (2.4) ¨ÐàËç¹ä´éÇèÒ »ÃÐÊÔ·¸ÔÀÒ¾ ¢Í§Ç§¨Ã TED ¨Ð¢Ö ¹ ÍÂÙè ¡Ñº ¤èÒ µÑ´ÊÔ¹ã¨ (decision)

{r̂k }

´Ñ§¹Ñ ¹ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ

¨Ðà» ¹¿ §¡ìªÑ¹¢Í§¤ÇÒÁ¹èÒàª× Í¶×Í¢Í§¤èÒµÑ´ÊÔ¹ã¨áÅÐ SNR ·Õ ãªé ¨Ö§à» ¹àËµØ¼ÅÇèÒ ·ÓäÁÇ§¨ÃµÃÇ¨ËÒ 4

ÊÑÅÑ¡É³ì (symbol detector) ·Õ ãªéã¹ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ ¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ [15] ·Õ ÁÕ»ÃÔÁÒ³¡ÒÃË¹èÇ§àÇÅÒÊÓËÃÑº¡ÒÃµÑ´ÊÔ¹ã¨ (decision delay) à·èÒ¡Ñº

(Viterbi detector)

Ë¹èÇÂ (àªè¹

d = 4)

á·¹¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒ¢Õ´àÃÔ Áà»ÅÕ Â¹áººËÅÒÂÃÐ´Ñº (multi level threshold detector) [27] ËÅÑ§¨Ò¡¹Ñ ¹ ¤èÒ»ÃÐÁÒ³¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ

²̂k

¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§Ç§¨Ã¡ÃÍ§ÅÙ» à¾× Í¡Ó¨Ñ´

ÊÑÒ³Ãº¡Ç¹·Õ á½§ÍÂÙè ã¹ÊÑÒ³¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ áÅÐÍÍ¿à«µ·Ò§à¿Ê¢Í§¡ÒÃªÑ¡ µÑÇÍÂèÒ§ (sampling phase o set) µÑÇ ¶Ñ´ ä» 4

τ̂k+1

¡ç ¨Ð¶Ù¡ »ÃÑº ¤èÒ (update) â´ÂÇ§¨Ã PLL ÍÑ¹´Ñº ·Õ ÊÍ§

ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ä´éã¹º··Õ 4

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

(second order PLL) µÒÁ¤ÇÒÁÊÑÁ¾Ñ¹¸ì´Ñ§¹Õ [4]

àÁ× Í

θ̂k

θ̂k+1 = θ̂k + β²̂k ,

(2.5)

τ̂k+1 = τ̂k + α²̂k + θ̂k+1

(2.6)

¤×Í ¤èÒ »ÃÐÁÒ³¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§¤ÇÒÁ¶Õ (frequency error) [27], áÅÐ

áÅÐ

¤×Í

¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL [4] «Ö §¨Ðà» ¹µÑÇ¡ÓË¹´ áº¹´ìÇÔ´·ì¢Í§ÅÙ» (loop bandwidth) áÅÐÍÑµÃÒ ¡ÒÃÅÙèà¢éÒ (convergence rate) ¡ÅèÒÇ¤×Í ¶éÒ¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ÂÔ §ÁÒ¡ áº¹´ìÇÔ´·ì¢Í§ÅÙ»¡ç ¨Ð¡ÇéÒ§ «Ö §¨Ð·ÓãËéÍÑµÃÒ¡ÒÃÅÙèà¢éÒ¡ç¨ÐàÃçÇ áµèÊÑÒ³Ãº¡Ç¹·Õ à¢éÒÁÒã¹Ç§¨Ã PLL ¡ç¨ÐÁÕÁÒ¡ ÊÓËÃÑº ã¹¡Ã³Õ·Õ ÃÐººÁÕà©¾ÒÐ¢éÍ¼Ô´¾ÅÒ´·Ò§à¿Ê (phase error) à·èÒ¹Ñ ¹ Ç§¨ÃÀÒ¤ÃÑºÍÒ¨¨Ð¹ÓÇ§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö § ( rst order PLL) ÁÒãªé§Ò¹á·¹Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§¡çä´é â´Â·Õ ÍÍ¿à«µ·Ò§à¿Ê ¢Í§¡ÒÃªÑ¡µÑÇÍÂèÒ§µÑÇ¶Ñ´ä»

τ̂k+1

¨Ð¶Ù¡»ÃÑº¤èÒµÒÁ¤ÇÒÁÊÑÁ¾Ñ¹¸ì´Ñ§¹Õ [4]

τ̂k+1 = τ̂k + α²̂k

(2.7)

â´Â·Ñ Çä» ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨Ð·Ó§Ò¹à» ¹ 2 ÀÒÇÐ (mode) ¤×Í

1) ÀÒÇÐ¡ÒÃä´é ÁÒ (acquisition mode) ¨Ð·Ó§Ò¹ã¹µÍ¹àÃÔ Áµé¹ ¢Í§¡ÃÐºÇ¹¡ÒÃà¢éÒ ¨Ñ§ËÇÐ´éÇÂ ¤ÇÒÁªèÇÂàËÅ×Í ¢Í§áºº¢éÍÁÙÅ (data pattern) ·Õ àÃÕÂ¡ÇèÒ preamble [27] à¹× Í§¨Ò¡ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ÃÙé á¹è¹Í¹ÇèÒ preamble ÁÕ ÅÑ¡É³Ðà» ¹ ÍÂèÒ§äÃ ¨Ö§ ·ÓãËé ÊÒÁÒÃ¶·ÃÒºä´é ÇèÒ ¤èÒ ¶Ù¡µéÍ§¤×Í¤èÒÍÐäÃ ´Ñ§¹Ñ ¹ã¹ªèÇ§ÀÒÇÐ¡ÒÃä´éÁÒ¹Õ Ç§¨Ã PLL ¨Ðãªé¤èÒ ËÒ¤èÒ

²̂k

r̂k = rk

r̂k

·Õ

ã¹¡ÒÃ¤Ó¹Ç³

µÒÁÊÁ¡ÒÃ (2.4) (Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì·Õ ãªéã¹ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ¨ÐÂÑ§äÁè¶Ù¡ãªé§Ò¹

ã¹ªèÇ§¹Õ ) «Ö § ¨Ð·ÓãËé ä´é ¤èÒ ·Õ ¶Ù¡µéÍ§ à¾ÃÒÐ©Ð¹Ñ ¹ ¡ÃÐºÇ¹¡ÒÃä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ã¹ªèÇ§¹Õ ¨Ö§ ÁÕ ¤ÇÒÁ¹èÒàª× Í¶×ÍÁÒ¡ â´Â¨Ø´»ÃÐÊ§¤ìËÅÑ¡¢Í§ÀÒÇÐ¡ÒÃä´éÁÒ ¡ç¤×Í ¡ÒÃËÒ¤èÒ»ÃÐÁÒ³àÃÔ Áµé¹¢Í§ ÍÍ¿à«µ·Ò§à¿ÊáÅÐÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ (frequency o set) ·Õ á½§ÍÂÙè ã¹ÊÑÒ³áÍ¹ÐÅçÍ¡ ·Õ ¨Ð·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§

2) ÀÒÇÐ¡ÒÃµÔ´µÒÁ (tracking mode) ¨Ð·Ó§Ò¹µèÍ¨Ò¡ÀÒÇÐ¡ÒÃä´éÁÒ â´Âã¹¢Ñ ¹µÍ¹¹Õ ¤èÒ ãªéã¹¡ÒÃ¤Ó¹Ç³ËÒ¤èÒ

²̂k

r̂k

·Õ

µÒÁÊÁ¡ÒÃ (2.4) ¨Ðä´éÁÒ¨Ò¡Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì·Õ ãªéã¹ä·ÁÁÔ §

ÃÔ¤Ñ¿àÇÍÃÕ («Ö §ÍÒ¨¨ÐÁÕ¤Ø³ÀÒ¾äÁè´Õ àÁ× Íà·ÕÂº¡Ñº¡ÒÃãªé

¨ÃÔ§æ) ´Ñ§¹Ñ ¹ ¨Ø´»ÃÐÊ§¤ìËÅÑ¡¢Í§

2.3.

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

ÀÒÇÐ¡ÒÃµÔ´µÒÁ ¡ç ¤×Í à» ¹ ¡ÒÃá¡éä¢áÅÐ»ÃÑº»ÃØ§ ¤èÒ àÃÔ Áµé¹ ¢Í§ÍÍ¿à«µ·Ò§à¿ÊáÅÐÍÍ¿à«µ ·Ò§¤ÇÒÁ¶Õ ·Õ ä´éÁÒ¨Ò¡ÀÒÇÐ¡ÒÃä´éÁÒ

¨ÐàËç¹ä´éÇèÒã¹ªèÇ§ÀÒÇÐ¡ÒÃä´éÁÒ Ç§¨Ã PLL ·ÃÒºá¹è¹Í¹ÇèÒ preamble ¤×ÍÍÐäÃ ´Ñ§¹Ñ ¹ Ç§¨Ã PLL ¨Ö§ÊÒÁÒÃ¶·Õ ¨Ðãªé¤èÒ

áÅÐ

·Õ ÁÕ¤èÒÁÒ¡ä´é à¾× ÍªèÇÂ·ÓãËéÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ ÍÂèÒ§äÃ¡çµÒÁ ¤èÒ

·Õ ãªé¤ÇÃ·Õ ¨ÐÁÕ¤èÒÅ´Å§ àÁ× Íä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕà¢éÒÊÙèªèÇ§ÀÒÇÐ¡ÒÃµÔ´µÒÁ à¾× ÍÅ´¼Å¡ÃÐ·º¢Í§

ÊÑÒ³Ãº¡Ç¹·Õ ¨Ðà¢éÒÁÒã¹Ç§¨Ã PLL [28] ´Ñ§¹Ñ ¹ ¹Ñ¡ÍÍ¡áººÃÐºº¨ÐµéÍ§»ÃÐ¹Õ»ÃÐ¹ÍÁÃÐËÇèÒ§ áº¹´ìÇÔ´·ì¢Í§ÅÙ»áÅÐÍÑµÃÒ¡ÒÃÅÙèà¢éÒ ã¹ÃÐËÇèÒ§·Õ ·Ó¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì

2.3

áÅÐβ

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

¨Ò¡¼Å¡ÒÃ·´ÅÍ§·Õ ä´é ÃÑº ¨Ò¡¡ÒÃ¨ÓÅÍ§ÃÐºº (system simulation) ¾ºÇèÒ ÇÔ¸Õ¡ÒÃ·Õ ´Õ ·Õ ÊØ´ ã¹¡ÒÃ ÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL (·Ñ §

α áÅÐ β ) ¤×Í ¡ÒÃàÅ×Í¡ãªé¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ·Õ

·ÓãËéÃÐººÁÕ BER ¹éÍÂÊØ´ ³ ·Õ Ç§¨ÃÀÒ¤ÃÑº ÍÂèÒ§äÃ¡çµÒÁ ÇÔ¸Õ¹Õ äÁèÊÒÁÒÃ¶ãªé§Ò¹ä´é¨ÃÔ§ã¹·Ò§»¯ÔºÑµÔ à¹× Í§¨Ò¡ µéÍ§ãªé ÃÐÂÐàÇÅÒ¹Ò¹ã¹¡ÒÃ·Õ ¨ÐËÒ¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL ·Õ àËÁÒÐÊØ´ ´Ñ§¹Ñ ¹ â´Â ·Ñ Çä»áÅéÇ áºº¨ÓÅÍ§¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ»áººàªÔ§àÊé¹ÁÑ¡¨Ð¶Ù¡¹ÓÁÒãªéã¹¡ÒÃÍÍ¡áºº¤èÒ ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL [4] à¡³±ì (criterion) Ë¹Ö §·Õ à» ¹ä»ä´é ¡ç¤×Í ¡ÒÃàÅ×Í¡ãªé¤èÒ

áÅÐ

·Õ

·ÓãËé ¼ÅµÍºÊ¹Í§¢Í§ÃÐºº (system response) ÊÒÁÒÃ¶·Õ ¨ÐµÒÁ·Ñ¹ ¡ÒÃà»ÅÕ Â¹á»Å§¢Í§à¿ÊáÅÐ ¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³ read back ÀÒÂã¹ªèÇ§ C ºÔµ ËÃ×Í ¤ÒºàÇÅÒ¢Í§ºÔµ (bit period) «Ö § ÍÒ¨¨Ð ¾Ô¨ÒÃ³Òä´éÇèÒ à¡³±ì¹Õ ÊÍ´¤ÅéÍ§¡ÑºÍÑµÃÒ¡ÒÃÅÙèà¢éÒ ¡ÅèÒÇ¤×Í ¶éÒ¤èÒ

ÂÔ §¹éÍÂ ¡çËÁÒÂ¤ÇÒÁÇèÒ ä·ÁÁÔ §

ÃÔ¤Ñ¿àÇÍÃÕ¨ÐÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒ·Õ ÂÔ §àÃçÇ

2.3.1

¡ÒÃÇÔà¤ÃÒÐËìàªÔ§àÊé¹¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö §

Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö § ( rst order PLL) ¨ÐÊÒÁÒÃ¶¨Ñ´¡ÒÃ¡Ñº¢éÍ¼Ô´¾ÅÒ´·Ò§à¿Êä´éà¾ÕÂ§ÍÂèÒ§à´ÕÂÇ (äÁè ÊÒÁÒÃ¶¨Ñ´¡ÒÃ¡Ñº ¢éÍ¼Ô´¾ÅÒ´·Ò§¤ÇÒÁ¶Õ ä´é) ã¹ÊèÇ¹¹Õ ¨ÐÍ¸ÔºÒÂ¡ÒÃÍÍ¡áºº¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§ Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö § «Ö §¨Ðà» ¹»ÃÐâÂª¹ìµèÍ¡ÒÃàÃÕÂ¹ÃÙéÇ§¨Ã PLL ÍÑ¹´ÑºÊÙ§æ µèÍä» ÊÓËÃÑºã¹¡ÒÃ ÇÔà¤ÃÒÐËì¹Õ ¢éÍ¼Ô´¾ÅÒ´·Ò§à¿Ê¨Ð¶Ù¡¨ÓÅÍ§ãËéà» ¹¿ §¡ìªÑ¹¢Ñ ¹ºÑ¹ä´ (step function) ¹Ñ ¹¤×Í

τk = T

àÁ× Í

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

k≥0

áÅÐ

τk = 0

àÁ× Í

k<0

τ̂k+1

¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº

·Õ Ë¹Ö § ´Ñ§µèÍä»¹Õ

τ̂k+1 = τ̂k + α²̂k−d àÁ× Í

(2.8)

¤×Í »ÃÔÁÒ³Ë¹èÇ§àÇÅÒã¹ä·ÁÁÔ §ÅÙ» (timing loop) ÁÕË¹èÇÂà» ¹ºÔµà«ÅÅì

¤èÒ»ÃÐÁÒ³¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ, timing error), áÅÐ

²k

τk − τ̂k

T , ²̂k

²k + vk

¤×Í

¤×Í ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ·Õ ËÅ§àËÅ×ÍÍÂÙè (residual

¤×Í ÊÑÒ³Ãº¡Ç¹ã¹Ç§¨Ã TED ¶éÒÊÁÁØµÔãËé

ÁÕ¤èÒ¹éÍÂÁÒ¡ (ÊÒÁÒÃ¶·Õ

¨Ðà¾Ô¡à©Âä´é) ´Ñ§¹Ñ ¹ ¿ §¡ìªÑ¹¶èÒÂâÍ¹ (transfer function) [12] ¢Í§ÃÐººµÒÁÊÁ¡ÒÃ (2.8) ÊÒÁÒÃ¶ ·Õ ¨ÐËÒä´éâ´Â¡ÒÃãªé¡ÒÃá»Å§«Õ (Z transform) [12, 16] ¹Ñ ¹¤×Í

G(z) = àÁ× Í

Γ̂(z)

áÅÐ

¢éÍ¼Ô´¾ÅÒ´

²k

Γ(z) =

Γ̂(z) αz −(d+1) = Γ(z) 1 − z −1 + αz −(d+1)

¤×Í ¼Å¡ÒÃá»Å§«Õ¢Í§

τk − τ̂k

τ̂k

áÅÐ

E(z)

µÒÁÅÓ´Ñº à¾ÃÒÐ©Ð¹Ñ ¹ ¿ §¡ìªÑ¹¶èÒÂâÍ¹¢Í§

ÊÒÁÒÃ¶à¢ÕÂ¹ä´éà» ¹

E(z) = Γ(z) − Γ̂(z) = àÁ× Í

τk

(2.9)

¤×Í ¼Å¡ÒÃá»Å§«Õ¢Í§

1 − z −1 Γ(z) 1 − z −1 + αz −(d+1)

(2.10)

²k

à¡³±ì ·Õ ÍÒ¨¨Ð¹ÓÁÒãªé ã¹¡ÒÃàÅ×Í¡¤èÒ

¤×Í ¡ÒÃàÅ×Í¡¤èÒ

·Õ ·ÓãËé àÊ¶ÕÂÃÀÒ¾ (stable) ¢Í§

ÃÐººáÅÐÍÑµÃÒ¡ÒÃÅÙèà¢éÒà» ¹·Õ ¹èÒ¾Íã¨ ÊÓËÃÑºáµèÅÐ¤èÒ¢Í§»ÃÔÁÒ³Ë¹èÇ§àÇÅÒã¹ÅÙ»

(loop delay)

·Õ ¡ÓË¹´ãËéÁÒ ÇÔ¸Õ¡ÒÃ¹Õ ÊÒÁÒÃ¶·Óä´éâ´Âãªé·Ñ §ÊÁ¡ÒÃ (2.9) ËÃ×Í (2.10) ¡çä´é ¡ÅèÒÇ¤×Í ¢Ñ ¹µÍ¹áÃ¡ ãËé ËÒ¤èÒ

·Ñ §ËÁ´·Õ ·ÓãËé ÃÐººÁÕ ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ ¨Ò¡ÊÁ¡ÒÃ (2.9) áÅÐ (2.10) ÃÐºº¨ÐÁÕ ¤ÇÒÁ

àÊ¶ÕÂÃÀÒ¾ ¡ç µèÍàÁ× Í ·Ø¡ â¾Å (all poles) ËÃ×Í ÃÒ¡¤ÓµÍº (root) ¢Í§µÑÇ ÊèÇ¹ ¢Í§ÊÁ¡ÒÃ (2.9) ËÃ×Í (2.10) ÍÂÙèÀÒÂã¹Ç§¡ÅÁË¹Ö §Ë¹èÇÂ [16] ¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ¨Ðä´éÇèÒ ¤èÒ

·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁ

àÊ¶ÕÂÃÀÒ¾ ÊÒÁÒÃ¶ËÒä´é¨Ò¡ [4]

µ 0 < α < 2 sin ÃÙ» ·Õ 2.3 áÊ´§¤èÒ ÁÒ¡ÊØ´ ¢Í§

π 4d + 2

·Õ ÂÑ§¤§·ÓãËé ÃÐººÁÕ ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ ÊÓËÃÑº áµèÅÐ¤èÒ

(2.11)

¨ÐàËç¹

2.3.

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

α (PLL gain parameter)

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4

max

0.2 0

Normalized loop delay, d

ÃÙ»·Õ 2.3: ¤èÒÁÒ¡ÊØ´¢Í§

ä´é ªÑ´à¨¹ÇèÒ ªèÇ§àÊ¶ÕÂÃÀÒ¾¢Í§¤èÒ ¤èÒ

·Õ ÂÑ§¤§·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ ÊÓËÃÑºáµèÅÐ¤èÒ

¨ÐÅ´Å§ÍÂèÒ§ÃÇ´àÃçÇ àÁ× Í

ËÅÒÂ¤èÒ ·Õ ·ÓãËé ÃÐººÁÕ ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ áµè ¨ÐàÅ×Í¡ãªé

ÁÕ ¤èÒ à¾Ô Á ¢Ö ¹ áÅÐ¶Ö§áÁéÇèÒ ¨ÐÁÕ

à¾ÕÂ§¤èÒ à´ÕÂÇ·Õ ·ÓãËé ¼ÅµÍºÊ¹Í§

¢Í§ÃÐººÊÒÁÒÃ¶·Õ ¨ÐµÔ´µÒÁ¼ÅµÍºÊ¹Í§¢Ñ ¹ºÑ¹ä´ (step response) ÀÒÂã¹ ¤ÇÒÁ¤ÅÒ´à¤Å× Í¹ä´é

±5%

ºÔµ â´ÂÂÍÁãËé ÁÕ

â´Â·Õ µÑÇàÅ¢ 5% ¹Õ ¶Ù¡ ¹Óãªé à¾× Í à» ¹ ¡ÒÃ¼èÍ¹»Ã¹à¡³±ì ¡ÒÃÍÍ¡áºº

à¾× Í·Õ ¨Ðä´éÅ´¼Å¡ÃÐ·º¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ¨Ðà¢éÒÁÒã¹Ç§¨Ã PLL ÃÙ»·Õ 2.4(a) áÊ´§¤èÒ

·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾áÅÐÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒÀÒÂã¹ (¹Ñ ¹¤×Í ¤èÒ

¾ºÇèÒÁÕà¾ÕÂ§ ÊÓËÃÑº

ÁÕ¤èÒ¹éÍÂ) ¤èÒ

¡ç¨ÐÂÔ §ÁÕ¤èÒÁÒ¡ ¨Ò¡·Õ áÊ´§ã¹ÃÙ»·Õ 2.4(a) àÁ× Í¡ÓË¹´

ºÒ§¤èÒ·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ÊÓËÃÑº¤èÒ

µÑ §áµè ¤èÒ 0 ¶Ö§

30T

= 0 ¶Ö§

30T

à¹× Í§¨Ò¡

·Õ

ÁÒãËé ¨Ð

¤èÒË¹Ö § µÑÇÍÂèÒ§àªè¹ ¨ÐÁÕ¤èÒ

α100

à·èÒ¹Ñ ¹ ·Õ ·ÓãËé ÃÐººÁÕ ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾áÅÐÁÕ ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ ÀÒÂã¹

«Ö §ÊÍ´¤ÅéÍ§¡Ñºà¡³±ì¡ÒÃÍÍ¡áºº

α100

αC

ºÔµ ÊÑ§à¡µ¨Ð¾ºÇèÒ ÍÑµÃÒ¡ÒÃÅÙèà¢éÒÂÔ §àÃçÇ

100 ºÔµ ÃÙ»·Õ 2.4(b) áÊ´§¼ÅµÍºÊ¹Í§¢Ñ ¹ºÑ¹ä´¢Í§ÃÐººµÒÁÊÁ¡ÒÃ (2.9) â´Âãªé

α100

ÊÓËÃÑº

·Õ µÑ §äÇé

¶Ù¡ÍÍ¡áººÁÒà¾× ÍãËéÃÐººÊÒÁÒÃ¶·Õ ¨ÐµÔ´µÒÁ¼ÅµÍºÊ¹Í§¢Ñ ¹ºÑ¹ä´ÀÒÂã¹ 100

ºÔµ ´éÇÂ¤èÒ¤ÇÒÁ¤ÅÒ´à¤Å× Í¹ÂÔ¹ÂÍÁ (tolerance)

±5% ´Ñ§¹Ñ ¹ ¤èÒÊÑÁºÙÃ³ì¢Í§¢¹Ò´¢Í§¼ÅµÍºÊ¹Í§

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

0.05

α (PLL gain parameter)

0.045 0.04 0.035 0.03

0.025

0.02

0.01 0.005

α200

0.015

100

α300 0

(a) Normalized loop delay, d

d increases 1.05 0.95

Magnitude

± 5% tolerance

d increases

Convergence rate within 100 samples

100

200

300

400

500

(b) Time (in bit periods)

ÃÙ»·Õ 2.4: (a) ¤èÒ

αC

·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾áÅÐÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒÀÒÂã¹

áÅÐ (b) ¼ÅµÍºÊ¹Í§¢Í§ÃÐººàÁ× Íãªé

¢éÍ¼Ô´¾ÅÒ´ (error response)

E(z)

α100

ÊÓËÃÑº¤èÒ

¨Ò¡ 0 ¶Ö§

ºÔµ ÊÓËÃÑºáµèÅÐ

30T

µÒÁÊÁ¡ÒÃ (2.10) ¤ÇÃ·Õ ¨ÐÁÕ ¢¹Ò´¹éÍÂ¡ÇèÒ 0.05 ËÅÑ§¨Ò¡·Õ

¢éÍÁÙÅ¼èÒ¹ä» 100 ºÔµ µÒÁ·Õ áÊ´§ã¹ÃÙ»·Õ 2.5 ÊÓËÃÑº

d = 14T

ÊÑ§à¡µ¨Ð¾ºÇèÒ ÁÕ¤èÒ

α100

¨Ó¹Ç¹

2.3.

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

1.4

α = 0.055 α = 0.035

Magnitude

1.05 1 0.95

α = 0.0218 α = 0.01 α = 0.005

100

150

200

250

(a) Time (in bit periods) 1

Magnitude

α = 0.005 α = 0.0218

α = 0.01

0.05 0 −0.05

α = 0.035 α = 0.055 −0.4

100

150

200

250

(b) Time (in bit periods)

ÃÙ»·Õ 2.5: (a) ¼ÅµÍºÊ¹Í§¢Ñ ¹ºÑ¹ä´¢Í§ÃÐºº áÅÐ (b) ¼ÅµÍºÊ¹Í§¢éÍ¼Ô´¾ÅÒ´ÊÓËÃÑº áÅÐ¤èÒ

2 ¤èÒ ¤×Í

d = 14T

µèÒ§æ

α = 0.0218

¤ÅÒ´à¤Å× Í¹ÂÔ¹ÂÍÁ

áÅÐ

±5%

α = 0.055

·Õ ·ÓãËéÃÐººÁÕÍÑµÃÒ¡ÒÃÅÙèà¢éÒÀÒÂã¹ 100 ºÔµ ´éÇÂ¤èÒ¤ÇÒÁ

ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ ¤èÒ

·Õ ÁÕ¤èÒ¹éÍÂ¡ÇèÒ ¨Ð¶Ù¡àÅ×Í¡ÁÒãªé§Ò¹ã¹

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Ç§¨Ã PLL à¾× Í·Õ ¨Ð·ÓãËéáº¹´ìÇÔ´·ì¢Í§ÅÙ»ÁÕ¤èÒ¹éÍÂ «Ö §¨ÐªèÇÂÅ´¼Å¡ÃÐ·º¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ¨Ð à¢éèÒÁÒã¹Ç§¨Ã PLL ä´é

2.3.2

¡ÒÃÇÔà¤ÃÒÐËìàªÔ§àÊé¹¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§

ã¹¡Ã³Õ ·Õ ÃÐººÁÕ Í§¤ì»ÃÐ¡Íº¢Í§ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ (frequency o set) Ç§¨Ã PLL ÍÑ¹´Ñº ·Õ ÊÍ§ áÅÐ

ÊÓËÃÑº¤èÒ

¨ÐµéÍ§¶Ù¡¹ÓÁÒãªé§Ò¹á·¹Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö § «Ö §¾ÒÃÒÁÔàµÍÃì·Õ ¨ÐµéÍ§¤Ó¹Ç³ËÒ ¤×Í ã¹¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§¹Õ ¨ÐàÃÔ Áµé¹¨Ò¡¡ÒÃËÒ¤èÒ áÅÐ

·Õ ¡ÓË¹´ÁÒãËé â´ÂÊÁÁØµÔÇèÒ ã¹ÃÐººÁÕà¾ÕÂ§á¤è¢éÍ¼Ô´¾ÅÒ´·Ò§à¿Êà·èÒ¹Ñ ¹ (¹Ñ ¹¤×Í ãªéÇÔ¸Õ¡ÒÃ

ÍÍ¡áºº¤èÒ

µÒÁ·Õ Í¸ÔºÒÂã¹ËÑÇ¢éÍ ·Õ 2.3.1) ¨Ò¡¹Ñ ¹ àÁ× Í ä´é ¤èÒ

·Õ µéÍ§¡ÒÃáÅéÇ ¡ç ¨ÐàÃÔ Á ËÒ¤èÒ

â´Âãªé¡ÒÃÇÔà¤ÃÒÐËìàªÔ§àÊé¹¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§ ÊÓËÃÑº»ÃÔÁÒ³¢Í§ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ ·Õ ãËéÁÒ

τk

¢Í§ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ ÁÕË¹èÇÂà» ¹à»ÍÃìà«ç¹µì (percent) ¢Í§ºÔµà«ÅÅì

«Ö §ã¹¡ÒÃÇÔà¤ÃÒÐËì¹Õ ¢éÍ¼Ô´¾ÅÒ´·Ò§¤ÇÒÁ¶Õ ¨Ð¶Ù¡¨ÓÅÍ§ãËéÁÕ¤èÒà» ¹

kfd

τ̂k+1

àÁ× Í

¤×Í »ÃÔÁÒ³

¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº

·Õ ÊÍ§ ´Ñ§µèÍä»¹Õ

θ̂k+1 = θ̂k + β²̂k−d

(2.12)

τ̂k+1 = τ̂k + α²̂k−d + θ̂k+1

(2.13)

àªè¹à´ÕÂÇ¡Ñ¹ ¶éÒÊÁÁØµÔÇèÒäÁèÁÕÊÑÒ³Ãº¡Ç¹ã¹Ç§¨Ã TED ¹Ñ ¹¤×Í

²̂k

²k

τk − τ̂k ,

à¾ÃÒÐ©Ð¹Ñ ¹

¿ §¡ìªÑ¹ ¶èÒÂâÍ¹¢Í§ÃÐººµÒÁÊÁ¡ÒÃ (2.12) áÅÐ (2.13) ÊÒÁÒÃ¶·Õ ¨ÐËÒä´é â´Â¡ÒÃãªé ¡ÒÃá»Å§«Õ ´Ñ§¹Õ

G(z) =

Γ̂(z) (α + β)z −(d+1) − αz −(d+2) = Γ(z) 1 − 2z −1 + z −2 + (α + β)z −(d+1) − αz −(d+2)

(2.14)

áÅÐ¿ §¡ìªÑ¹¶èÒÂâÍ¹¢Í§¢éÍ¼Ô´¾ÅÒ´ ¤×Í

E(z) = Γ(z) − Γ̂(z) =

1 − 2z −1 + z −2 Γ(z) 1 − 2z −1 + z −2 + (α + β)z −(d+1) − αz −(d+2)

ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ à¡³±ì·Õ ÍÒ¨¨Ð¹ÓÁÒãªéã¹¡ÒÃàÅ×Í¡¤èÒ

¤×Í ¡ÒÃàÅ×Í¡¤èÒ

(2.15)

·Õ ·ÓãËéàÊ¶ÕÂÃÀÒ¾

¢Í§ÃÐººáÅÐÍÑµÃÒ¡ÒÃÅÙèà¢éÒà» ¹·Õ ¹èÒ¾Íã¨ ÊÓËÃÑº»ÃÔÁÒ³¢Í§ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ ·Õ ¡ÓË¹´ÁÒãËé¢Í§

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

Maximum magnitude of E(z) after C samples

2.3.

0.2

C = 100

0.18

C = 50 0.16

0.5% frequency offset

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0.2% frequency offset 0

0.5

ÃÙ»·Õ 2.6: ¢¹Ò´ÁÒ¡ÊØ´¢Í§

áµèÅÐ

d, C

áÅÐ

αC

E(z)

β (PLL gain parameter)

ËÅÑ§¨Ò¡·Õ ¢éÍÁÙÅ¼èÒ¹ä»

2 −3

x 10

ºÔµ àÁ× Íãªé

«Ö § ÊÒÁÒÃ¶·Õ ¨Ð¤Ó¹Ç³ËÒä´é ´Ñ§¹Õ ÊÓËÃÑº ¤èÒ

¢Ñ ¹µÍ¹áÃ¡ ¤×Í ¡ÒÃàÅ×Í¡¤èÒ

1.5

d, C

d = 14

áÅÐ

αC

áÅÐ

·Õ ¡ÓË¹´ÁÒãËé

·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ ¨Ò¡ÊÁ¡ÒÃ (2.14) áÅÐ (2.15) ÃÐºº

¨ÐÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾¡çµèÍàÁ× Í ·Ø¡â¾ÅËÃ×ÍÃÒ¡¤ÓµÍº¢Í§µÑÇÊèÇ¹¢Í§ÊÁ¡ÒÃ (2.14) ËÃ×Í (2.15) ÍÂÙè ÀÒÂã¹Ç§¡ÅÁË¹Ö §Ë¹èÇÂ áÅÐ¶Ö§áÁéÇèÒ¨ÐÁÕ¤èÒ

à¾ÕÂ§¤èÒà´ÕÂÇ·Õ ·ÓãËé

E(z)

ËÅÒÂ¤èÒ·Õ ·ÓãËéÃÐººÁÕ¤ÇÒÁàÊ¶ÕÂÃÀÒ¾ áµè¨ÐàÅ×Í¡

ÁÕ¢¹Ò´¹éÍÂÊØ´ ËÅÑ§¨Ò¡·Õ ¢éÍÁÙÅ¼èÒ¹ä»

ºÔµ à¾× Í·Õ ¨ÐÅ´¼Å¡ÃÐ·º

¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ¨Ðà¢éèÒÁÒã¹Ç§¨Ã PLL ÃÙ»·Õ 2.6 áÊ´§¢¹Ò´ÁÒ¡ÊØ´ (maximum magnitude) ¢Í§

E(z)

µÒÁÊÁ¡ÒÃ (2.15) ËÅÑ§¨Ò¡·Õ ¢éÍÁÙÅ¼èÒ¹ä»

¾ºÇèÒ ÇÔ¸Õ¡ÒÃÇÔà¤ÃÒÐËì¹Õ ¨ÐãËéä´é¤èÒ à¾ÕÂ§áµè¢¹Ò´¢Í§

ËÁÒÂàËµØ

E(z)

ºÔµ ÊÓËÃÑº

d = 14T

áÅÐ

αC

ÊÑ§à¡µ¨Ð

¨ÐµèÒ§¡Ñ¹à·èÒ¹Ñ ¹ µÒÁ»ÃÔÁÒ³¢Í§ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ

ÇÔ¸Õ¡ÒÃÍÍ¡áºº¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL µÒÁ·Õ ¡ÅèÒÇÁÒ¢éÒ§µé¹ ¹Õ ¨ÐÍÂÙè º¹¾× ¹°Ò¹

¢Í§ÊÁÁØµÔ°Ò¹·Õ ÇèÒ ¤ÇÒÁªÑ¹ ¢Í§àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ (S curve) ¢Í§ÊÁ¡ÒÃ (2.4) ÁÕ ¤èÒ à» ¹ ¤èÒ Ë¹Ö § ³ ¨Ø´¡Óà¹Ô´ áÅÐäÁè ÁÕ ÊÑÒ³Ãº¡Ç¹ÀÒÂã¹Ç§¨Ã TED à¾ÃÒÐ©Ð¹Ñ ¹ ¡èÍ¹·Õ ¨Ð¹Ó¤èÒ

áÅÐ

·Õ ä´é

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¨Ò¡ÇÔ¸Õ¡ÒÃÍÍ¡áººµÒÁ·Õ ¡ÅèÒÇÁÒ¢éÒ§µé¹ ¹Õ ä»ãªé §Ò¹ ¼Ùéãªé ¨ÐµéÍ§·ÓãËé ¤ÇÒÁªÑ¹ ¢Í§àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ ¢Í§Ç§¨Ã TED ÁÕ¤èÒà» ¹¤èÒË¹Ö § ³ ¨Ø´¡Óà¹Ô´¡èÍ¹àÊÁÍ

2.3.3

¡ÒÃËÒàÊé¹â¤é§ÃÙ»µÑÇàÍÊ

ä·ÁÁÔ § ¿ §¡ìªÑ¹ (timing function) ËÃ×Í àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ (S curve) [22] ¨Ð¹ÔÂÒÁâ´Â ¤èÒà©ÅÕ Â (mean) ¢Í§ =

{²̂k }â´ÂÊÁÁØµÔÇèÒ

ÊÓËÃÑº·Ø¡¤èÒ

¤èÒ

r̂k

·Õ ä´é¨Ò¡Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ìÁÕ¤èÒ¶Ù¡µéÍ§·Ñ §ËÁ´ ¹Ñ ¹¤×Í

r̂k

áÅÐ¢éÍÁÙÅÍÔ¹¾ØµáµèÅÐºÔµäÁèÁÕÊËÊÑÁ¾Ñ¹¸ì¡Ñ¹ (uncorrelated) áÅÐÁÕ¾ÅÑ§§Ò¹

à·èÒ¡Ñº 1 Ë¹èÇÂ ´Ñ§¹Ñ ¹

STED (²) = E[²̂k | ², r̂k = rk for ∀k] àÁ× Í

² = τ − τ̂

(2.16)

¤×Í ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ à¹× Í§¨Ò¡ ÃÙ» ¡ÃÒ¿¢Í§ä·ÁÁÔ § ¿ §¡ìªÑ¹ ÁÕ ÅÑ¡É³Ð¤ÅéÒÂ

µÑÇÍÑ¡ÉÃ S (àÁ× ÍËÁØ¹ÃÙ»¡ÃÒ¿ 90 Í§ÈÒ) ´Ñ§¹Ñ ¹ ¨Ö§àÃÕÂ¡¡Ñ¹ÇèÒ àÊé¹â¤é§ÃÙ»µÑÇàÍÊ (S curve) «Ö § ÊÒÁÒÃ¶·Õ ¨Ð¹ÓÁÒãªéÇÑ´»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨Ã TED ä´é ¹Í¡¨Ò¡¹Õ ã¹¡Ã³Õ ·Õ ·ÃÒºÇèÒ ¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¢Í§ªèÍ§ÊÑÒ³¤×Í ÍÐäÃ àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ ÊÒÁÒÃ¶·Õ ¨Ð¤Ó¹Ç³ËÒä´é â´ÂµÃ§ [22] µÑÇÍÂèÒ§àªè¹ ãËé ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§¢Í§ªèÍ§ÊÑÒ³ PR4 (partial response class IV) ã¹ÃÙ»·Õ 2.2 àÁ× Í

H(D)

1 − D2

´Ñ§¹Ñ ¹ àÊé¹â¤é§ÃÙ»µÑÇàÍÊ¢Í§Ç§¨Ã

M&M TED ÊÓËÃÑºªèÍ§ÊÑÒ³¹Õ ËÒä´é¨Ò¡

STED (²) = E[²̂k | ², r̂k−1 = rk−1 , r̂k = rk ] = KT E[rk−1 yk − rk yk−1 ] X = KT E[(ak−1 − ak−3 ) ai h(kT − iT − ²) i

− (ak − ak−2 )

ai h(kT − T − iT − ²)]

= â´Â·Õ

rk = ak −ak−2

i ai h(kT

− iT − ²)

3T {−h(−T − ²) + 2h(T − ²) − h(3T − ²)} 16

(2.17)

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµµÑÇ·Õ

¢Í§ªèÍ§ÊÑÒ³·Õ »ÃÒÈ¨Ò¡ÊÑÒ³Ãº¡Ç¹,

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµµÑÇ·Õ

¢Í§Ç§¨ÃªÑ¡µÑÇÍÂèÒ§, áÅÐ

h(t)

q(t) − q(t − 2T )

2.3.

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

n(t) PR-IV pulse

h(t) = q(t) - q(t-2T)

p(t)

LPF

y( t )

yk t k = kT

to data detection

z −d

symbol detector

yk −d

rˆk −d

εˆk

TED

ÃÙ»·Õ 2.7: áºº¨ÓÅÍ§ÊÓËÃÑº¡ÒÃËÒàÊé¹â¤é§ÃÙ»µÑÇàÍÊ

¤×Í ÊÑÒ³¾ÑÅÊìáºº PR4 ¤èÒ¤§µÑÇ

3T /16

¶Ù¡ãªéà¾× ÍªèÇÂ·ÓãËé¤ÇÒÁªÑ¹¢Í§àÊé¹â¤é§ÃÙ»µÑÇ

àÍÊã¹ÊÁ¡ÒÃ (2.17) ÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § ³ ¨Ø´¡Óà¹Ô´

ÊÓËÃÑºã¹¡Ã³Õ·Õ äÁè·ÃÒº¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¢Í§ªèÍ§ÊÑÒ³ àÊé¹â¤é§ÃÙ»µÑÇàÍÊ¡çÂÑ§ÊÒÁÒÃ¶·Õ ¨ÐËÒä´éâ´Â¡ÒÃ·Ó¡ÒÃ¨ÓÅÍ§ÃÐºº «Ö §·Óä´éâ´Â¡ÒÃà» ´ä·ÁÁÔ §ÅÙ»¢Í§áºº¨ÓÅÍ§ã¹ÃÙ»·Õ 2.2 (¡ÅèÒÇ¤×Í µÑ´Ç§¨Ã¡ÃÍ§ÅÙ»áÅÐÇ§¨Ã VCO ÍÍ¡¨Ò¡áºº¨ÓÅÍ§) «Ö §¨Ð·ÓãËéä´éà» ¹áºº¨ÓÅÍ§ãËÁèµÒÁÃÙ»·Õ 2.7 ¨Ò¡ÃÙ» ÊÑÒ³

´éÇÂ

¨Ð¶Ù¡ ·Ó¡ÒÃªÑ¡ µÑÇÍÂèÒ§·Õ àÇÅÒ

(¹Ñ ¹¤×Í ¡ÓË¹´ãËé

¨Ò¡¹Ñ ¹ ·Ó¡ÒÃ¤Ó¹Ç³ËÒ¤èÒà©ÅÕ Â ·Ò§àÇÅÒ (time average) ¢Í§

à¾× ÍãËéä´éà» ¹¤èÒ

−0.5T

y(t)

¶Ö§¤èÒ

STED (²)

0.5T

¤èÒà´ÕÂÇ ·ÓÅÑ¡É³Ð¹Õ ä»àÃ× ÍÂæ à¾× ÍËÒ¤èÒ

ÊØ´·éÒÂ¡ç·Ó¡ÒÃÇÒ´¡ÃÒ¿ÃÐËÇèÒ§

²/T

áÅÐ

τ̂ = 0)

{²̂k }

STED (²)

STED (²)/T

áÅÐá·¹¤èÒ

ÊÓËÃÑº áµèÅÐ¤èÒ

ÊÓËÃÑº

ÊÓËÃÑº¤èÒ

à¾× ÍãËéä´éà» ¹àÊé¹â¤é§

ÃÙ»µÑÇàÍÊ

ÃÙ» ·Õ 2.8 áÊ´§àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ¢Í§Ç§¨Ã M&M TED ÊÓËÃÑº ªèÍ§ÊÑÒ³áºº PR4 ·Õ ãªé ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä» ³ ÃÐ´Ñº SNR µèÍ ºÔµ ËÃ×Í

Eb /N0

µèÒ§æ ÁÕ Ë¹èÇÂà» ¹ à´«ÔàºÅ

(dB) â´ÂãªéÇ§¨Ã PLL ¨Ðãªé¤èÒµÑ´ÊÔ¹ã¨¢³ÐË¹Ö §áººá¢ç§ (instantaneous hard decision) ·Õ ä´éÃÑº ¨Ò¡Ç§¨ÃµÃÇ¨ËÒ¢Õ´àÃÔ Áà»ÅÕ Â¹·Õ äÁèÁÕË¹èÇÂ¤ÇÒÁ¨Ó (memoryless threshold detector) áºº 3 ÃÐ´Ñº

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

0.5 0.4 0.3

10 dB

S TED(ε)/T

0.2

20 dB 0.1

Mean 0

Eb/N0 = 5 dB −0.1 −0.2 −0.3 −0.4

Normalized timing funtion −0.5 −0.5

0.5

Normalized timing error (ε/T)

ÃÙ»·Õ 2.8: àÊé¹â¤é§ÃÙ»µÑÇàÍÊ¢Í§Ç§¨Ã M&M TED ÊÓËÃÑºªèÍ§ÊÑÒ³ PR4 ·Õ ãªéä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé¡Ñ¹·Ñ Çä»

â´ÂÁÕÃÐ´Ñº¢Õ´àÃÔ Áà»ÅÕ Â¹ (threshold level) ·Õ ¤èÒ

     r̂k =

   

±1

¹Ñ ¹¤×Í

2 if yk > 1 −2 if yk < −1

(2.18)

0 else

àÊé¹¡ÃÒ¿¢Í§ ä·ÁÁÔ §¿ §¡ìªÑ¹áºº¹ÍÃìÁÍÅäÅ«ì (normalized timing function) ¨Ðä´éÁÒ¨Ò¡ÊÁ¡ÒÃ (2.17) ¨Ò¡ÃÙ»·Õ 2.8 ¨Ð¾ºÇèÒ àÊé¹â¤é§ÃÙ»µÑÇàÍÊÁÕÅÑ¡É³ÐÊÁÁÒµÃáºº¤Õ (odd symmetric) àÁ× Íà·ÕÂº ¡Ñº

²=0

«Ö §ËÁÒÂ¤ÇÒÁËÁÒÂÇèÒ ÍÍ¿à«µ·Ò§à¿Ê¢Í§¡ÒÃªÑ¡µÑÇÍÂèÒ§·Õ ¶Ù¡»ÃÑº¤èÒ´éÇÂÇ§¨Ã PLL ¨Ð

ÊÔ ¹ÊØ´ ³ ¨Ø´àÊ¶ÕÂÃÀÒ¾ (stable point) ·Õ

²=0

ÊÑ§à¡µ¨Ð¾ºÇèÒ àÊé¹â¤é§ÃÙ»µÑÇàÍÊ

ä´é¨Ò¡¡ÒÃ¨ÓÅÍ§ÃÐºº¨ÐÊÍ´¤ÅéÍ§¡Ñºä·ÁÁÔ §¿ §¡ìªÑ¹áºº¹ÍÃìÁÍÅäÅ«ìàÁ× Í à¾ÃÒÐÇèÒ ÊÁÁØµÔ°Ò¹·Õ ¡ÓË¹´ãËé

r̂k

à» ¹ àËµØ¼ÅÇèÒ ·ÓäÁªèÇ§¢Í§¡ÃÒ¿·Õ

ÊÓËÃÑº·Ø¡¤èÒ

STED (²)/T

¨Ðãªéä´éäÁè´Õ àÁ× Í

²/T ²/T

STED (²)/T

·Õ

ÁÕ¤èÒ¹éÍÂ ·Ñ §¹Õ à» ¹ ÁÕ¤èÒÁÒ¡ ´Ñ§¹Ñ ¹¨Ö§

ÊÍ´¤ÅéÍ§¡Ñº ä·ÁÁÔ § ¿ §¡ìªÑ¹ áºº¹ÍÃìÁÍÅäÅ«ì àÁ× Í

2.3.

¡ÒÃÍÍ¡ààºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL

Timing estimate

0.5T

Estimated τ 0

−0.5T

Actual τ −T

500

1000

1500

2000

2500

3000

3500

4000

Time (in bit periods)

ÃÙ»·Õ 2.9: µÑÇÍÂèÒ§ÅÑ¡É³Ð¢Í§ä«à¤ÔÅÊÅÔ»

Eb /N0

ÁÕ¤èÒÊÙ§ ¨Ö§ÁÕ¤ÇÒÁ¡ÇéÒ§ÁÒ¡¡ÇèÒªèÇ§¢Í§¡ÃÒ¿ àÁ× Í

¹Í¡¨Ò¡¹Õ ¨Ø´ ·Õ àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊµÑ´ ¡Ñº àÊé¹ á¡¹

Eb /N0

ÁÕ¤èÒ¹éÍÂ

¹Ñ ¹¤×Í àÁ× Í

STED (²)/T

¨ÐàÃÕÂ¡ÇèÒ

¨Ø´ÊÁ´ØÅ (equilibrium point) ¢Í§¡ÒÃ·Ó§Ò¹ «Ö §à» ¹¨Ø´·Õ Ç§¨Ã PLL ¨ÐÊÒÁÒÃ¶µÔ´µÒÁÍÍ¿à«µ ·Ò§àÇÅÒä´é à» ¹ ÍÂèÒ§´Õ ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ ¨Ø´ ÊÁ´ØÅ ¨ÐÁÕ ËÅÒÂµÓáË¹è§ ¤×Í

±2T, . . . , ±nT

àÁ× Í

0, ±T ,

n ¤×Í àÅ¢¨Ó¹Ç¹àµçÁ à¹× Í§¨Ò¡ ÊÑÒ³Ãº¡Ç¹áÅÐ¡ÒÃÃº¡Ç¹ (disturbance)

ã¹ÃÐººÍÒ¨¨Ð·ÓãËé à¡Ô´ ¢éÍ¼Ô´¾ÅÒ´¢¹Ò´ãËè ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ»ÃÑº ¤èÒ ÍÍ¿à«µ·Ò§à¿Ê¢Í§¡ÒÃ ªÑ¡ µÑÇÍÂèÒ§ «Ö § à» ¹ ¼Å·ÓãËé¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ã PLL à¡Ô´ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡¨Ø´ ÊÁ´ØÅ ¨Ø´ Ë¹Ö § ä» ÂÑ§ ¨Ø´ ÊÁ´ØÅ ÍÕ¡ ¨Ø´ Ë¹Ö § àËµØ¡ÒÃ³ì àªè¹¹Õ ¨ÐàÃÕÂ¡¡Ñ¹ ÇèÒ ä«à¤ÔÅÊÅÔ» (cycle slip) «Ö § ¨Ð·ÓãËé à¡Ô´ ¢éÍ¼Ô´¾ÅÒ´¨Ó¹Ç¹ÁÒ¡·Õ Ç§¨ÃµÃÇ¨ËÒ (detector) ÃÙ» ·Õ 2.9 áÊ´§µÑÇÍÂèÒ§ÅÑ¡É³Ð¢Í§ä«à¤ÔÅÊÅÔ» ¨Ò¡ÃÙ»¨Ð¾ºÇèÒ Ç§¨Ã PLL ÊÒÁÒÃ¶µÔ´µÒÁ¡ÒÃà»ÅÕ Â¹á»Å§¢Í§

ä´é´Õ ³ ¨Ø´àÃÔ Áµé¹¢Í§¡ÅØèÁ¢éÍÁÙÅ

(data packet) áµè àÁ× Í ÁÕ ä«à¤ÔÅÊÅÔ» à¡Ô´ ¢Ö ¹ Ç§¨Ã PLL ¨Ð¤èÍÂæ ÊÙàÊÕÂ ¡ÒÃµÔ´µÒÁ¤èÒ

¨¹¡ÃÐ·Ñ §

Ç§¨Ã PLL à¢éÒ ÊÙè ¨Ø´ ÊÁ´ØÅ ãËÁè ÍÕ¡ ¨Ø´ Ë¹Ö § ´Ñ§¹Ñ ¹ ÍÒ¨¨Ð¡ÅèÒÇä´é ÇèÒ ä«à¤ÔÅÊÅÔ» à» ¹ ÊÒàËµØ ·ÓãËé Ç§¨Ã

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

PLL ·Ó§Ò¹·Õ ¨Ø´ÊÁ´ØÅÍÕ¡¨Ø´Ë¹Ö § «Ö §à» ¹àËµØ¼ÅÇèÒ·ÓäÁ

τ̂

¨Ö§ÁÕ¤èÒµèÒ§¨Ò¡

»ÃÐÁÒ³

àÁ× ÍÊÔ ¹ÊØ´

¢Í§¡ÅØèÁ ¢éÍÁÙÅ ¨ÐàËç¹ä´éÇèÒ ä«à¤ÔÅÊÅÔ»à» ¹ ÊÔ § ·Õ ÍÑ¹µÃÒÂÁÒ¡ÊÓËÃÑº ÃÐººä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ´Ñ§¹Ñ ¹ ¹Ñ¡ÇÔ¨ÑÂ ¨Ö§ ä´é àÊ¹ÍÇÔ¸Õ ¡ÒÃµèÒ§æ ·Õ ¨Ð¹Óãªé ã¹¡ÒÃ¨Ñ´¡ÒÃ¡Ñº ä«à¤ÔÅÊÅÔ» ÊÓËÃÑº ¼Ùé Ê¹ã¨ÊÒÁÒÃ¶ÈÖ¡ÉÒ ÃÒÂÅÐàÍÕÂ´ä´éã¹ [29, 30, 31, 32, 33]

2.4

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR4 ·Õ áÊ´§ã¹ÃÙ» ·Õ 2.2 ¨ÐàËç¹ä´éÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áÅÐÇ§¨Ã µÃÇ¨ËÒÊÑÅÑ¡É³ì ¨Ð·Ó§Ò¹áÂ¡¨Ò¡¡Ñ¹ ´Ñ§¹Ñ ¹ »ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐºº·Õ äÁè ä´é ¶Ù¡ à¢éÒ ÃËÑÊ (un coded system) ¨Ð¢Ö ¹ÍÂÙè¡Ñº¤Ø³ÀÒ¾¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ ã¹ÊèÇ¹¹Õ ¨ÐáÊ´§»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» àÁ× Í·Ó§Ò¹ã¹ÃÐºº·Õ ÁÕáÅÐ äÁè ÁÕ ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ ¹Í¡¨Ò¡¹Õ Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì ·Õ ãªé ã¹Ç§¨Ã PLL ¤×Í Ç§¨ÃµÃÇ¨ËÒ ¢Õ´ àÃÔ Á à»ÅÕ Â¹·Õ äÁè ÁÕ Ë¹èÇÂ¤ÇÒÁ¨ÓáººËÅÒÂÃÐ´Ñº (multi level memoryless threshold detector) â´Â¢éÍÁÙÅ àÍÒµì¾Øµ ·Õ ä´é ¨Ðà» ¹ ä»µÒÁÊÁ¡ÒÃ (2.18) ÊÓËÃÑº ¡ÃÐºÇ¹¡ÒÃµÃÇ¨ËÒ¢éÍÁÙÅ ÅÓ´Ñº ¢éÍÁÙÅ

{yk }

60T

à¾× Í

ËÒÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ ·Õ à» ¹ ä»ä´é ÁÒ¡·Õ ÊØ´ ¹Í¡¨Ò¡¹Õ BER áµèÅÐ¤èÒ ·Õ ä´é ¨Ð¶Ù¡ ¤Ó¹Ç³â´Âãªé ¡ÅØèÁ ¢éÍÁÙÅ¨Ó¹Ç¹ÁÒ¡¨¹¡ÇèÒ¨Ðà¡Ô´¢éÍ¼Ô´¾ÅÒ´ÃÇÁ·Ñ §ËÁ´ 1000 ºÔµ ÊÓËÃÑº ÃÐºº·Õ äÁè ÁÕ ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ Ç§¨ÃÀÒ¤ÃÑº ÊÒÁÒÃ¶·Õ ¨Ðãªé Ç§¨Ã PLL ÍÑ¹´Ñº ·Õ Ë¹Ö § ä´é ã¹¡Ã³Õ¹Õ ¨ÐÊÁÁØµÔãËé ÃÐººÁÕ¡ÒÃà¢éÒ¨Ñ§ËÇÐã¹ªèÇ§ÀÒÇÐ¡ÒÃä´éÁÒáººÊÁºÙÃ³ì (perfect acquisition) «Ö § ·Óä´é â´Â¡ÒÃ¡ÓË¹´ãËé

τ0 = 0

à¾× Í ·Õ ÇèÒ ¨Ðä´é äÁè µéÍ§ãªé ¢éÍÁÙÅ preamble áÅÐ¡ÓË¹´ãËé ¢éÍÁÙÅ

Ë¹Ö § ¡ÅØèÁ ÁÕ ¨Ó¹Ç¹ 4096 ºÔµ ÃÙ» ·Õ 2.10 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒáººÃÒ¡ ¡ÓÅÑ§ ÊÍ§à©ÅÕ Â (RMS: root mean square) ¹Ñ ¹¤×Í

σ²

E[(τk − τ̂k )2 ]

áÅÐ BER â´Â¤èÒ

¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL (α) ·Õ ãªé¨Ð¶Ù¡ÍÍ¡áººÁÒà¾× ÍãËéÊÒÁÒÃ¶µÔ´µÒÁ¡ÒÃà»ÅÕ Â¹á»Å§·Ò§à¿Ê ä´é ÀÒÂã¹ 100 ºÔµ (¹Ñ ¹¤×Í

α100

= 0.0295) µÒÁ·Õ ä´é Í¸ÔºÒÂã¹ËÑÇ¢éÍ ·Õ 2.3.1 ¨ÐàËç¹ä´éÇèÒ àÁ× Í

ÃÐ´Ñº ¤ÇÒÁÃØ¹áÃ§¢Í§¨Ôµ àµÍÃì ·Ò§àÇÅÒ ¢Í§

σ² /T

σw /T

áÅÐ BER) ¹Í¡¨Ò¡¹Õ ¶éÒÃÐººÁÕ¤èÒ

ÂÔ § ÁÒ¡ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¡ç ¨ÐÂÔ § áÂè (·Ñ § ã¹ÃÙ»

σ² /T

¹éÍÂ ÃÐºº¡ç¨ÐÁÕ BER µ Ó ´Ñ§¹Ñ ¹ ¾ÒÃÒÁÔàµÍÃì

áÅÐ BER ¨Ö§ÊÒÁÒÃ¶·Õ ¨Ð¹ÓÁÒãªéà» ¹à¡³±ìã¹¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººä·ÁÁÔ §

2.4.

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº·Õ ãªé¡Ñ¹·Ñ Çä»

RMS timing error σε/T (%)

16 14 12 10

σw/T = 1%

8 6 4

σ /T = 0.1% w

2 0

(a) Eb/N0 (dB) −1

−2

BER

σw/T = 1% σw/T = 0.1%

−3

−4

−5

(b) Eb/N0 (dB)

ÃÙ»·Õ 2.10:

(a) ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒáºº RMS

ªèÍ§ÊÑÒ³ÍØ´Á¤µÔáºº PR4 ·Õ ÁÕ¤èÒ

σw /T

σ² /T

áÅÐ (b) »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ BER ÊÓËÃÑº

µèÒ§æ ¡Ñ¹ (àÁ× ÍÃÐººäÁèÁÕÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ )

ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ ä´é ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ÊÓËÃÑºÃÐºº·Õ ÁÕÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ Ç§¨ÃÀÒ¤ÃÑº¨ÐµéÍ§ãªéÇ§¨Ã PLL ÍÑ¹´Ñº·Õ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Conventional timing recovery with hard decision −1

C = 50 C = 100

−2

BER

C = 256 Perfect timing

−3

−4

−5

Eb/N0 (dB)

ÃÙ»·Õ 2.11: »ÃÐÊÔ·¸ÔÀÒ¾ BER ¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»¢Í§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔáºº PR4 ÊÓËÃÑº

σw /T = 0.5%

áÅÐÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ 0.2%

ÊÍ§ã¹¡ÒÃ¨Ñ´¡ÒÃ¡ÑºÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ ¹Õ â´Â¨Ð¾Ô¨ÒÃ³ÒÃÐºº·Õ ·Ó§Ò¹ã¹ÊÀÒÇÐ»Ò¹¡ÅÒ§ (moder ate condition) ¹Ñ ¹¤×ÍÁÕ áÅÐ

σw /T = 0.5%

áÅÐÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ 0.2% àªè¹à´ÕÂÇ¡Ñ¹ ¾ÒÃÒÁÔàµÍÃì

·Õ ãªé¨Ð¶Ù¡ÍÍ¡áººÁÒà¾× ÍãËéÊÒÁÒÃ¶µÔ´µÒÁ¡ÒÃà»ÅÕ Â¹á»Å§·Ò§à¿ÊáÅÐ·Ò§¤ÇÒÁ¶Õ ä´éÀÒÂã¹

ºÔµ µÒÁ·Õ ä´é Í¸ÔºÒÂã¹ËÑÇ¢éÍ ·Õ 2.3.2 «Ö § ¨Ðä´é ÇèÒ ¤èÒ

·Õ ¶Ù¡ ÍÍ¡áººÊÓËÃÑº

= 50, 100, áÅÐ 256 ¤×Í 0.012, 0.029, áÅÐ 0.058, µÒÁÅÓ´Ñº ã¹¢³Ð·Õ ¤èÒ ÊÓËÃÑº

d=0

áÅÐ

d = 0 β

áÅÐ

·Õ ¶Ù¡ ÍÍ¡áºº

= 50, 100, áÅÐ 256 ¤×Í 0.00015, 0.000885, áÅÐ 0.00325, µÒÁÅÓ´Ñº

¹Í¡¨Ò¡¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐ¡Ã³Õ·Õ Ç§¨Ã PLL ãªé¤èÒ

áÅÐ¤èÒ

à´ÕÂÇ¡Ñ¹ ÊÓËÃÑº·Ñ §ªèÇ§ÀÒÇÐ¡ÒÃä´é

ÁÒáÅÐÀÒÇÐ¡ÒÃµÔ´µÒÁ â´Â¢éÍÁÙÅË¹Ö §¡ÅØèÁ¨Ð»ÃÐ¡Íºä»´éÇÂ preamble ¨Ó¹Ç¹

ºÔµ áÅÐÊèÇ¹·Õ

à» ¹ºÔµ¢èÒÇÊÒÃ¨Ó¹Ç¹ 4096 ºÔµ ÃÙ»·Õ 2.11 áÊ´§»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» àÁ× Íãªé¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ·Õ ÍÍ¡áººÊÓËÃÑºáµèÅÐ ãªé á·¹ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä» ·Õ ãªé

τ̂k

τk

àÊé¹¡ÃÒ¿·Õ à¢ÕÂ¹ÇèÒ Perfect timing

ÊÓËÃÑº ¡ÒÃªÑ¡ µÑÇÍÂèÒ§ÊÑÒ³

y(t)

¨Ð

2.5.

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº´Ô¨Ô·ÑÅ

àËç¹ä´éÇèÒ ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»äÁèÊÒÁÒÃ¶·Ó§Ò¹ä´é´Õ àÁ× Í·Ó§Ò¹ã¹ÃÐºº·Õ µéÍ§¡ÒÃÍÑµÃÒ ¡ÒÃÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ ËÃ×Í ÍÕ¡ ¹ÑÂ Ë¹Ö § ¡ç ¤×Í àÁ× Í ãªé §Ò¹¡Ñº ¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL ·Õ ¶Ù¡ ÍÍ¡áºº ÊÓËÃÑº

2.5

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕààºº´Ô¨Ô·ÑÅ

¹éÍÂæ

ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä»·Õ Í¸ÔºÒÂã¹º·¹Õ ¨ÐÁÕ ÅÑ¡É³Ð¡ÒÃ·Ó§Ò¹à» ¹ áºº¼ÊÁ (hybrid) ¹Ñ ¹¤×Í ÁÕ ·Ñ § ÊèÇ¹·Õ ·Ó§Ò¹¡Ñº ÊÑÒ³áÍ¹ÐÅçÍ¡ áÅÐÊèÇ¹·Õ ·Ó§Ò¹¡Ñº ÊÑÒ³´Ô¨Ô·ÑÅ ¾Ô¨ÒÃ³Ò¨Ò¡ ÃÙ» ·Õ 2.2 â´Â·Ñ Çä» Ç§¨Ã VCO ÁÑ¡¨Ðà» ¹ Ç§¨ÃáÍ¹ÐÅçÍ¡«Ö § ÁÕ ÅÑ¡É³Ð¡ÒÃ·Ó§Ò¹·Õ «Ñº«éÍ¹áÅÐÁÕ ÃÒ¤Òá¾§ ã¹ÊèÇ¹¹Õ ¨Ð¡ÅèÒÇ¶Ö§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ·Õ ÁÕÅÑ¡É³Ðà» ¹áºº´Ô¨Ô·ÑÅ·Ñ §ËÁ´ «Ö §ÁÕãªéã¹ªÔ» ªèÍ§ÊÑÒ³ÍèÒ¹ (read channel chip) ºÒ§ÃØè¹ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº´Ô¨Ô·ÑÅ ¨Ðãªé ÍÑµÃÒ¡ÒÃªÑ¡ µÑÇÍÂèÒ§ (sampling rate) ·Õ äÁè à¢éÒ ¨Ñ§ËÇÐ (asyn chronous) ¡ÑºÊÑÒ³áÍ¹ÐÅçÍ¡·Õ ä´éÃÑº à¾ÕÂ§áµè¢ÍãËéÁÕ¤ÇÒÁ¶Õ ¡ÒÃªÑ¡µÑÇÍÂèÒ§ (sampling frequen 5

cy) ÊÙ§¡ÇèÒ¤ÇÒÁ¶Õ ä¹¤ÇÔµÊì

(Nyquist frequency) [2, 10] ¢Í§ÊÑÒ³áÍ¹ÐÅçÍ¡ ËÃ×ÍÍÒ¨¨Ð¡ÅèÒÇ 6

(oversampling rate) [34, 35] à¹× Í§¨Ò¡

¢éÍÁÙÅá«Áà» Å·Õ ä´é¨Ò¡Ç§¨ÃªÑ¡µÑÇÍÂèÒ§¹Õ ¨ÐäÁèà¢éÒ¨Ñ§ËÇÐ¡Ñº¢éÍÁÙÅºÔµ·Õ Êè§ÁÒ¨Ò¡µé¹·Ò§ ´Ñ§¹Ñ ¹ ¨Ö§µéÍ§ ÁÕ ¡ÒÃ»ÃÑº¤èÒ·Ò§àÇÅÒ (timing adjustment) ´éÇÂÇÔ¸Õ¡ÒÃ·Ò§´Ô¨Ô·ÑÅ·Õ àÃÕÂ¡ÇèÒ à·¤¹Ô¤¡ÒÃ»ÃÐÁÒ³ ¤èÒ ã¹ªèÇ§ (interpolation technique) à¾× ÍãËé ä´é ¢éÍÁÙÅ á«Áà» Å ·Õ ÊÍ´¤ÅéÍ§¡Ñº ¢éÍÁÙÅ ºÔµ ·Õ Êè§ ÁÒ¨Ò¡ µé¹·Ò§ ÃÐººä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ·Õ ãªé à·¤¹Ô¤ ¹Õ ¨ÐàÃÕÂ¡¡Ñ¹ ·Ñ Çä»ÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº»ÃÐÁÒ³¤èÒ ã¹ªèÇ§ (interpolated timing recovery) «Ö § ÁÕ â¤Ã§ÊÃéÒ§µÒÁÃÙ» ·Õ 2.12 â´ÂÊèÇ¹»ÃÐ¡Íº·Ø¡ ÊèÇ¹ ã¹Ç§¨Ã PLL ¨ÐÁÕ ÅÑ¡É³Ð¡ÒÃ·Ó§Ò¹à» ¹ áºº´Ô¨Ô·ÑÅ ·Ñ §ËÁ´ «Ö § ¨ÐªèÇÂ·ÓãËé ÊÒÁÒÃ¶Å´¤èÒãªé¨èÒÂã¹ ¡ÒÃÊÃéÒ§ÃÐººä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ä´é ¨Ò¡¡ÒÃ·´ÅÍ§¾ºÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº»ÃÐÁÒ³¤èÒ ã¹ªèÇ§ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾à·ÕÂºà·èÒ ¡Ñº ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä» ¶éÒ ÁÕ ¡ÒÃàÅ×Í¡ãªé Ç§¨Ã¡ÃÍ§¡ÒÃ»ÃÐÁÒ³ ¤èÒ ã¹ ªèÇ§ (interpolation lter) ·Õ àËÁÒÐÊÁ ÊÓËÃÑº ¼Ùé Ê¹ã¨ ÊÒÁÒÃ¶ ÈÖ¡ÉÒ ÃÒÂÅÐàÍÕÂ´ ¢Í§ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕáºº»ÃÐÁÒ³¤èÒã¹ªèÇ§à¾Ô ÁàµÔÁä´é¨Ò¡ [34, 35, 36, 37] 5

¤ÇÒÁ¶Õ ä¹¤ÇÔµÊì¢Í§ÊÑÒ³áÍ¹ÐÅçÍ¡ ÁÕ¤èÒà·èÒ¡ÑºÊÍ§à·èÒ¢Í§¤ÇÒÁ¶Õ ÊÙ§ÊØ´¢Í§ÊÑÒ³áÍ¹ÐÅçÍ¡¹Ñ ¹

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

A/D converter

y (t )

interpolation filter

t i = iTs

Viterbi detector

âk

t k = ( mk + µ k )Ts

fixed sampling frequency (1 / Ts )

τˆk digital accumulator

symbol detector

z −d

interpolator control unit

loop filter

εˆk

yk − d

rˆk −d

TED

ÃÙ»·Õ 2.12: â¤Ã§ÊÃéÒ§¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº»ÃÐÁÒ³¤èÒã¹ªèÇ§

2.6

àà¹Çâ¹éÁ¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕã¹Í¹Ò¤µ

¨Ò¡¼ÅÅÑ¾¸ì ·Õ áÊ´§ã¹ÃÙ» ·Õ 2.10 áÅÐ 2.11 ÊÃØ» ä´é ÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä»¨Ð·Ó§Ò¹ ä´é äÁè ´Õ ¶éÒ ÃÐººÁÕ ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒÁÒ¡ ËÃ×Í àÁ× Í ·Ó§Ò¹ã¹ÃÐºº·Õ µéÍ§¡ÒÃÍÑµÃÒ¡ÒÃÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ ÇÔ¸Õ¡ÒÃá¡éä¢» ËÒ·Õ §èÒÂ·Õ ÊØ´ ã¹¡ÒÃà¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ § ÃÔ ¤Ñ¿ àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä» ¡ç ¤×Í ¡ÒÃà»ÅÕ Â¹Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì ·Õ ãªé ã¹ä·ÁÁÔ § ÅÙ» ¨Ò¡ Ç§¨ÃµÃÇ¨ËÒ¢Õ´ àÃÔ Á à»ÅÕ Â¹áººá¢ç§ (hard threshold detector) ä»à» ¹Ç§¨ÃµÃÇ¨ËÒ¢Õ´àÃÔ Áà»ÅÕ Â¹áººÍèÍ¹ (soft threshold detector) [33] ËÃ×Í ÍÒ¨¨Ðãªé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Õ ÁÕ »ÃÔÁÒ³Ë¹èÇ§àÇÅÒÊÓËÃÑº ¡ÒÃµÑ´ÊÔ¹ã¨

ÊÑ ¹ ¡çä´é [27] ÍÂèÒ§äÃ

¡çµÒÁ ÇÔ¸Õ¡ÒÃ·Õ ¡ÅèÒÇÁÒàËÅèÒ¹Õ ¨ÐªèÇÂà¾Ô Á»ÃÐÊÔ·¸ÔÀÒ¾·Õ ä´éà¾ÕÂ§àÅç¡¹éÍÂà·èÒ¹Ñ ¹ ´Ñ§¹Ñ ¹ ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººãËÁè·Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» ¨Ö§à» ¹ÊÔ §·Õ µéÍ§¡ÒÃÍÂèÒ§ÁÒ¡ ã¹ [30, 38] ä´é¹ÓàÊ¹Íä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕÃÙ»áººãËÁè·Õ àÃÕÂ¡ÇèÒ à¾Íà«ÍÃì äÇàÇÍÃìä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ (per survivor timing recovery) «Ö §ãªé§Ò¹¡ÑºÃÐºº·Õ äÁèä´é¶Ù¡à¢éÒÃËÑÊ «Ö §ÁÕ

¨ÐºÍ¡

10−4

ËÃ×ÍÍÕ¡

»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» ´Ñ§áÊ´§ã¹ÃÙ»·Õ 2.13 â´Â·Õ àÊé¹á¡¹ ¶Ö§»ÃÔÁÒ³

Eb /N0

(ÁÕË¹èÇÂà» ¹ dB) ·Õ ÃÐººµéÍ§¡ÒÃ ã¹¡ÒÃ·Õ ¨Ð·ÓãËéÃÐººÁÕ BER =

¹ÑÂË¹Ö §¡ç¤×Í àÊé¹á¡¹

¨ÐºÍ¡¶Ö§¡ÓÅÑ§ (power) ·Õ Ç§¨ÃÀÒ¤Êè§µéÍ§ãªéã¹¡ÒÃÊè§¢éÍÁÙÅ à¾× Í·Õ ¨Ð·ÓãËé

àà¹Çâ¹éÁ¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕã¹Í¹Ò¤µ

11 Conventional timing recovery with hard decision (d = 0) Conventional timing recovery with tentative decision (d = 4) Per−survivor timing recovery (d = 0) Genie−aided detector (d = 0)

10.8 10.6

Eb/N0 required to achieve BER = 10

−4

(in dB)

2.6.

10.4 10.2 10 9.8 9.6 9.4 9.2 9 0.1

0.2

0.3

0.4

0.5

0.6

σw/T (%)

0.7

0.8

0.9

ÃÙ»·Õ 2.13: »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ ¢Í§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔáºº PR4

Ç§¨ÃÀÒ¤ÃÑºÁÕ BER =

10−4

¨Ò¡ÃÙ»·Õ 2.13 àÊé¹¡ÃÒ¿·Õ à¢ÕÂ¹ÇèÒ Genie aided detector ËÁÒÂ¶Ö§

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»·Õ Ç§¨Ã PLL ãªé

r̂k

(´ÙÃÙ»·Õ 2.2) ã¹¡ÒÃ»ÃÑº¤èÒÍÍ¿à«µ·Ò§

à¿Ê¢Í§¡ÒÃªÑ¡µÑÇÍÂèÒ§µÑÇ¶Ñ´ä», áÅÐ tentative decision (d = 4) ËÁÒÂ¶Ö§ ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº ·Õ ãªé ¡Ñ¹ ·Ñ Çä»·Õ Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì ·Õ ãªéè ã¹ä·ÁÁÔ § ÅÙ» ¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Õ ÁÕ »ÃÔÁÒ³Ë¹èÇ§ àÇÅÒ

d = 4T

¨Ð¼Å¡ÒÃ·´ÅÍ§¾ºÇèÒ à¾Íà«ÍÃì äÇàÇÍÃì ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾´Õ ¡ÇèÒ ä·ÁÁÔ §

ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» (à¹× Í§¨Ò¡ ãªé

Eb /N0

¹éÍÂ¡ÇèÒ ã¹¡ÒÃ·Õ ¨Ð·ÓãËéÃÐººÁÕ BER =

à·èÒ¡Ñ¹) â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í·Ó§Ò¹·Õ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ä·ÁÁÔ §¨ÔµàµÍÃì

σw /T

10−4

ÊÙ§

ã¹¡ÒÃµÃÇ¨ÊÍºÍÑµÃÒ¡ÒÃÅÙèà¢éÒ ¢Í§ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áººµèÒ§æ ¨Ðãªé áºº¨ÓÅÍ§ã¹ÃÙ» ·Õ 2.2 â´Â ¡ÓË¹´ãËé

σw /T = 0%, τ̂0 = 0.5T ,

PLL ¨Ð¶Ù¡ÍÍ¡áººÁÒÊÓËÃÑº

ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ à·èÒ¡Ñº 0%, áÅÐ¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã

= 50 ¹Ñ ¹¤×Í

α50

ÊÓËÃÑº

= 0 áÅÐ

¤×Í 0.058 áÅÐ 0.049

µÒÁÅÓ´Ñº ÃÙ»·Õ 2.14 à»ÃÕÂºà·ÕÂºÍÑµÃÒ¡ÒÃÅÙèà¢éÒ¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ â´Â¤Ô´à©ÅÕ Â¨Ò¡¡ÅØèÁ ¢éÍÁÙÅ 50000 ¡ÅØèÁ â´Â·Õ ÃÐºº¨Ð¶Ù¡¾Ô¨ÒÃ³ÒÇèÒ»ÃÐÊº¤ÇÒÁÊÓàÃç¨ã¹¡ÒÃÅÙèà¢éÒ ³ àÇÅÒ·Õ

¡çµèÍàÁ× Í

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

100

Genie−aided detector

Percentage of convergence

90 80 70

PSP−MM

Conventional timing recovery with hard decision (d = 0)

50 40 30

Conventional timing recovery with tentative decision (d = 4)

20 10 50

100

150

200

250

300

350

400

450

500

Time (in bit periods)

ÃÙ»·Õ 2.14: ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººµèÒ§æ àÁ× Íãªé

τ̂i

ÊÓËÃÑº

i≥k

ÁÕ ¤èÒ à·èÒ ¡Ñº ¤èÒ 0 ËÃ×Í

α50

·Õ

Eb /N0 = 10

´éÇÂ¤èÒ ¤ÇÒÁ¤ÅÒ´à¤Å× Í¹ÂÔ¹ÂÍÁ

±10%

ÇèÒ ÃÐºº·Õ ãªé Genie aided detector ¨ÐÅÙèà¢éÒÀÒÂã¹ 50 ºÔµ «Ö §¨ÐÊÍ´¤ÅéÍ§¡Ñº Ç§¨Ã PLL ¢Í§ Genie aided detector ãªé¤èÒ·Õ ¶Ù¡µéÍ§ (¹Ñ ¹¤×Í

r̂k

rk )

α50

¨Ò¡ÃÙ» ¨Ð¾º ·Õ ãªé à¾ÃÒÐÇèÒ

ã¹¡ÒÃ»ÃÑº¤èÒÍÍ¿à«µ

·Ò§à¿Ê¢Í§¡ÒÃªÑ¡µÑÇÍÂèÒ§µÑÇ¶Ñ´ä» ¹Í¡¨Ò¡¹Õ ÂÑ§¾ºÇèÒ à¾Íà«ÍÃìäÇàÇÍÃìä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕÁÕÍÑµÃÒ¡ÒÃ ÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ àÁ× Íà·ÕÂº¡Ñºä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» »ÃÐÊÔ·¸ÔÀÒ¾¢Í§à¾Íà«ÍÃì äÇàÇÍÃì ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ ÊÒÁÒÃ¶·Õ ¨Ð·ÓãËé à¾Ô Á ¢Ö ¹ ä´é ÍÕ¡ â´Â¡ÒÃ¹Óä» ãªé §Ò¹ÃèÇÁ¡Ñ¹ ¡Ñº ÃËÑÊ á¡éä¢¢éÍ¼Ô´¾ÅÒ´ (ECC: error correction code) «Ö § ¼ÅÅÑ¾¸ì ·Õ ä´é ¨ÐàÃÕÂ¡ÇèÒ à¾Íà«ÍÃì äÇàÇÍÃì ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Ó§Ò¹« Ó (per survivor iterative timing recovery) [30, 39, 40] â´Â¨Ðãªé §Ò¹¡Ñº ÃÐºº·Õ ¶Ù¡ à¢éÒ ÃËÑÊ (coded system) «Ö § ¨Ò¡¼Å¡ÒÃ·´ÅÍ§¾ºÇèÒ à¾Íà«ÍÃì äÇàÇÍÃì ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Ó§Ò¹« Ó ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä»ÁÒ¡ â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í ÃÐººÁÕ ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒÁÒ¡ ËÃ×Í àÁ× Í ·Ó§Ò¹ã¹ÃÐºº·Õ µéÍ§¡ÒÃÍÑµÃÒ¡ÒÃ ÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ ÊÓËÃÑº¼ÙéÊ¹ã¨ÊÒÁÒÃ¶ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´à¾Ô ÁàµÔÁä´éã¹ [30, 39, 40] «Ö §ÊÒÁÒÃ¶´ÒÇ¹ì âËÅ´àÍ¡ÊÒÃàËÅèÒ¹Õ ä´é·Õ http://home.npru.ac.th/∼t3058

2.7.

ÊÃØ»·éÒÂº·

2.7

ÊÃØ»·éÒÂº·

ã¹º·¹Õ ä´éÍ¸ÔºÒÂ¶Ö§ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» ÃÇÁä»¶Ö§ÇÔ¸Õ¡ÒÃÍÍ¡áºº ¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL â´Âãªé áºº¨ÓÅÍ§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ» áººàªÔ§ àÊé¹ ¨Ò¡¼Å¡ÒÃ·´ÅÍ§¾º ÇèÒ ¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL ·Õ ä´é ¨Ò¡¡ÒÃÍÍ¡áººµÒÁà¡³±ì ·Õ ¡ÓË¹´äÇé ÁÕ ¤èÒ à´ÕÂÇ¡Ñ¹ äÁèÇèÒ ã¹ ÃÐºº¨ÐÁÕ »ÃÔÁÒ³ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ à·èÒã´ áÅÐ¡èÍ¹·Õ ¨Ð¹Ó¤èÒ ¾ÒÃÒÁÔàµÍÃì ¢Í§Ç§¨Ã PLL ·Õ ä´é ¨Ò¡ ÇÔ¸Õ¡ÒÃÍÍ¡áººµÒÁ·Õ Í¸ÔºÒÂã¹º·¹Õ ä»ãªé §Ò¹ ¼Ùéãªé ¨ÐµéÍ§·ÓãËé ¤ÇÒÁªÑ¹ ¢Í§àÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ¢Í§ Ç§¨Ã TED ÁÕ¤èÒà» ¹¤èÒË¹Ö § ³ ¨Ø´¡Óà¹Ô´¡èÍ¹àÊÁÍ ¹Í¡¨Ò¡¹Õ ¼Å¡ÒÃ·´ÅÍ§áÊ´§ãËéàËç¹ÇèÒ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»·Ó§Ò¹ä´éäÁè´Õ àÁ× ÍÃÐººÁÕ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒÁÒ¡ ËÃ×ÍàÁ× Í·Ó§Ò¹ã¹ÃÐºº ·Õ µéÍ§¡ÒÃÍÑµÃÒ¡ÒÃÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ ä·ÁÁÔ § ÃÔ¤Ñ¿àÇÍÃÕ áºº·Õ ãªé ¡Ñ¹ ·Ñ Çä»¡ç ÂÑ§ à» ¹ ·Õ ¹ÔÂÁãªé §Ò¹¡Ñ¹ ÁÒ¡ã¹ à¡×Íº¨Ð·Ø¡§Ò¹»ÃÐÂØ¡µì à¹× Í§¨Ò¡à» ¹Ç§¨Ã·Õ §èÒÂµèÍ¡ÒÃÊÃéÒ§áÅÐÊÒÁÒÃ¶·Ó§Ò¹ä´é´Õà¾ÕÂ§¾Í ¶éÒàÅ×Í¡ ãªé¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ·Õ àËÁÒÐÊÁ ÃÇÁ·Ñ §ÃÐººÁÕ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒäÁèÁÒ¡¹Ñ¡ áÅÐÃÐºº äÁèÁÕ¤ÇÒÁµéÍ§¡ÒÃÍÑµÃÒ¡ÒÃÅÙèà¢éÒ·Õ ÃÇ´àÃçÇ

2.8

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§Í¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ» (PLL: phased lock loop) ÁÒ¾ÍÊÑ§à¢»

2. ¨§Í¸ÔºÒÂ¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ Ë¹Ö §

3. ¨§Í¸ÔºÒÂ¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì¢Í§Ç§¨Ã PLL ÍÑ¹´Ñº·Õ ÊÍ§

5. ¨§¤Ó¹Ç³ËÒÊÁ¡ÒÃàÊé¹â¤é§ ÃÙ» µÑÇ àÍÊ¢Í§Ç§¨Ã M&M TED áÅÐÇÒ´ÃÙ» ä·ÁÁÔ § ¿ §¡ìªÑ¹ ¢Í§ ªèÍ§ÊÑÒ³

H(D)

µèÍä»¹Õ

5.1)

H(D)

1−D

5.2)

H(D)

1+D

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

5.3)

H(D)

1 + 2D + D2

5.4)

H(D)

1 + D − D2 − D3

5.5)

H(D)

1 + 3D + 3D2 + D3

6. ¨§à»ÃÕÂºà·ÕÂºËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä»áÅÐä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº »ÃÐÁÒ³¤èÒã¹ªèÇ§ ÁÒ¾ÍÊÑ§à¢»

º··Õ 3

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµààÅÐÍÕ¤ÇÍäÅà«ÍÃì

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ (target) áÅÐÍÕ¤ÇÍäÅà«ÍÃì (equalizer) ãËé àËÁÒÐÊÁ ¡Ñº ªèÍ§ÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì â´Â·Õ ·ÒÃìà¡çµ·Õ ´Õ ¨ÐµéÍ§ÁÕ ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ·Õ ã¡Åéà¤ÕÂ§ ¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³ãËé ÁÒ¡·Õ ÊØ´ ã¹·Ò§»¯ÔºÑµÔ ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áÅÐ ÍÕ¤ÇÍäÅà«ÍÃì ÊÒÁÒÃ¶·Óä´é ËÅÒÂÇÔ¸Õ áµè ã¹º·¹Õ ¨Ð¡ÅèÒÇ¶Ö§ à©¾ÒÐÇÔ¸Õ¡ÒÃ ¢éÍ¼Ô´¾ÅÒ´¡ÓÅÑ§ ÊÍ§à©ÅÕ Â ·Õ ¹éÍÂÊØ´ (MMSE: minimum mean squared error) à·èÒ¹Ñ ¹ [19] à¹× Í§¨Ò¡ à» ¹ÇÔ¸Õ·Õ §èÒÂµèÍ¡ÒÃ¹Ó ä»ãªé §Ò¹¨ÃÔ§ ¾ÃéÍÁ·Ñ § à»ÃÕÂºà·ÕÂº¼Å¡ÒÃ·´ÅÍ§·Õ ä´é ¨Ò¡¡ÒÃãªé ·ÒÃìà¡çµ áººµèÒ§æ ã¹ªèÍ§ÊÑÒ³ ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

3.1

º·¹Ó

ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ (Viterbi detector) [15] ¨Ð¶Ù¡ ¹ÓÁÒãªé §Ò¹ÃèÇÁ¡Ñ¹ ¡Ñº ÍÕ¤ÇÍäÅà«ÍÃì áºº PR

(partial response equalizer) «Ö § ÍÕ¤ÇÍäÅà«ÍÃì

¹Õ ¡ç¤×Í Ç§¨Ã¡ÃÍ§áººàªÔ§àÊé¹ (linear lter) ·Õ ·ÓË¹éÒ·Õ ã¹¡ÒÃ»ÃÑºÃÙ»ÃèÒ§¢Í§¼ÅµÍºÊ¹Í§ÃÇÁ¢Í§ 1

ªèÍ§ÊÑÒ³ãËéÍÂÙèã¹ÃÙ»¢Í§¼ÅµÍºÊ¹Í§·Õ µéÍ§¡ÒÃ ËÃ×Í·Õ àÃÕÂ¡¡Ñ¹ÇèÒ ·ÒÃìà¡çµ 1

(target) ¨Ò¡¹Ñ ¹

·ÒÃìà¡çµ ¤×Í Ç§¨Ã¡ÃÍ§áººàªÔ§ àÊé¹ ·Õ ÁÕ ¨Ó¹Ç¹á·ç» (tap) ¹éÍÂ àÁ× Í à·ÕÂº¡Ñº ¨Ó¹Ç¹á·ç» ¢Í§ªèÍ§ÊÑÒ³ áµè ÁÕ ¼Å

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¡ç ¨Ð¹ÓàÍÒ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ÁÒ·Ó¡ÒÃµÃÇ¨ËÒÅÓ´Ñº (sequence detection) áºº¤ÇÃ¨Ðà» ¹ ÁÒ¡ÊØ´ (ML: maximum likelihood) à¾× Í ¤Ó¹Ç³ËÒÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ ·Õ Êè§ ÁÒ¨Ò¡Ç§¨ÃÀÒ¤Êè§ ¢Ñ ¹µÍ¹·Ñ § 2 ¹Õ ÃÇÁàÃÕÂ¡¡Ñ¹ ÇèÒ à·¤¹Ô¤ ¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹¤ÇÃ¨Ðà» ¹ ÁÒ¡ÊØ´ (PRML: partial response maximum likelihood) «Ö § ¶×Í ÇèÒ à» ¹ ËÑÇã¨ÊÓ¤Ñ ¢Í§ÃÐºº¡ÒÃ »ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìã¹» ¨¨ØºÑ¹ ·ÒÃìà¡çµáºº PR ·Õ à» ¹·Õ ÂÍÁÃÑº¡Ñ¹ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ (longitudinal recording) ¨ÐÍÂÙèã¹ÃÙ»¢Í§¾ËØ¹ÒÁ (polynomial)

H(D) = (1 − D)(1 + D)n â´Â·Õ

¤×Í àÅ¢¨Ó¹Ç¹àµçÁºÇ¡ áÅÐ

(3.1)

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃË¹èÇ§àÇÅÒ (delay operator) ¨Ò¡ÊÁ¡ÒÃ

(3.1) ¨Ð¾ºÇèÒ ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ¹Õ ¨ÐÁÕÊà»¡µÃÑÁ¤èÒÈÙ¹Âì (spectral null) ³ ¤ÇÒÁ¶Õ ¤èÒÈÙ¹ÂìáÅÐ¤ÇÒÁ¶Õ ä¹¤ÇÔµÊì (Nyquist frequency) à¹× Í§¨Ò¡ ÁÕ¾¨¹ì·Õ à» ¹

(1−D)

áÅÐ

(1+D)

µÒÁ

ÅÓ´Ñº ã¹¢³Ð·Õ ÊÑÒ³ read back ¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § (perpendicular recording) ¨ÐÁÕÍ§¤ì»ÃÐ¡Íº¢Í§ä¿¿ Ò¡ÃÐáÊµÃ§ (d.c. component) ´Ñ§¹Ñ ¹ ¾¨¹ì

(1 − D)

¨Ö§äÁè¨Óà» ¹ÊÓËÃÑº

ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § à¾ÃÒÐ©Ð¹Ñ ¹ ·ÒÃìà¡çµ áºº PR ·Õ à» ¹ ·Õ ÂÍÁÃÑº ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡ áºº á¹ÇµÑ § ¨ÐÍÂÙèã¹ÃÙ»¢Í§¾ËØ¹ÒÁ

H(D) = (1 + D)n

(3.2)

µÒÃÒ§·Õ 3.1 áÊ´§·ÒÃìà¡çµ áºº PR ·Õ à» ¹ ·Õ ÂÍÁÃÑº ¡Ñ¹ ·Ñ Çä» ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ áÅÐáººá¹ÇµÑ § áÅÐÃÙ»·Õ 3.1 áÊ´§¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµáººµèÒ§æ àÁ× Íà»ÃÕÂºà·ÕÂº ¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³·Õ ND = 2 áÅÐ 2.5 ¨Ò¡ÃÙ» ·Õ 3.1 ¨Ð¾ºÇèÒ àÁ× Í ¤èÒ ND ¢Í§ªèÍ§ÊÑÒ³ÁÕ ¤èÒ à¾Ô Á ¢Ö ¹ ·ÒÃìà¡çµ·Õ ãªé ¡ç ¤ÇÃ·Õ ¨ÐÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡¢Ö ¹ (¤èÒ

ÁÒ¡¢Ö ¹)

à¾× Í·Õ ¨Ð·ÓãËé ÁÕ ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ·Õ ÊÍ´¤ÅéÍ§¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³ãËé ÁÒ¡·Õ ÊØ´ ÍÂèÒ§äÃ¡çµÒÁ ·ÒÃìà¡çµ·Õ ãªé äÁè ¤ÇÃ·Õ ¨ÐÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡à¡Ô¹ ¤ÇÒÁ¨Óà» ¹ à¾ÃÒÐ¨ÐÊè§ ¼Å·Ó ãËéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕ¤ÇÒÁ«Ñº«éÍ¹ (complexity) ÁÒ¡¢Ö ¹ «Ö §¨ÐÍ¸ÔºÒÂµèÍä»ã¹º··Õ 4 ¨Ò¡ÊÁ¡ÒÃ (3.1) áÅÐ (3.2) ÊÑ§à¡µ¨Ð¾ºÇèÒ·ÒÃìà¡çµáºº PR ¨ÐÁÕ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§áµèÅÐá·ç» à» ¹àÅ¢¨Ó¹Ç¹àµçÁ áµè¶éÒÃÐºº PRML ÂÍÁãªé·ÒÃìà¡çµ·Õ ÁÕ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§áµèÅÐá·ç»à» ¹àÅ¢¨Ó¹Ç¹ ¨ÃÔ§¨Ð¾ºÇèÒ·ÒÃìà¡çµáºº¹Õ ¨ÐÊÒÁÒÃ¶ªèÇÂà¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐººä´é ÁÒ¡ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §

3.1.

º·¹Ó

µÒÃÒ§·Õ 3.1: µÑÇÍÂèÒ§·ÒÃìà¡çµáºº PR ·Õ à» ¹·Õ ÂÍÁÃÑº¡Ñ¹ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

n=1

·ÒÃìà¡çµáºº PR ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹

PR4

n=2

[1 0 − 1]

1 − D2 ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §

PR1

EPR4

n=3

[1 1 − 1 − 1]

1 + D − D2 − D3

[1 1]

PR2

[1 2 1]

[1 2 0 − 2 − 1]

1 + 2D − 2D3 − D4 EPR2

1 + 2D + D2

1+D

EEPR4

[1 3 3 1]

1 + 3D + 3D2 + D3

·Õ ND ÊÙ§æ â´Â·ÒÃìà¡çµ ÅÑ¡É³Ð¹Õ ¨ÐàÃÕÂ¡¡Ñ¹ ·Ñ Çä»ÇèÒ ·ÒÃìà¡çµáºº GPR (generalized partial response) «Ö §ÊÒÁÒÃ¶·Õ ¨ÐËÒä´é¨Ò¡ËÅÒÂÇÔ¸Õ¡ÒÃ àªè¹ [41, 42, 43, 44, 45, 46]

1) ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ â´ÂãËé ¼ÅµÍºÊ¹Í§·ÒÃìà¡çµ (target response) ÁÕ ÃÙ»ÃèÒ§àËÁ×Í¹¡Ñº ¼Å µÍºÊ¹Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð (transition response) ËÃ×Í¼ÅµÍºÊ¹Í§ä´ºÔµ (dibit response) ¢Í§ªèÍ§ÊÑÒ³ ·Ñ §ã¹â´àÁ¹àÇÅÒ (time domain) áÅÐâ´àÁ¹¤ÇÒÁ¶Õ (frequency domain) ÇÔ¸Õ¡ÒÃ¹Õ ¨Ð·Ó¡ÒÃËÒ·ÒÃìà¡çµ·Õ ÁÕÃÙ»ÃèÒ§¢Í§¼ÅµÍºÊ¹Í§·ÒÃìà¡çµàËÁ×Í¹¡Ñº¼ÅµÍºÊ¹Í§ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐËÃ×Í ¼ÅµÍºÊ¹Í§ä´ºÔµ¢Í§ªèÍ§ÊÑÒ³áµèÅÐ ND ·Ñ § ã¹â´àÁ¹àÇÅÒáÅÐ â´àÁ¹¤ÇÒÁ¶Õ µÑÇÍÂèÒ§àªè¹ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ·ÒÃìà¡çµ·Õ ÊÍ´¤ÅéÍ§¡Ñº¼ÅµÍºÊ¹Í§ ä´ºÔµ [43] ã¹â´àÁ¹àÇÅÒ ä´éá¡è [1

−4

1], [1

−2 −2

1], áÅÐ [1 0

−8

0 1] à» ¹µé¹

¹Í¡¨Ò¡¹Õ ·ÒÃìà¡çµ ºÒ§áººÍÒ¨¨ÐäÁè ÊÍ´¤ÅéÍ§¡Ñº ¼ÅµÍºÊ¹Í§¢Í§ªèÍ§ÊÑÒ³ã¹â´àÁ¹ àÇÅÒ áµè¨ÐÊÍ´¤ÅéÍ§¡Ñº¼ÅµÍºÊ¹Í§¢Í§ªèÍ§ÊÑÒ³ã¹â´àÁ¹¤ÇÒÁ¶Õ ÁÒ¡¡çä´é ã¹·Ò§»¯ÔºÑµÔ ¤ÇÒÁÊÍ´¤ÅéÍ§¡Ñº ¼ÅµÍºÊ¹Í§¢Í§ªèÍ§ÊÑÒ³ã¹â´àÁ¹¤ÇÒÁ¶Õ à» ¹ ÊÔ § ·Õ µéÍ§¡ÒÃÁÒ¡¡ÇèÒ ¤ÇÒÁÊÍ´¤ÅéÍ§ã¹â´àÁ¹àÇÅÒ à¹× Í§¨Ò¡ ¨ÐªèÇÂºÍ¡ãËé ·ÃÒº¶Ö§ ¤Ø³ÊÁºÑµÔ à¡Õ ÂÇ¡Ñº ÍÑµÃÒ¡ÒÃ ¢ÂÒÂÊÑÒ³Ãº¡Ç¹ (noise enhancement) ä´é

2) ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ·Õ ·ÓãËé ¡ÓÅÑ§ ÃÇÁ¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ ÇÔ¸Õ¡ÒÃ¹Õ ¨ÐÊÁÁØµÔ ÇèÒ ¹Ñ¡ÍÍ¡áººÃÐºº·ÃÒºÇèÒ ªèÍ§ÊÑÒ³¤×Í ÍÐäÃ à¾× Í·Õ ¨Ðä´é ¹ÓàÍÒ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

1.2

Channel (ND = 2) Channel (ND = 2.5) PR4 [1 0 −1] EPR4 [1 1 −1 −1] EEPR4 [1 2 0 −2 −1]

Normalized magnitude

1.0

0.8

0.6

0.4

0.2

0.0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

(a) Normalized frequency (fT) 1.0

Channel (ND = 2) Channel (ND = 2.5) PR2 [1 2 1] EPR2 [1 3 3 1] EEPR2 [1 4 6 4 1]

Normalized magnitude

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

(b) Normalized frequency (fT)

ÃÙ»·Õ 3.1: ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµáººµèÒ§æ ÊÓËÃÑºÃÐºººÑ¹·Ö¡ (a) áººá¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ §

ªèÍ§ÊÑÒ³¹Ñ ¹ ÁÒãªé ã¹¡ÒÃ¤Ó¹Ç³ËÒ¿ §¡ìªÑ¹ ¶èÒÂâÍ¹¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ¨Ò¡¹Ñ ¹ ¡ç ¨Ð·Ó¡ÒÃ ¤Ó¹Ç³ËÒ¡ÓÅÑ§ ÃÇÁ¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃì áÅÐàÁ× Í ä´é ¡ÓÅÑ§ ÃÇÁ

3.2.

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ÍÂÙè ã¹ÃÙ» ¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃì áÅéÇ ¡ç ¨Ð·Ó¡ÒÃËÒ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§·ÒÃìà¡çµ ·Õ ·ÓãËé ¡ÓÅÑ§ ÃÇÁ¢Í§ÊÑÒ³Ãº¡Ç¹ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ â´Âãªé à·¤¹Ô¤ ¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì (di erentiation) ÊÓËÃÑºÃÒÂÅÐàÍÕÂ´¢Í§ÇÔ¸Õ¡ÒÃ¹Õ ÊÒÁÒÃ¶ÈÖ¡ÉÒà¾Ô ÁàµÔÁä´é¨Ò¡ [41]

3) ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ·Õ ·ÓãËé ¤èÒ SNR »ÃÐÊÔ·¸Ô¼Å (e ective SNR) ·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨Ã µÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕ¤èÒÁÒ¡·Õ ÊØ´ ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áººµèÒ§æ µÒÁ·Õ ¡ÅèÒÇÁÒ¢éÒ§µé¹ ¹Õ äÁè ä´é ÃÑº»ÃÐ¡Ñ¹ ÇèÒ »ÃÐÊÔ·¸Ô ÀÒ¾ÃÇÁ¢Í§ÃÐººã¹ÃÙ» ¢Í§ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´ºÔµ (BER: bit error rate) ·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ ã¹ [19, 42] ä´é àÊ¹ÍÇÔ¸Õ¡ÒÃËÒ ·ÒÃìà¡çµ·Õ àËÁÒÐ·Õ ÊØ´ (optimal target) ·Õ ¨Ð·ÓãËé ¤èÒ SNR »ÃÐÊÔ·¸Ô¼Å·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÕ ¤èÒ ÁÒ¡·Õ ÊØ´ ËÃ×ÍÍÕ¡¹ÑÂË¹Ö §¡ç¤×Í ·ÒÃìà¡çµ·Õ ·ÓãËé BER ¢Í§ÃÐºº àÁ× ÍÇÑ´·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨Ã µÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ ÊÓËÃÑº¼ÙéÊ¹ã¨ÊÒÁÒÃ¶ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´à¾Ô ÁàµÔÁä´éã¹ [19, 42]

4) ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ·Õ ·ÓãËé¢éÍ¼Ô´¾ÅÒ´¡ÓÅÑ§ÊÍ§à©ÅÕ Â (MSE: mean squared error) ÃÐËÇèÒ§ ÊÑÒ³·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃìáÅÐÊÑÒ³·Õ µéÍ§¡ÒÃ (¹Ñ ¹¤×Í ÊÑÒ³µÒÁ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ) ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ ¨Ò¡¡ÒÃÈÖ¡ÉÒ¾ºÇèÒ ÇÔ¸Õ¡ÒÃ¹Õ à» ¹ ÇÔ¸Õ¡ÒÃ·Õ §èÒÂáÅÐàËÁÒÐÊÓËÃÑº ¡ÒÃ¹ÓÁÒãªé §Ò¹¨ÃÔ§ ã¹ ·Ò§»¯ÔºÑµÔ [19] ¹Í¡¨Ò¡¹Õ ·ÒÃìà¡çµ·Õ ä´é ¨ÐÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ã¡Åéà¤ÕÂ§¡Ñº ·ÒÃìà¡çµ ·Õ àËÁÒÐ·Õ ÊØ´ ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áºº¹Õ ¨ÐÃÙé¨Ñ¡ ¡Ñ¹ ã¹ª× Í ÇèÒ ÇÔ¸Õ¡ÒÃ ¢éÍ¼Ô´¾ÅÒ´¡ÓÅÑ§ ÊÍ§à©ÅÕ Â ·Õ ¹éÍÂ ÊØ´ (MMSE: minimum mean squared error) «Ö §¨ÐÍ¸ÔºÒÂÃÒÂÅÐàÍÕÂ´ÇÔ¸Õ¡ÒÃ¹Õ ´Ñ§µèÍä»¹Õ

3.2

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE [19] ¨Ð·ÓãËéäé´é·ÒÃìà¡çµËÅÒÂÃÙ»áººµÒÁà§× Í¹ä¢ºÑ§¤Ñº (con straint) ·Õ ¡ÓË¹´Å§ä»ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃÍÍ¡áºº ãËé¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ÃÐººã¹ÃÙ»·Õ 3.2 â´Â ·Õ ÍÕ¤ÇÍäÅà«ÍÃì¨Ð¾ÂÒÂÒÁÊÃéÒ§¢éÍÁÙÅàÍÒµì¾Øµ

ãËéÁÕ¤èÒã¡Åéà¤ÕÂ§¡Ñº¢éÍÁÙÅ·Õ µéÍ§¡ÒÃ

ãËéÁÒ¡·Õ ÊØ´

N = 2K +1

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

n(t) equalizer

1 − D bk g(t) {±1} 2

p(t)

∆t k

s(t)

LPF

F(D)

t k = kT

y k Viterbi âk detector

target

H(D)

ÃÙ»·Õ 3.2: áºº¨ÓÅÍ§ÊÓËÃÑº¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

á·ç» áÅÐÊÁÁØµÔ ãËé á·ç» ÈÙ¹Âì¡ÅÒ§ÍÂÙè ·Õ àÇÅÒ ÍÂÙèã¹ÃÙ»ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìã¹â´àÁ¹

k =0

à¾ÃÒÐ©Ð¹Ñ ¹ ÍÕ¤ÇÍäÅà«ÍÃì ÊÒÁÒÃ¶·Õ ¨Ðà¢ÕÂ¹ãËé

ä´é ¤×Í

K X

F (D) =

fk Dk

(3.3)

k=−K àÁ× Í

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃË¹èÇ§àÇÅÒ

H(D) =

L−1 X

ä´é ¤×Í

hk Dk

(3.4)

k=0 â´Â·Õ

áÅÐ

à» ¹¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ·Õ à» ¹àÅ¢¨Ó¹Ç¹¨ÃÔ§ã¹áµèÅÐá·ç»¢Í§ÍÕ¤ÇÍäÅà«ÍÃìáÅÐ·ÒÃìà¡çµ

µÒÁÅÓ´Ñº ¨Ø´»ÃÐÊ§¤ì ã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ´éÇÂÇÔ¸Õ¡ÒÃ MMSE ¤×Í ¨Ð·Ó¡ÒÃ¤Ó¹Ç³ËÒ¤èÒ ÊÑÁ»ÃÐ ÊÔ·¸Ô ¢Í§

F (D)

áÅÐ

H(D) yk

àÍÒµì¾Øµ ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô

and

ä» ¾ÃéÍÁ¡Ñ¹ ã¹ àÇÅÒ à´ÕÂÇ¡Ñ¹ â´Â ¡ÒÃ ·Ó ãËé ¤èÒ MSE ÃÐËÇèÒ§ ¢éÍÁÙÅ

áÅÐ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§·ÒÃìà¡çµ

ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ ËÃ×Í ÍÕ¡ ¹ÑÂ Ë¹Ö § ¤×Í

¨Ð¶Ù¡àÅ×Í¡ à¾× Í·Õ ·ÓãËé¤èÒ

£ ¤ £ ¤ E wk2 = E {(sk ∗ fk ) − (ak ∗ hk )}2 ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ àÁ× Í

yk − rk

¤×Í ¢éÍ¼Ô´¾ÅÒ´·Õ ä´é¨Ò¡¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ,

¤Í¹âÇÅÙªÑ¹ (convolution operator), áÅÐ tor)

E[·]

(3.5)

∗

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ¤èÒ¤Ò´ËÁÒÂ (expectation opera

3.2.

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

¶éÒ¡ÓË¹´ãËéàÇ¡àµÍÃìá¹ÇµÑ § â´Â·Õ

and

[h0 , h1 , · · · , hL−1 ]T

¤×Í ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§

H(D)

áÅÐ

F (D)

and

¢éÍÁÙÅ

sk , A

¤×Í àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì¢¹Ò´

áÅÐá¹ÇµÑ §·Õ

K = 10

[·]T

¤×Í à¤Ã× Í§ËÁÒÂ

(ÍÕ¤ÇÍäÅà«ÍÃìÁÕ·Ñ §ËÁ´ 21

¤×Í àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì (auto correlation matrix) ¢¹Ò´

¢éÒÁ (cross correlation matrix) ¢¹Ò´ ·Õ

[f−K , · · · , f0 , · · · , fK ]T

µÒÁÅÓ´Ñº, áÅÐ

àÁ·ÃÔ¡«ìÊÅÑºà»ÅÕ Â¹ (transpose matrix) ã¹º·¹Õ ¨Ð¡ÓË¹´ãËé á·ç») ¶éÒ¡ÓË¹´ãËé

L×L

N ×L

¢Í§¢éÍÁÙÅ

ÃÐËÇèÒ§¢éÍÁÙÅ

ak ,

áÅÐ

N ×N

¢Í§

¤×Í àÁ·ÃÔ¡«ìÊËÊÑÁ¾Ñ¹¸ì

â´Â·Õ ÊÁÒªÔ¡

(i, j)

(á¶Ç

¢Í§àÁ·ÃÔ¡«ì·Ñ §ÊÒÁ¹Õ ¤×Í

R(i, j) = E

"S−1 X

# sk+K−i sk+K−j ,

k=0

A(i, j) = E P(i, j) = E

"S−1 X k=0 "S−1 X

−K ≤ i, j ≤ K

(3.6)

# ak−i ak−j ,

0 ≤ i, j ≤ L − 1

(3.7)

# sk+K−i ak−j ,

−K ≤ i ≤ K, 0 ≤ j ≤ L − 1

(3.8)

k=0

àÁ× Í

¤×Í ¤ÇÒÁÂÒÇ (ËÃ×Í¨Ó¹Ç¹ºÔµ) ¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak }

¨Ò¡µÑÇá»Ã·Õ ¡ÓË¹´ãËé¢éÒ§µé¹¹Õ ÊÁ¡ÒÃ (3.5) ÊÒÁÒÃ¶·Õ ¨Ðà¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§àÁ·ÃÔ¡«ìä´é ´Ñ§¹Õ

E[w2 ] = FT RF + HT AH − 2FT PH ã¹¡ÒÃ·ÓãËé¤èÒ

E[w2 ]

ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´â´Âà·ÕÂº¡Ñº

áÅÐ

(3.9)

¨ÐµéÍ§ÁÕ¡ÒÃ¡ÓË¹´à§× Í¹ä¢ºÑ§¤Ñºà¢éÒä»

ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ·ÓãËé ÁÕ ¤èÒ ¹éÍÂÊØ´ (minimization process) à¾× Í·Õ ¨ÐËÅÕ¡àÅÕ Â§¡ÒÃä´é ¼ÅÅÑ¾¸ì à» ¹

F=0

áÅÐ

3.2.1

áÅÐ

H=0

´Ñ§µèÍä»¹Õ

à§× Í¹ä¢ºÑ§¤ÑºààººâÁ¹Ô¡ (h0

= 1)

à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡ (monic constraint) ¨Ð¡ÓË¹´ãËé¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§á·ç»µÑÇáÃ¡¢Í§·ÒÃìà¡çµ ÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § ¹Ñ ¹¤×Í

h0 = 1

[19] ¶éÒ¡ÓË¹´ãËéàÇ¡àµÍÃìá¹ÇµÑ §

áÃ¡ÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § ÊèÇ¹ÊÁÒªÔ¡µÑÇÍ× ¹æ ÁÕ¤èÒà·èÒ¡Ñº¤èÒÈÙ¹Âì ¡ÅèÒÇ¤×Í à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡¹Õ ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§àÁ·ÃÔ¡«ìä´é ¤×Í

¢¹Ò´

L×1

·Õ ÁÕÊÁÒªÔ¡µÑÇ

[1, 0, · · · , 0]T

IT H = 1

´Ñ§¹Ñ ¹

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ´éÇÂÇÔ¸Õ¡ÒÃ¹Õ ¤×Í ¡ÒÃ·ÓãËé ¤èÒ MSE ã¹ÊÁ¡ÒÃ (3.9) ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ â´Â¾ÂÒÂÒÁÃÑ¡ÉÒãËé¤èÒ

IT H

ÍÂÙèµÅÍ´àÇÅÒ ¹Ñ ¹¤×Í ¡ÃÐºÇ¹¡ÒÃ¹Õ ¨Ð·ÓãËé¤èÒ

E[w2 ] = FT RF + HT AH − 2FT PH − 2λ(IT H − 1) ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ â´Â·Õ

(3.10)

¤×Í µÑÇ¤Ù³ ÅÒ¡ÃÒ¹¨ì (Lagrange multiplier) à» ¹¤èÒÊà¡ÅÒÃì (scalar) ¡ÒÃ

·ÓãËé ÊÁ¡ÒÃ (3.10) ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ ÊÒÁÒÃ¶·Óä´é â´Â¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì (di erentiation) ¢Í§ÊÁ¡ÒÃ (3.10) à·ÕÂº¡Ñº F, H, áÅÐ

µÒÁÅÓ´Ñº «Ö §¨Ðä´é¼ÅÅÑ¾¸ì´Ñ§¹Õ (ÃÒÂÅÐàÍÕÂ´ã¹ÀÒ¤¼¹Ç¡ ¤)

¡ ¢ ∂ E[w2 ] ¡ ∂F ¢ ∂ E[w2 ] ¡ ∂H ¢ ∂ E[w2 ] ∂λ

= 2RF − 2PH

(3.11)

= 2AH − 2PT F − 2λI

(3.12)

= −2IT H + 2

(3.13)

¨Ò¡¹Ñ ¹¡ç¡ÓË¹´ãËé ¼ÅÅÑ¾¸ì ¢Í§Í¹Ø¾Ñ¹¸ì ·Ñ §ËÁ´·Õ ä´é ¨Ò¡ÊÁ¡ÒÃ (3.11) (3.13) ÁÕ ¤èÒ à» ¹ ¤èÒ ÈÙ¹Âì ¹Ñ ¹¤×Í ¡ÓË¹´ãËéÊÁ¡ÒÃ (3.11) ÁÕ¤èÒà·èÒ¡Ñº¤èÒÈÙ¹Âì ¨Ðä´éÇèÒ

2RF − 2PH = 0 RF = PH F = R−1 PH

(3.14)

áÅÐ¡ÓË¹´ãËéÊÁ¡ÒÃ (3.12) ÁÕ¤èÒà·èÒ¡Ñº¤èÒÈÙ¹Âì ¨Ðä´éÇèÒ

2AH − 2PT F − 2λI = 0 AH − PT F = λI á·¹¤èÒ

(3.15)

¨Ò¡ÊÁ¡ÒÃ (3.14) Å§ã¹ÊÁ¡ÒÃ (3.15) ¨Ðä´é

¡ ¢ AH − PT R−1 PH = λI ¡ ¢ A − PT R−1 P H = λI ¡ ¢−1 I H = λ A − PT R−1 P

(3.16)

3.2.

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ¡ÓË¹´ãËéÊÁ¡ÒÃ (3.13) ÁÕ¤èÒà·èÒ¡Ñº¤èÒÈÙ¹Âì ¨Ðä´éÇèÒ

−2IT H + 2 = 0 IT H = 1 á·¹¤èÒ

(3.17)

¨Ò¡ÊÁ¡ÒÃ (3.16) Å§ã¹ÊÁ¡ÒÃ (3.17) ¨Ðä´é

¡ ¢−1 IT λ A − PT R−1 P I = 1 λ =

IT (A

1 − P R−1 P)−1 I T

(3.18)

à¾ÃÒÐ©Ð¹Ñ ¹â´ÂÊÃØ»áÅéÇ ¢Ñ ¹µÍ¹ã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃìÊÓËÃÑºà§× Í¹ä¢ºÑ§¤Ñºààºº âÁ¹Ô¡ (h0

= 1)

¤×Í

1) ¡ÓË¹´¨Ó¹Ç¹á·ç»¢Í§·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì (¤èÒ

áÅÐ

¹Ñ ¹¤×ÍÊÃéèÒ§àÇ¡àµÍÃì F áÅÐ

2) ËÒ¤èÒàÁ·ÃÔ¡«ì R, A, áÅÐ P ¨Ò¡ÊÁ¡ÒÃ (3.6) (3.8)

3) ÊÃéÒ§àÇ¡àµÍÃì I =

[1, 0, · · · , 0]T

4) ËÒ¤èÒµÑÇ¤Ù³ÅÒ¡ÃÒ¹¨ì

¢¹Ò´

¨Ò¡ÊÁ¡ÒÃ (3.18) ¹Ñ ¹¤×Í

1 − P R−1 P)−1 I

(3.19)

H = λ(A − PT R−1 P)−1 I

(3.20)

λ=

5) ËÒ¤èÒ·ÒÃìà¡çµ

L×1

IT (A

¨Ò¡ÊÁ¡ÒÃ (3.16) ¹Ñ ¹¤×Í

6) ËÒ¤èÒÍÕ¤ÇÍäÅà«ÍÃì

¨Ò¡ÊÁ¡ÒÃ (3.14) ¹Ñ ¹¤×Í

F = R−1 PH

(3.21)

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¤èÒ

·Õ ä´é¨Ò¡ÊÁ¡ÒÃ (3.19) à» ¹¤èÒ MMSE ·Õ ä´éÀÒÂãµéà§× Í¹ä¢ºÑ§¤Ñº¹Õ «Ö §ÊÒÁÒÃ¶¾ÔÊÙ¨¹ìä´éâ´Â

¡ÒÃá·¹¤èÒ F and H ¨Ò¡ÊÁ¡ÒÃ (3.20) (3.21) Å§ã¹ÊÁ¡ÒÃ (3.9) ¹Ñ ¹¤×Í

E[w2 ] = (R−1 PH)T R(R−1 PH) + HT AH − 2(R−1 PH)T PH = HT PT (R−1 )T PH + HT AH − 2HT PT (R−1 )T PH = HT (A − PT R−1 P)H © ª = λ2 [IT (A − PT R−1 P)−1 ]T (A − PT R−1 P)(A − PT R−1 P)−1 I © ª = λ2 IT (A − PT R−1 P)−1 I = λ

(3.22)

ÊÁ¡ÒÃ (3.22) ËÒä´éâ´ÂÍÒÈÑÂËÅÑ¡¤ÇÒÁ¨ÃÔ§·Õ ÇèÒ àÁ·ÃÔ¡«ì

áÅÐ

à» ¹àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ìáºº 2

ÊÁÁÒµÃ ¹Í¡¨Ò¡¹Õ àÁ·ÃÔ¡«ì R, A áÅÐ P ÂÑ§à» ¹àÁ·ÃÔ¡«ìáºº Toeplitz =

R−1

3.2.2

áÅÐ

£ ¤T (A − PT R−1 P)−1

à§× Í¹ä¢ºÑ§¤Ñºààºº

à§× Í¹ä¢ºÑ§¤Ñºáºº ¹Ñ ¹¤×Í

h1 = 1

«Ö §¨Ð·ÓãËéä´éÇèÒ

(R−1 )T

(A − PT R−1 P)−1

h1 = 1

h1 = 1 ¨Ð¡ÓË¹´ãËé¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§á·ç»µÑÇÊÍ§¢Í§·ÒÃìà¡çµÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö §

[19] ÊèÇ¹¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§á·ç» µÑÇ Í× ¹æ ¨Ðà» ¹ ¤èÒ ÍÐäÃ¡çä´é â´Âà§× Í¹ä¢ºÑ§¤Ñº ¹Õ ÁÕ

ÇÑµ¶Ø»ÃÐÊ§¤ìà¾× Íãªéã¹¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§·ÒÃìà¡çµáººµèÒ§æ ¶éÒ¡ÓË¹´ãËéàÇ¡àµÍÃìá¹Ç

µÑ §

¢¹Ò´

L×1

·Õ ÊÁÒªÔ¡µÑÇ·Õ ÊÍ§ÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § ÊèÇ¹ÊÁÒªÔ¡Í× ¹æ ÁÕ¤èÒà» ¹¤èÒÈÙ¹Âì ¡ÅèÒÇ¤×Í

[0, 1, 0, · · · , 0]T

´Ñ§¹Ñ ¹ à§× Í¹ä¢ºÑ§¤Ñº áºº

h1 = 1

ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè ã¹ÃÙ» ¢Í§àÁ·ÃÔ¡«ì ä´é

JT H = 1

¤×Í

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµâ´Âà§× Í¹ä¢ºÑ§¤Ñº¹Õ ¨ÐàËÁ×Í¹¡Ñº¡ÒÃÍÍ¡áºº·ÒÃìà¡çµâ´Âãªé à§× Í¹ä¢ºÑ§¤Ñº áººâÁ¹Ô¡ à¾ÕÂ§áµè à»ÅÕ Â¹¾¨¹ì ÊØ´·éÒÂã¹ÊÁ¡ÒÃ (3.10) ¨Ò¡

2λ(JT H − 1) à» ¹àÇ¡àµÍÃì 2

2λ(IT H − 1)

ä»à» ¹

´Ñ§¹Ñ ¹ ¼ÅÅÑ¾¸ì·Õ ä´é¡ç¨ÐàËÁ×Í¹¡ÑºÊÁ¡ÒÃ (3.19) (3.21) à¾ÕÂ§áµèà»ÅÕ Â¹àÇ¡àµÍÃì

àÁ·ÃÔ¡«ìáºº Toeplitz ¤×Í àÁ·ÃÔ¡«ì·Õ ÊÁÒªÔ¡ã¹á¹ÇàÊé¹·áÂ§ÁØÁà» ¹¤èÒ¤§·Õ ¤èÒà´ÕÂÇ¡Ñ¹

3.2.

¡ÒÃÍÍ¡ààºº·ÒÃìà¡çµ´éÇÂÇÔ¸Õ¡ÒÃ MMSE

3.2.3

à§× Í¹ä¢ºÑ§¤Ñºààºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ (H

H = 1)

à§× Í¹ä¢ºÑ§¤Ñº áºº¾ÅÑ§§Ò¹Ë¹Ö § Ë¹èÇÂ (unit energy) ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè ã¹ÃÙ» ¢Í§àÁ·ÃÔ¡«ì ä´é ¤×Í

HT H

«Ö §à» ¹¡ÒÃ¡ÓË¹´ãËé¾ÅÑ§§Ò¹¢Í§·ÒÃìà¡çµÁÕ¤èÒà·èÒ¡Ñº¤èÒË¹Ö § [19, 46]

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ´éÇÂÇÔ¸Õ¡ÒÃ¹Õ ¤×Í ¡ÒÃ·ÓãËé ¤èÒ MSE ã¹ÊÁ¡ÒÃ (3.9) ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ â´Â·Õ ¾ÂÒÂÒÁÃÑ¡ÉÒãËé¤èÒ

HT H

µÅÍ´àÇÅÒ ¡ÅèÒÇ¤×Í ¡ÃÐºÇ¹¡ÒÃ¹Õ ¨Ð·ÓãËé¤èÒ

E[w2 ] = FT RF + HT AH − 2FT PH − 2λ(HT H − 1) ÁÕ¤èÒµ ÓÊØ´ «Ö §ÊÒÁÒÃ¶·Óä´éâ´Â¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì¢Í§ÊÁ¡ÒÃ (3.23) à·ÕÂº¡Ñº F, H, áÅÐ

(3.23)

µÒÁÅÓ´Ñº

áÅéÇ ¡ÓË¹´ãËé ¼ÅÅÑ¾¸ì ¢Í§Í¹Ø¾Ñ¹¸ì ·Ñ §ËÁ´·Õ ä´é ÁÕ ¤èÒ à» ¹ ¤èÒ ÈÙ¹Âì â´ÂàÁ× Í ·ÓµÒÁ¢Ñ ¹µÍ¹¹Õ áÅéÇ ¨Ð¾º ÇèÒ ·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì ÊÒÁÒÃ¶ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ

(A − PT R−1 P)H = λH

(3.24)

«Ö §¡ÒÃá¡éÊÁ¡ÒÃ¹Õ ÁÕÅÑ¡É³Ð¤ÅéÒÂ¡Ñº ¡ÒÃá¡é» ËÒ¤èÒÅÑ¡É³Ðà©¾ÒÐ (eigenvalue problem) [12, 25] â´Â·Õ ¤èÒ (3.24) ¤èÒ

ã¹ÊÁ¡ÒÃ (3.24) ÊÒÁÒÃ¶¾ÔÊÙ¨¹ìä´éÇèÒ ¤×Í ¤èÒ MMSE ¹Ñ ¹àÍ§ ´Ñ§¹Ñ ¹ ¨Ò¡ÊÁ¡ÒÃ

¨ÃÔ§æ áÅéÇ ¡ç ¤×Í ¤èÒ ÅÑ¡É³Ðà©¾ÒÐ·Õ ¹éÍÂ·Õ ÊØ´ (minimum eigenvalue) ¢Í§àÁ·ÃÔ¡«ì

(A − PT R−1 P), H

¤×Í àÇ¡àµÍÃì ÅÑ¡É³Ðà©¾ÒÐáºº¹ÍÃì ÁÍÅäÅ«ì(normalized eigenvector) ·Õ

ÊÍ´¤ÅéÍ§¡Ñº¤èÒÅÑ¡É³Ðà©¾ÒÐ·Õ ¹éÍÂ·Õ ÊØ´, áÅÐ

3.2.4

¨ÐÁÕ¤èÒàËÁ×Í¹¡ÑºÊÁ¡ÒÃ (3.21)

à§× Í¹ä¢ºÑ§¤Ñºààºº·ÒÃìà¡çµà©¾ÒÐ

ÊÓËÃÑº à§× Í¹ä¢ºÑ§¤Ñº áºº·ÒÃìà¡çµ à©¾ÒÐ¹Õ ( xed target) ·ÒÃìà¡çµ¨Ð¶Ù¡ ¡ÓË¹´ÁÒãËé µÑ §áµè àÃÔ ÁáÃ¡ ÊÔ § ·Õ ÃÐººµéÍ§¡ÒÃ ¤×Í ÍÕ¤ÇÍäÅà«ÍÃì

·Õ àËÁÒÐÊÁ¡Ñº ·ÒÃìà¡çµ ·Õ ¡ÓË¹´ÁÒãËé «Ö § ÊÒÁÒÃ¶ËÒä´é ¨Ò¡

ÊÁ¡ÒÃ (3.21) ¹Ñ ¹¤×Í

F = R−1 PG

(3.25)

â´Â¨ÐÃÑº»ÃÐ¡Ñ¹ä´éÇèÒ¤èÒ MMSE ·Õ ä´é¨ÐÁÕ¤èÒà·èÒ¡Ñº¤èÒã¹ÊÁ¡ÒÃ (3.9) ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáºº¹Õ ÁÕ»ÃÐâÂª¹ìÁÒ¡ à¹× Í§¨Ò¡ã¹¡ÒÃãªé§Ò¹¨ÃÔ§ ªÔ»»ÃÐÁÇÅ¼ÅÊÑÒ³ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ¨Ð¶Ù¡ ÍÍ¡áººÁÒãËé ãªé §Ò¹¡Ñº ·ÒÃìà¡çµ áººã´áººË¹Ö § à·èÒ¹Ñ ¹ ´Ñ§¹Ñ ¹ ¼Ùéãªé §Ò¹

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¨ÐµéÍ§¾ÂÒÂÒÁ»ÃÑº¤èÒÊÑÁ»ÃÐÊÔ·¸Ô áµèÅÐá·ç»¢Í§ÍÕ¤ÇÍäÅà«ÍÃìãËéÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ·Õ ¡ÓË¹´ÁÒãËé à¾× ÍãËé ä´é ÊÑÒ³·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃìé ÁÕ ÃÙ»ÃèÒ§àËÁ×Í¹¡Ñº ÊÑÒ³·Õ µéÍ§¡ÒÃ «Ö § ¨ÐªèÇÂ·Ó ãËé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Ó§Ò¹ä´é §èÒÂ¢Ö ¹ ã¹·Ò§µÃ§¡Ñ¹¢éÒÁ ¶éÒ ·Ó¡ÒÃ»ÃÑº ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô áµèÅÐá·ç» ¢Í§ÍÕ¤ÇÍäÅà«ÍÃìáººÅÍ§¼Ô´ÅÍ§¶Ù¡ (trial and error) ¡ç¨Ð·ÓãËéàÊÕÂàÇÅÒÁÒ¡ áÅÐÍÕ¤ÇÍäÅà«ÍÃì·Õ ä´é ¡çÁÑ¡¨ÐäÁèÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ·Õ ¡ÓË¹´ÁÒãËé

ËÁÒÂàËµØ

ã¹¡ÒÃËÒ·ÒÃìà¡çµ H ¨Ò¡ÊÁ¡ÒÃ (3.20) áÅÐÍÕ¤ÇÍäÅà«ÍÃì

¨Ò¡ÊÁ¡ÒÃ (3.21) ¢Ñ ¹µÍ¹

áÃ¡·Õ ¤ÇÃ·Ó ¤×Í ¡ÒÃËÒ¤èÒ àÁ·ÃÔ¡«ì R, A, áÅÐ P «Ö § àÁ·ÃÔ¡«ì ·Ñ § ÊÒÁ¹Õ ÊÒÁÒÃ¶ËÒä´é §èÒÂã¹·Ò§ »¯ÔºÑµÔ ¡ÅèÒÇ¤×Í ¨Ò¡áºº¨ÓÅÍ§·Õ ãªé ã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ µÒÁÃÙ» ·Õ 3.2 ãËé ·Ó¡ÒÃÊè§ ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

{ak }

¨Ó¹Ç¹Ë¹Ö §à«¡àµÍÃì (sector) ËÃ×Í 4096 ºÔµ à¢éÒä»ã¹ÃÐºº à¾× Í·Ó¡ÒÃà¢ÕÂ¹¢éÍÁÙÅÅ§

ä»ã¹Ê× ÍºÑ¹·Ö¡ (¹Ñ ¹¤×Í ¼Ùéãªé·ÃÒºá¹è¹Í¹ÇèÒ

{ak }

¤×ÍÍÐäÃ) ¨Ò¡¹Ñ ¹ ¡çãËéËÑÇÍèÒ¹·Ó¡ÒÃÍèÒ¹¢éÍÁÙÅ

¨Ò¡Ê× Í ºÑ¹·Ö¡ áÅéÇ Êè§ ÊÑÒ³ read back ·Õ ä´é ¼èÒ¹ä»ÂÑ§ Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó áÅÐÇ§¨ÃªÑ¡ µÑÇÍÂèÒ§ ·Ó ãËéä´é¼ÅÅÑ¾¸ìà» ¹ÅÓ´Ñº¢éÍÁÙÅ à¾ÃÒÐ©Ð¹Ñ ¹ àÁ× Íä´é¢éÍÁÙÅ

{sk }

{ak }

«Ö §ã¹·Ò§»¯ÔºÑµÔ ¼ÙéãªéÊÒÁÒÃ¶·Õ ¨Ð·ÃÒºä´éÇèÒ¢éÍÁÙÅ

áÅÐ

{sk }

¤×ÍÍÐäÃ

áÅéÇ ¡ç·Ó¡ÒÃ¤Ó¹Ç³ËÒ¤èÒàÁ·ÃÔ¡«ì R, A, áÅÐ P â´Â

ãªéâ»Ãá¡ÃÁ MATLAB [13] ËÃ×Í SCILAB [14] ¨ÐàËç¹ä´éÇèÒ ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáºº MMSE ÊÒÁÒÃ¶·Óä´é§èÒÂã¹·Ò§»¯ÔºÑµÔ àÁ× Íà·ÕÂº¡ÑºÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáººÍ× ¹æ

3.3

¼Å¡ÒÃ·´ÅÍ§

·Õ 3.2 ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ §

¨Ò¡ÃÙ» ·Õ 3.2 ÊÑÒ³ read back ·Õ ä´é ¨Ò¡ËÑÇÍèÒ¹

ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ¤³ÔµÈÒÊµÃìä´é ¤×Í [40]

p(t) =

S−1 X

bk g(t − kT + ∆tk ) + n(t)

(3.26)

k=0

¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áººµèÒ§æ ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ ÊÒÁÒÃ¶ÈÖ¡ÉÒ

ÃÒÂÅÐàÍÕÂ´ä´éã¹ [19]

3.3.

¼Å¡ÒÃ·´ÅÍ§

â´Â·Õ

bk = (ak − ak−1 )/2

Ê¶Ò¹ÐºÇ¡ËÃ×ÍÅº áÅÐ ºÔµµÑÇ·Õ

¤×Í ºÔµà»ÅÕ Â¹Ê¶Ò¹Ð (àÁ× Í

bk = 0

∆t

¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § µÒÁÊÁ¡ÒÃ·Õ (1.2),

n(t)

ÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹á»Å§

ËÁÒÂ¶Ö§ äÁèÁÕ¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹Ð),

·Õ ÁÕ¨Ó¹Ç¹·Ñ §ËÁ´ 4096 ºÔµ (1 à«¡àµÍÃì),

a jitter noise), áÅÐ

bk = ±1

ak ∈ ±1

¤×Í ¢éÍÁÙÅÍÔ¹¾Øµ

g(t) ¤×Í ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð¢Í§ÃÐºº

¤×Í ÊÑÒ³Ãº¡Ç¹¨Ôµ àµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ (medi

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN) ·Õ ÁÕ ¤ÇÒÁË¹Òá¹è¹

Êà»¡µÃÑÁ ¡ÓÅÑ§áººÊÍ§´éÒ¹à·èÒ ¡Ñº

N0 /2

ã¹Ë¹Ñ§Ê×Í àÅèÁ ¹Õ ÊÑÒ³Ãº¡Ç¹¨Ôµ àµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡

¨Ð¶Ù¡ ¨ÓÅÍ§ãËé ÁÕ ÅÑ¡É³Ðà» ¹ ¡ÒÃàÅ× Í¹µÓáË¹è§ ¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐáººÊØèÁ (random transi tion shift) «Ö §ÁÕ¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹áººà¡ÒÊìà«ÕÂ¹ (Gaussian probability den sity function) ·Õ ÁÕ ¤èÒà©ÅÕ Â à·èÒ ¡Ñº ¤èÒ ÈÙ¹Âì áÅÐ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ ¡Ñº

N (0, |bk |σj2 ))

áÅÐ¶Ù¡¨Ó¡Ñ´ãËéÁÕ¤èÒäÁèà¡Ô¹

¤×Í ¤èÒÊÑÁºÙÃ³ì¢Í§

à«ÅÅì

áÅÐ

|bk |

ÊÑÒ³ read back,

p(t),

T /2)

àÁ× Í

σj

|bk |σj2

(¹Ñ ¹¤×Í

∆tk ∼

¨Ð¶Ù¡¡ÓË¹´à» ¹¨Ó¹Ç¹à»ÍÃìà«ç¹µì¢Í§ºÔµ

¨Ð¶Ù¡ Êè§ ¼èÒ¹ä»ÂÑ§ Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó ºÑµà·ÍÃìàÇÔÃìµ (Butterworth)

ÍÑ¹´Ñº·Õ 7 áÅÐ¨Ð·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§ÊÑÒ³

p(t)

´éÇÂÍÑµÃÒ¤ÇÒÁ¶Õ à·èÒ¡Ñº

1/T

(¹Ñ ¹¤×Í ¢éÍÁÙÅá«Á

à» ÅáµèÅÐá«Áà» Å·Õ ä´é¨Ò¡¡ÒÃªÑ¡µÑÇÍÂèÒ§¨ÐÍÂÙèËèÒ§¡Ñ¹ 1 ºÔµà«ÅÅì) â´Âã¹·Õ ¹Õ ¨ÐÊÁÁØµÔÇèÒ ¡ÃÐºÇ¹¡ÒÃ 4

à¢éÒ ¨Ñ§ËÇÐÃÐËÇèÒ§ÊÑÒ³ read back áÅÐÇ§¨ÃªÑ¡ µÑÇÍÂèÒ§ à» ¹ áººÊÁºÙÃ³ì nization) ¨Ò¡¹Ñ ¹ ÅÓ´Ñº¢éÍÁÙÅ

{sk }

(perfect synchro

µÒÁ·ÒÃìà¡çµ ·Õ ÃÐººµéÍ§¡ÒÃ áÅÐÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¡ç ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ ÅÓ´Ñº ¢éÍÁÙÅ ÅÓ´Ñº¢éÍÁÙÅ

{ak }

{yk }

à¾× Í ËÒ

·Õ à» ¹ä»ä´éÁÒ¡·Õ ÊØ´

ã¹¡ÒÃ·´ÅÍ§ ¨Ð¹ÔÂÒÁ Electronics SNR (ËÃ×ÍàÃÕÂ¡ÊÑ ¹æ ÇèÒ SNR) ãËéÁÕ¤èÒà·èÒ¡Ñº

µ SNR = 10 log10 â´Â·Õ

Vp = g(∞) = 1

pulse) ³ àÇÅÒ

∞

Vp 2 σ2

¶ (dB)

¤×Í ¢¹Ò´¢Í§ÊÑÒ³¾ÑÅÊì à»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È áÅÐ

σn2

N0 /(2T )

(3.27)

(isolated transition

¤×Í ¡ÓÅÑ§ ¢Í§ÊÑÒ³Ãº¡Ç¹

n(t)

¹Í¡¨Ò¡¹Õ

áµèÅÐ¨Ø´ ¢Í§ BER ¶Ù¡ ¤Ó¹Ç³â´Âãªé ¢éÍÁÙÅ ËÅÒÂæ à«¡àµÍÃì ¨¹¡ÇèÒ ¨Ðä´é ¢éÍ¼Ô´¾ÅÒ´ÃÇÁäÁè ¹éÍÂ¡ÇèÒ 1000 ºÔµ áÅÐ·ÒÃìà¡çµ áÅÐÍÕ¤ÇÍäÅà«ÍÃì ·Õ ãªé ¨Ð¶Ù¡ ÍÍ¡áººãËé àËÁÒÐÊÁ¡Ñº ¡ÒÃ·Ó§Ò¹ã¹áµèÅÐ ND 4

¹Ñ ¹¤×Í Ç§¨ÃªÑ¡µÑÇÍÂèÒ§·ÃÒºÇèÒ ¨Ð·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§ÊÑÒ³ read back ·Õ µÓáË¹è§ã´ à¾× ÍãËé¢éÍÁÙÅá«Áà» Å·Õ ä´éÍÍ¡

ÁÒÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ÊØ´

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

³ ÃÐ´Ñº BER =

µÑÇÍÂèÒ§·Õ 3.1

10−5

µÑÇÍÂèÒ§¹Õ ¨ÐáÊ´§¢Ñ ¹µÍ¹¡ÒÃ¤Ó¹Ç³ËÒ·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì µÒÁÊÁ¡ÒÃ (3.19)

(3.21) ãËé¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §ã¹ÃÙ»·Õ 3.2 ÊÓËÃÑº ND = 1.5 áÅÐ S NR = 20 dB ¶éÒ¡ÓË¹´ãËéÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ ¢Òà¢éÒ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ·Õ ÊÍ´¤ÅéÍ§¡Ñº

{ak }

¤×Í

{1,

{sk }

1, 1,

−1,

−1}

áÅÐÅÓ´Ñº¢éÍÁÙÅ´éÒ¹

{−0.5337, −0.0662,

0.8821, 0.8122,

0.3219, 0.0260} ¨§¤Ó¹Ç³ËÒ·ÒÃìà¡çµáºº GPR ¢¹Ò´ 3 á·ç» áÅÐÍÕ¤ÇÍäÅà«ÍÃì¢¹Ò´ 5 á·ç» ·Õ ÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ µÒÁà§× Í¹ä¢ºÑ§¤Ñº ´Ñ§µèÍä»¹Õ ¡) à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡

¢) à§× Í¹ä¢ºÑ§¤Ñºáºº

h0 = 1

h1 = 1

¤) à§× Í¹ä¢ºÑ§¤Ñºáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ

§) à§× Í¹ä¢ºÑ§¤Ñºáºº·ÒÃìà¡çµà©¾ÒÐ àÁ× Í¡ÓË¹´ãËé ÇÔ¸Õ ·Ó

H(D) = 1 + 2D + D2

¢Ñ ¹µÍ¹áÃ¡ã¹¡ÒÃËÒ·ÒÃìà¡çµ áÅÐÍÕ¤ÇÍäÅà«ÍÃì ¤×Í ¡ÒÃËÒ¤èÒ àÁ·ÃÔ¡«ì R, A, áÅÐ P µÒÁ

ÊÁ¡ÒÃ (3.6) (3.8) àÁ× Í

S = 6, K = 2,

áÅÐ

L=3

«Ö § ¨Ò¡¡ÒÃ¤Ó¹Ç³¨Ðä´éÇèÒ àÁ·ÃÔ¡«ì

ÁÕ¤èÒà·èÒ¡Ñº



 0.3052

0.1926

−0.0549 −0.1440 −0.0868

1.0000

−0.2000

     0.1926 0.3052 0.1926 −0.0549 −0.1440      R =  −0.0549 0.1926 0.3052 0.1926 −0.0549       −0.1440 −0.0549 0.1926 0.3052 0.1926    −0.0868 −0.1440 −0.0549 0.1926 0.3052 àÁ·ÃÔ¡«ì

ÁÕ¤èÒà·èÒ¡Ñº



 0.5000

    A =  −0.2000 1.0000 −0.2000    0.5000 −0.2000 1.0000

3.3.

¼Å¡ÒÃ·´ÅÍ§

áÅÐàÁ·ÃÔ¡«ì

ÁÕ¤èÒà·èÒ¡Ñº



 0.4976

0.3867

0.1740

   0.2664 0.4976 0.3867   P =  −0.0390 0.2664 0.4976    −0.1983 −0.0390 0.2664  −0.0994 −0.1983 −0.0390 â´Âã¹·Õ ¹Õ ¨Ð¢ÍáÊ´§µÑÇÍÂèÒ§¡ÒÃ¤Ó¹Ç³ËÒÊÁÒªÔ¡ ËÒä´é¨Ò¡

A(i, j) = E

" 5 X

(i, j)

         

ºÒ§µÑÇ ¢Í§àÁ·ÃÔ¡«ì A ´Ñ§¹Õ àÁ·ÃÔ¡«ì A

# ak−i ak−j , 0 ≤ i, j ≤ 2

k=0

{ak } = {a0 , a1 , a2 , a3 , a4 , a5 } # " 5 X ak ak A(0, 0) = E

à¹× Í§¨Ò¡ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{1,

1, 1,

−1,

−1}

´Ñ§¹Ñ ¹

k=0

= E [a0 a0 + a1 a1 + a2 a2 + a3 a3 + a4 a4 + a5 a5 ] 1 = [(1)(1) + (1)(1) + (1)(1) + (−1)(−1) + (1)(1) + (−1)(−1)] 6 = 1 A(0, 1) = E

" 5 X

# ak ak−1

k=0

= E [a1 a0 + a2 a1 + a3 a2 + a4 a3 + a5 a4 ] 1 = [(1)(1) + (1)(1) + (−1)(1) + (1)(−1) + (−1)(1)] 5 = −0.2 A(0, 2) = E

" 5 X

# ak ak−2

k=0

= E [a2 a0 + a3 a1 + a4 a2 + a5 a3 ] 1 = [(1)(1) + (−1)(1) + (1)(1) + (−1)(−1)] 4 = 0.5

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊÓËÃÑº ÊÁÒªÔ¡ ¢Í§àÁ·ÃÔ¡«ìÍ× ¹æ ¡ç ÊÒÁÒÃ¶¤Ó¹Ç³ËÒä´é ã¹ÅÑ¡É³Ðà´ÕÂÇ¡Ñ¹ àÁ× Í ä´é àÁ·ÃÔ¡«ì R, A, áÅÐ P áÅéÇ áÅÐ¨Ò¡â¨·Âì¨Ðä´éÇèÒ

[h0 , h1 , h2 ]T

áÅÐ

[f−2 , f−1 , f0 , f1 , f2 ]T

à¾ÃÒÐ©Ð¹Ñ ¹

·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃìÊÒÁÒÃ¶ËÒ¤èÒä´éµÒÁÊÁ¡ÒÃ (3.19) (3.21) µÒÁà§× Í¹ä¢ºÑ§¤ÑºµèÒ§æ ´Ñ§¹Õ

¡) à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡

−0.8587]T ,

áÅÐ

¢) à§× Í¹ä¢ºÑ§¤Ñº áºº

−1.6613]T ,

áÅÐ

h0 = 1

[1, 0, 0]T , λ = −0.0837, H

¨Ðä´é ÇèÒ

[0, 1, 0]T , λ = −2.2814, H

[4.7796, 1,

[7.0507, 1.8111, −4.6115, 3.0835, −1.9107]T

¤) à§× Í¹ä¢ºÑ§¤Ñºáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ ¨Ðä´éÇèÒ¤èÒÅÑ¡É³Ðà©¾ÒÐ¢Í§àÁ·ÃÔ¡«ì ¤×Í

[1, 0.1754,

[1.0936, −0.0722, −0.9953, −0.2400, −0.0805]T

h1 = 1 F

¨Ðä´éÇèÒ

{1.5182, −0.0476, −1.0211}, H

[0.3843, 0.7335, 0.5607]T ,

(A − PT R−1 P)

áÅÐ

[1.7138,

1.1288, 0.0256, 1.5285, −0.6140]T §) à§× Í¹ä¢ºÑ§¤Ñºáºº·ÒÃìà¡çµà©¾ÒÐ àÁ× Í

[1, 2, 1]T

¨Ðä´éÇèÒ

[4.2431, 2.6064, 0.1106,

3.1983, −1.3164]T

ã¹¡ÒÃ·´ÅÍ§¹Õ ¨Ð·Ó¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áººµèÒ§æ ·Ñ § 5 áºº ¤×Í

1) ·ÒÃìà¡çµáºº PR1 ¹Ñ ¹¤×Í

2) ·ÒÃìà¡çµ PR2 ¹Ñ ¹¤×Í

H(D) = 1 + D

ËÃ×Íà¢ÕÂ¹á·¹´éÇÂ

H(D) = 1 + 2D + D2

3) ·ÒÃìà¡çµ·Õ ÍÍ¡áººµÒÁà§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡

4) ·ÒÃìà¡çµ·Õ ÍÍ¡áººµÒÁà§× Í¹ä¢ºÑ§¤Ñºáºº

[1, 1]

ËÃ×Íà¢ÕÂ¹á·¹´éÇÂ

[1, 2, 1]

h0 = 1

h1 = 1

5) ·ÒÃìà¡çµ·Õ ÍÍ¡áººµÒÁà§× Í¹ä¢ºÑ§¤Ñºáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ

ÃÙ» ·Õ 3.3 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµµèÒ§æ ÊÓËÃÑº ND = 2 â´Â·Õ ÃÐºº¨Ðãªé ·ÒÃìà¡çµáºº GPR ·Õ ÁÕ¨Ó¹Ç¹ 3 á·ç» «Ö Ö§ã¹·Õ ¹Õ ¨Ðä´éÇèÒ ·ÒÃìà¡çµáººâÁ¹Ô¡

h0 = 1

¤×Í

1 + 1.15D

3.3.

¼Å¡ÒÃ·´ÅÍ§

−1

PR1 [1 1] PR2 [1 2 1] h0 = 1 h1 = 1 Unit energy

−2

BER

−3

−4

−5

10 14

SNR (dB)

ÃÙ»·Õ 3.3: »ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» BER ¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµµèÒ§æ ÊÓËÃÑº ND = 2

0.48D2 ,

·ÒÃìà¡çµáºº

0.45 + 0.77D

h1 = 1

0.45D2

¤×Í

0.55 + D

0.55D2 ,

áÅÐ·ÒÃìà¡çµáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ ¤×Í

¨Ò¡ÃÙ»·Õ 3.3 ¨ÐàËç¹ä´éÇèÒ â´ÂÀÒ¾ÃÇÁáÅéÇÃÐºº·Õ ãªé·ÒÃìà¡çµáºº GPR

¨ÐÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÃÐºº·Õ ãªé·ÒÃìà¡çµáºº PR áÅÐÃÐºº·Õ ãªé·ÒÃìà¡çµáººâÁ¹Ô¡¨ÐãËé»ÃÐÊÔ·¸ÔÀÒ¾ ´Õ·Õ ÊØ´ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §·Õ ND ÊÙ§æ à¾× Íà» ¹¡ÒÃÂ×¹ÂÑ¹ÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒ·ÒÃìà¡çµáºº PR ¨Ð·Ó¡ÒÃà»ÃÕÂº à·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ND = 2.5 áµè ¤ÃÒÇ¹Õ ¨Ðãªé ·ÒÃìà¡çµ áºº GPR ·Õ ÁÕ ¨Ó¹Ç¹ 5 á·ç» (¨Ó¹Ç¹á·ç»ÁÒ¡¢Ö ¹ à¾× ÍÃÍ§ÃÑº ND ·Õ à¾Ô Á¢Ö ¹) «Ö §ã¹¡Ã³Õ¹Õ ¨Ðä´éÇèÒ ·ÒÃìà¡çµáººâÁ¹Ô¡

1 + 1.42D + 1.06D2 + 0.43D3 + 0.08D4 , 0.53D3 + 0.14D4 , 0.2D4

·ÒÃìà¡çµáºº

áÅÐ·ÒÃìà¡çµáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ ¤×Í

h1 = 1

¤×Í

h0 = 1

¤×Í

0.47 + D + 0.96D2 +

0.20 + 0.5D + 0.66D2 + 0.5D3 +

ÃÙ» ·Õ 3.4 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµµèÒ§æ ·Õ ND = 2.5 ¨Ò¡¼ÅÅÑ¾¸ì ·Õ

ä´é¨Ð¾ºÇèÒ ÃÐºº·Õ ãªé·ÒÃìà¡çµáºº

h0 = 1

¨ÐãËé»ÃÐÊÔ·¸ÔÀÒ¾´Õ·Õ ÊØ´ ·Ñ §¹Õ à» ¹à¾ÃÒÐÇèÒ ·ÒÃìà¡çµáºº

GPR (â´Âà©¾ÒÐÍÂèÒ§ÂÔ § ·ÒÃìà¡çµáººâÁ¹Ô¡

h0 = 1)

¨ÐÁÕ ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ã¡Åéà¤ÕÂ§¡Ñº ¼Å

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

−1

PR1 [1 1] PR2 [1 2 1] h0 = 1 h1 = 1 Unit energy

−2

BER

−3

−4

−5

10 19.0

19.5

20.0

20.5

21.0

21.5

22.0

SNR (dB)

ÃÙ»·Õ 3.4: »ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» BER ¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµµèÒ§æ ·Õ ND = 2.5

µÍºÊ¹Í§¢Í§ªèÍ§ÊÑÒ³ÁÒ¡¡ÇèÒ·ÒÃìà¡çµáºº PR ´Ñ§áÊ´§ã¹ÃÙ»·Õ 3.5 ¹Í¡¨Ò¡¹Õ ·ÒÃìà¡çµ áºº GPR ÁÕ á¹Çâ¹éÁ ·Õ ¨ÐªèÇÂ·ÓãËé Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹ ¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇ (white noise) «Ö §à» ¹¢éÍ¡ÓË¹´ ËÅÑ¡·Õ ¨ÐªèÇÂ·ÓãËéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ÊØ´ [15] ¡ÒÃµÃÇ¨ ÊÍºÊÑÒ³Ãº¡Ç¹

ÇèÒÁÕ¤Ø³ÊÁºÑµÔà» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇËÃ×ÍäÁè ·Óä´éâ´Â¡ÒÃËÒ¤èÒÍÑµÊË

ÊÑÁ¾Ñ¹¸ì (auto correlation) ¢Í§ÅÓ´Ñº¢éÍÁÙÅ

{wk }

(´ÙÃÙ»·Õ 3.2) ¶éÒ¼ÅÅÑ¾¸ì·Õ ä´éÁÕ¤èÒà©¾ÒÐµÓáË¹è§

·Õ ¼ÅµèÒ§¢Í§àÇÅÒÁÕ¤èÒà·èÒ¡Ñº¤èÒÈÙ¹Âì áÅÐÁÕ¤èÒÈÙ¹Âì (ËÃ×Í¤èÒã¡ÅéÈÙ¹Âì) àÁ× Í¼ÅµèÒ§¢Í§àÇÅÒÁÕ¤èÒà» ¹¤èÒ Í× ¹æ ¨ÐÊÃØ» ä´é ÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ ÊÑÁ¾Ñ¹¸ì ¢Í§ÅÓ´Ñº ¢éÍÁÙÅ

{wk }

ÃÐºº·Õ ãªé·ÒÃìà¡çµáººâÁ¹Ô¡

ÁÕ ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹ÊÕ ¢ÒÇ ÃÙ» ·Õ 3.6 áÊ´§¤èÒ ÍÑµÊË

ÊÓËÃÑº ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áººµèÒ§æ ·Õ ND = 2.5 ¨Ò¡ÃÙ» ¨Ð¾ºÇèÒ

h0 = 1

¨ÐÁÕ¼Å·ÓãËéÍ§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇÁÒ¡·Õ ÊØ´ àÁ× Íà·ÕÂº¡Ñº·ÒÃìà¡çµáººÍ× ¹æ à¹× Í§¨Ò¡ ·ÒÃìà¡çµáººâÁ¹Ô¡

h0 = 1

ãËé »ÃÐÊÔ·¸ÔÀÒ¾´Õ ·Õ ÊØ´ àÁ× Í à»ÃÕÂºà·ÕÂº¡Ñº ·ÒÃìà¡çµ áºº

3.3.

¼Å¡ÒÃ·´ÅÍ§

1.0

Channel ND=2.5 PR1 [1 1] PR2 [1 2 1] h0 = 1 h1 = 1

0.9

Normalized magnitude

0.8 0.7

Unit energy 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Normalized frequency (fT)

ÃÙ»·Õ 3.5: ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµáººµèÒ§æ à·ÕÂº¡ÑºªèÍ§ÊÑÒ³·Õ ND = 2.5

GPR Í× ¹æ ã¹ÊèÇ¹µèÍä»¹Õ ÊÑÅÑ¡É³ì GPRn ¨Ð¶Ù¡ãªéá·¹·ÒÃìà¡çµáººâÁ¹Ô¡

h0 = 1

·Õ ÁÕ¨Ó¹Ç¹

á·ç» ÃÙ» ·Õ 3.7(a) à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§·ÒÃìà¡çµ áººµèÒ§æ ·Õ ND µèÒ§æ ÊÓËÃÑº ¡Ã³Õ ·Õ

äÁèÁÕÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡ (σj /T µéÍ§¡ÒÃà¾× Í·Õ ¨Ð·ÓãËéä´é BER =

10−4

= 0%)

â´Â·Õ àÊé¹á¡¹

áÊ´§ SNR ·Õ ÃÐºº

´Ñ§¹Ñ ¹ ÃÐºº·Õ ãªé SNR ¹éÍÂ¡ÇèÒ¡çáÊ´§ÇèÒÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ

¡ÇèÒ ¨Ò¡ÃÙ»¨ÐàËç¹ä´éÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒ·ÒÃìà¡çµáºº PR â´Âà©¾ÒÐÍÂèÒ§ÂÔ § ·Õ ND ÊÙ§æ ·Ñ §¹Õ à» ¹à¾ÃÒÐÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ã¡Åéà¤ÕÂ§¡ÑºªèÍ§ÊÑÒ³ ÁÒ¡¡ÇèÒ·ÒÃìà¡çµáºº PR (´ÙÃÙ»·Õ 3.5) ÃÙ»·Õ 3.7(b) à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§·ÒÃìà¡çµáººµèÒ§æ ·Õ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§

σj /T

µèÒ§æ

ÊÓËÃÑº ND = 2.5 ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹¨Ðä´éÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒ (µéÍ§¡ÒÃ S NR ¹éÍÂ¡ÇèÒ à¾× ÍãËéä´é BER =

10−4

à·èÒ¡Ñ¹) ·ÒÃìà¡çµáºº PR ³ ·Ø¡ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§

σj /T

ÊÑ§à¡µ¨Ð¾ºÇèÒ ·ÒÃìà¡çµáºº PR2 µéÍ§¡ÒÃ SNR ¹éÍÂ¡ÇèÒ (ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒ) ·ÒÃìà¡çµáºº EPR2 áÅÐ EEPR2 àÁ× Í ¤ÇÒÁÃØ¹áÃ§¢Í§

σj /T

ÁÕ ¤èÒ ÁÒ¡ ·Ñ §¹Õ ÍÒ¨¨Ðà» ¹ à¾ÃÒÐÇèÒ ·ÒÃìà¡çµ áºº PR ·Õ ÁÕ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

1.2

PR1 [1 1] PR2 [1 2 1] Monic (h0 = 1) h1 = 1 Unit energy

1.0

Normalized amplitude

0.8

0.6

0.4

0.2

0.0

−0.2

−0.4

−0.6 0

Time difference (in bit period)

ÃÙ»·Õ 3.6: ÍÑµÊËÊÑÁ¾Ñ¹¸ì¢Í§ÅÓ´Ñº¢éÍÁÙÅ

{wk }

ÊÓËÃÑºÃÐºº·Õ ·ÒÃìà¡çµáººµèÒ§æ ·Õ ND = 2.5

¨Ó¹Ç¹á·ç» ¹éÍÂ¨ÐÁÕ ¤ÇÒÁÍèÍ¹äËÇ (sensitive) ¡Ñº ÊÑÒ³Ãº¡Ç¹¨Ôµ àµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ ¹éÍÂ¡ÇèÒ ·ÒÃìà¡çµ áºº PR ·Õ ÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡ ã¹·Ò§µÃ§¡Ñ¹¢éÒÁ ·ÒÃìà¡çµáºº GPR ¨ÐãËé »ÃÐÊÔ·¸ÔÀÒ¾·Õ ´Õ ¢Ö ¹àÊÁÍ àÁ× Í ·ÒÃìà¡çµ·Õ ãªéÁÕ¨Ó¹Ç¹á·ç»ÁÒ¡¢Ö ¹ â´ÂäÁè¤Ó¹Ö§¶Ö§ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§

3.4

σj /T

ÊÃØ»·éÒÂº·

·ÒÃìà¡çµáºº GPR ãËé »ÃÐÊÔ·¸ÔÀÒ¾´Õ ¡ÇèÒ ·ÒÃìà¡çµ áºº PR â´Âà©¾ÒÐÍÂèÒ§ÂÔ § ·Õ ND ÊÙ§æ ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ã¡Åéà¤ÕÂ§¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ ÊÑÒ³ÁÒ¡¡ÇèÒ ·ÒÃìà¡çµ áºº PR ¹Í¡¨Ò¡¹Õ ·ÒÃìà¡çµáºº GPR ÂÑ§ ÁÕ á¹Çâ¹éÁ ·Õ ¨ÐªèÇÂ·ÓãËé Í§¤ì »ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÕ ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹ÊÕ ¢ÒÇ «Ö §Êè§¼Å·ÓãËéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡ÂÔ §¢Ö ¹ ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áÅÐÍÕ¤ÇÍäÅà«ÍÃì ÊÒÁÒÃ¶·Óä´é ËÅÒÂÇÔ¸Õ¡ÒÃ áµè ã¹·Ò§»¯ÔºÑµÔ ¨Ð¾ºÇèÒ¡ÒÃ

3.4.

ÊÃØ»·éÒÂº·

ND 2 2.5 3

SNR required to achieve BER = 10

−4

in dB

5−tap GPR targets [1 1.14 0.58 0.16 0.03] [1 1.34 0.99 0.43 0.09] [1 1.44 1.31 0.74 0.22]

PR2 [1 2 1] EPR2 [1 3 3 1] EEPR2 [1 4 6 4 1] GPR5

2.1

2.2

2.3

(a)

2.4

2.5

2.6

2.7

2.8

2.9

Normalized density (ND)

SNR required to achieve BER = 10−4 in dB

Jitter (%) 0 3 6 9

[1 [1 [1 [1

5−tap GPR targets 1.34 0.99 0.43 0.09] 1.33 0.94 0.36 0.06] 1.27 0.72 0.13 −0.03] 1.02 0.15 −0.16 −0.01]

PR2 [1 2 1] EPR2 [1 3 3 1] EEPR2 [1 4 6 4 1] GPR5

(b)

ÃÙ»·Õ 3.7: (a) ¡ÃÒ¿ÃÐËÇèÒ§ SNR ·Õ µéÍ§¡ÒÃ áÅÐ ND àÁ× Í ·Õ µéÍ§¡ÒÃ áÅÐ

σj

·Õ ND = 2.5

Jitter (%)

σj = 0%

áÅÐ (b) ¡ÃÒ¿ÃÐËÇèÒ§ SNR

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÍÍ¡áºº·ÒÃìà¡çµ ´éÇÂÇÔ¸Õ¡ÒÃ MMSE ÊÒÁÒÃ¶·Óä´é §èÒÂ¡ÇèÒ ÇÔ¸Õ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áººÍ× ¹æ áÅÐ à¹× Í§¨Ò¡¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ´éÇÂÇÔ¸Õ¡ÒÃ MMSE ÁÕ à§× Í¹ä¢ºÑ§¤Ñº ËÅÒÂáºº áµè ¨Ò¡¡ÒÃ·´ÅÍ§¾º ÇèÒ ·ÒÃìà¡çµ·Õ ÍÍ¡áººâ´Âà§× Í¹ä¢ºÑ§¤Ñº áººâÁ¹Ô¡ ¨ÐãËé »ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒ ·ÒÃìà¡çµ ·Õ ÍÍ¡áººâ´Â à§× Í¹ä¢ºÑ§¤ÑºÍ× ¹ ¹Í¡¨Ò¡¹Õ ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ·Õ ´Õ¡ç¤ÇÃ·Õ ¨ÐÍÍ¡áºº·ÒÃìà¡çµãËéàËÁÒÐÊÁ¡ÑºÊÀÒ¾ áÇ´ÅéÍÁã¹¡ÒÃ·Ó§Ò¹¢Í§µÑÇªÔ»ªèÍ§ÊÑÒ³ÍèÒ¹ (read channel chip) àªè¹ ÍÍ¡áºº·ÒÃìà¡çµÊÓËÃÑº áµèÅÐ ND, SNR, áÅÐ

σj /T

à» ¹µé¹ à¾× Í·Õ ¨Ð·ÓãËé ä´é ·ÒÃìà¡çµ ·Õ ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ÊØ´ÀÒÂãµé

ÊÀÒ¾áÇ´ÅéÍÁ¡ÒÃ·Ó§Ò¹·Õ ¡ÓË¹´

3.5

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§¾ÔÊÙ¨¹ìÊÁ¡ÒÃ (3.9)

2. ¨§¾ÔÊÙ¨¹ìÊÁ¡ÒÃ (3.24)

3. ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§µÒÁÃÙ»·Õ 3.2 áµèà» ¹ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ (longitudinal record ing) ·Õ ND = 2 áÅÐ SNR = 20 dB ¶éÒ¡ÓË¹´ãËéÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ 1, 1} áÅÐÅÓ´Ñº¢éÍÁÙÅ´éÒ¹¢Òà¢éÒ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì·Õ ÊÍ´¤ÅéÍ§¡Ñº 0.6184,

−0.1537,

0.0469,

−0.2469,

{ak }

¤×Í

{1, −1,

{sk }

−1,

{0.0767,

0.2096} ¨§¤Ó¹Ç³ËÒ·ÒÃìà¡çµ áºº GPR ¢¹Ò´ 3

á·ç» áÅÐÍÕ¤ÇÍäÅà«ÍÃì¢¹Ò´ 5 á·ç» ·Õ ÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ µÒÁà§× Í¹ä¢ºÑ§¤ÑºµèÍä»¹Õ

¡) à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡ ¢) à§× Í¹ä¢ºÑ§¤Ñºáºº

h0 = 1

h1 = 1

¤) à§× Í¹ä¢ºÑ§¤Ñºáºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ §) à§× Í¹ä¢ºÑ§¤Ñºáºº·ÒÃìà¡çµà©¾ÒÐ àÁ× Í¡ÓË¹´ãËé

H(D) = 1 − D2

4. ¨§à¢ÕÂ¹â»Ãá¡ÃÁ´éÇÂÀÒÉÒ SCILAB ËÃ×Í MATLAB à¾× ÍÇÒ´ÃÙ»ÊÑÒ³¢Í§·ÒÃìà¡çµáºº [1

−4

1], [1

−2 −2

1], áÅÐ [1 0

−8

0 1] à¾× Í¾ÔÊÙ¨¹ìÇèÒ ·ÒÃìà¡çµàËÅèÒ¹Õ ÊÍ´¤ÅéÍ§¡Ñº¼Å

µÍºÊ¹Í§ä´ºÔµã¹â´àÁ¹àÇÅÒ¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §

º··Õ 4

Ç§¨ÃµÃÇ¨ËÒ PRML

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¾× ¹°Ò¹¡ÒÃ·Ó§Ò¹¢Í§à·¤¹Ô¤ ¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹¤ÇÃ¨Ðà» ¹ ÁÒ¡ÊØ´ (PRML: partial response maximum likelihood) [27] «Ö §à» ¹à·¤¹Ô¤ËÅÑ¡·Õ ãªéã¹¡ÒÃµÃÇ¨ËÒ¢éÍÁÙÅ¢Í§ÃÐºº ¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì â´Â¨Ðà¹é¹ ä»·Õ ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ (Viterbi algorithm) «Ö § ¶×Í ÇèÒ à» ¹ ÍÑÅ ¡ÍÃÔÖ ·ÖÁ ·Õ ãªé ã¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ·Õ ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ãªé ã¹ ÎÒÃì´´ÔÊ¡ìä´Ã¿ì» ¨¨ØºÑ¹

4.1

º·¹Ó

à» ¹ ·Õ ·ÃÒº¡Ñ¹ ÇèÒ àÁ× Í ¤ÇÒÁ¨Ø ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì à¾Ô Á ¢Ö ¹ ¼Å¡ÃÐ·º·Õ à¡Ô´ ¨Ò¡¡ÒÃá·Ã¡ÊÍ´ÃÐËÇèÒ§ ÊÑÅÑ¡É³ì (ISI) ¡ç¨ÐÂÔ §ÁÒ¡¢Ö ¹ ·ÓãËéäÁèÊÒÁÒÃ¶ãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒ¨Ø´ÊÙ§ÊØ´ (peak detector) ä´éÍÕ¡ µèÍä» ´Ñ§¹Ñ ¹ à¾× Í¨Ñ´¡ÒÃ¡Ñº ISI ¨Ó¹Ç¹ÁÒ¡àËÅèÒ¹Õ Ç§¨ÃµÃÇ¨ËÒ PRML [27] ¨Ö§ä´é¶Ù¡¾Ñ²¹ÒáÅÐ ¹ÓÁÒãªé§Ò¹ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì¨¹¶Ö§·Ø¡ÇÑ¹¹Õ â´Â·Ñ Çä» ¤ÓÇèÒ PRML ËÁÒÂ¶Ö§ à·¤¹Ô¤¡ÒÃãªé§Ò¹ÃèÇÁ ¡Ñ¹ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃìáºº PR áÅÐÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ µÒÁÃÙ»·Õ 4.1 «Ö §ÊÒÁÒÃ¶áºè§¢Ñ ¹µÍ¹¡ÒÃ ·Ó§Ò¹ÍÍ¡à» ¹ 2 ¢Ñ ¹µÍ¹ ¤×Í

1) »ÃÑºÃÙ»ÃèÒ§¢Í§ÊÑÒ³ãËéà» ¹ä»µÒÁ·ÒÃìà¡çµ·Õ µéÍ§¡ÒÃ

2) ¶Í´ÃËÑÊ¢éÍÁÙÅâ´ÂãªéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ·Õ ÊÃéÒ§¨Ò¡·ÒÃìà¡çµ·Õ ¡ÓË¹´äÇé 65

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

noise

{± 1}

receiving filter

channel

detector

equalizer

âk

target response

ÃÙ»·Õ 4.1: ËÅÑ¡¡ÒÃ¾× ¹°Ò¹¢Í§à·¤¹Ô¤ PRML

A( D)

N (D)

C (D)

F ( D)

detector

Â ( D )

ÃÙ»·Õ 4.2: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ

¢éÍ´Õ¢Í§¡ÒÃãªéà·¤¹Ô¤ PRML ¤×Í ÃÐºº¨Ðà¼ªÔ¡Ñº¡ÒÃ¢ÂÒÂÊÑÒ³Ãº¡Ç¹ (noise enhancement) ·Õ µ Ó áÅÐ¤ÇÒÁ«Ñº«éÍ¹¢Í§ÃÐºº¨Ð¹éÍÂÅ§ ã¹ÊèÇ¹µèÍä»¹Õ ¨ÐÍ¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ÍÕ¤ÇÍäÅà«ÍÃì áºº PR áÅÐÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔÍÂèÒ§ÅÐàÍÕÂ´

4.2

ÍÕ¤ÇÍäÅà«ÍÃì

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁè µèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ (equivalent discrete time chan nel model) µÒÁÃÙ» ·Õ 4.2 â´Â¢éÍÁÙÅ µèÒ§æ ¨ÐÍÂÙè ã¹â´àÁ¹

áÅÐÊÁÁØµÔ ãËé

N (D)

Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN) ¨Ò¡ÃÙ» ¨Ðä´é ÇèÒ ÊÑÒ³·Õ Ç§¨ÃÀÒ¤ÃÑº ä´é ÃÑº

à» ¹ ÊÑÒ³

P (D)

ÊÒÁÒÃ¶

à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃì ¤×Í

P (D) = A(D)C(D) + N (D)

(4.1)

4.2.

ÍÕ¤ÇÍäÅà«ÍÃì

â´Â·Ñ Çä»ªèÍ§ÊÑÒ³

C(D)

¨ÐÁÕ ÅÑ¡É³Ðà» ¹ Ç§¨Ã¡ÃÍ§·Õ ÁÕ ¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì ¨Ó¡Ñ´ (FIR:

nite impulse response) áÅÐÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡ (¡èÍ ãËé à¡Ô´ ISI ÁÒ¡) ¶éÒ äÁè ÁÕ ¡ÒÃãªé ÍÕ¤ÇÍäÅà«ÍÃì

F (D)

à¾× ÍÅ´¼Å¡ÃÐ·º¢Í§ ISI ãËé¹éÍÂÅ§ Ç§¨ÃµÃÇ¨ËÒ (detector) ·Õ ãªé¨ÐµéÍ§ÁÕ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡

à¾× Í ¨Ñ´¡ÒÃ¡Ñº ISI ¨Ó¹Ç¹ÁÒ¡ à¾ÃÒÐ©Ð¹Ñ ¹ à¾× Í Å´¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ ¨Ö§ ä´é ÁÕ ¡ÒÃ¹Ó ÍÕ¤ÇÍäÅà«ÍÃì ÁÒãªé §Ò¹ à¾× Í »ÃÑº ÃÙ»ÃèÒ§¢Í§ÊÑÒ³ãËé à» ¹ ä»µÒÁ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ (à» ¹ Ç§¨Ã¡ÃÍ§ áºº FIR ·Õ ÁÕ¨Ó¹Ç¹á·ç»¹éÍÂ) «Ö §¨ÐªèÇÂÅ´¼Å¡ÃÐ·º¢Í§ ISI ãËé¹éÍÂÅ§ä´é ÍÂèÒ§äÃ¡çµÒÁ ¡ÒÃ¹Ó ÍÕ¤ÇÍäÅà«ÍÃìÁÒãªé§Ò¹ÁÕ¢éÍàÊÕÂ ¤×Í (¶éÒÇÒ§ÍÕ¤ÇÍäÅà«ÍÃìäÇéËÅÑ§Ç§¨ÃªÑ¡µÑÇÍÂèÒ§) ¨Ð·ÓãËéà¡Ô´»ÃÔÁÒ³ Ë¹èÇ§àÇÅÒ (delay) ¨Ó¹Ç¹ÁÒ¡ã¹ä·ÁÁÔ §ÅÙ» ¡ÅèÒÇ¤×Í ¨Ó¹Ç¹á·ç»¢Í§ÍÕ¤ÇÍäÅà«ÍÃìÂÔ §ÁÒ¡ »ÃÔÁÒ³ Ë¹èÇ§àÇÅÒ¡ç¨ÐÂÔ §ÁÒ¡ «Ö §¨ÐÊè§¼Å·ÓãËéÍÑµÃÒ¡ÒÃÅÙèà¢éÒ (convergence rate) ¢Í§ÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ ªéÒÅ§ ·ÓãËéÇ§¨Ãà¿ÊÅçÍ¡ÅÙ» (PLL) äÁèÊÒÁÒÃ¶µÔ´µÒÁ¡ÒÃà»ÅÕ Â¹á»Å§à¿ÊáÅÐ¤ÇÒÁ¶Õ ¢Í§ÊÑÒ³ áÍ¹ÐÅçÍ¡·Õ ¨Ð·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§ä´é·Ñ¹ «Ö §ÍÒ¨¨ÐÊè§¼Å·ÓãËéÕà¡Ô´¡ÒÃÊÙàÊÕÂ¡ÃÐºÇ¹¡ÒÃà¢éÒ¨Ñ§ËÇÐä´é

4.2.1

ÍÕ¤ÇÍäÅà«ÍÃìààºº¼ÅµÍºÊ¹Í§àµçÁ

ÍÕ¤ÇÍäÅà«ÍÃìáºº¼ÅµÍºÊ¹Í§àµçÁ (full response equalizer) ËÁÒÂ¶Ö§ÍÕ¤ÇÍäÅà«ÍÃì·Õ ¨Ð·ÓãËé¢éÍÁÙÅ àÍÒµì¾Øµ·Õ ä´éÁÕ¤èÒà·èÒ¡Ñº ¢éÍÁÙÅÍÔ¹¾Øµ

A(D)

ºÇ¡¡ÑºÊÑÒ³Ãº¡Ç¹

W (D)

´Ñ§¹Ñ ¹ ¨Ò¡ÃÙ»·Õ 4.2 ¨Ð

ä´é ÇèÒ ÍÕ¤ÇÍäÅà«ÍÃì áºº¼ÅµÍºÊ¹Í§àµçÁ ¨ÐÁÕ ¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì (impulse response) ã¹â´àÁ¹

¤×Í

F (D) = áÅÐ¢éÍÁÙÅàÍÒµì¾Øµ

Y (D)

1 C(D)

(4.2)

¢Í§ÍÕ¤ÇÍäÅà«ÍÃì¹Õ ¤×Í

Y (D) = P (D)F (D) á·¹¤èÒ

F (D)

(4.3)

¨Ò¡ÊÁ¡ÒÃ (4.2) Å§ã¹ÊÁ¡ÒÃ (4.1) ¨Ðä´é

Y (D) = {A(D)C(D) + N (D)} = A(D) +

N (D) C(D) | {z } W (D)

1 C(D) (4.4)

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¹Ñ ¹¤×Í Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ¨Ðà¢éÒ ä»ã¹Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì (symbol detector) ¤×Í

W (D) = N (D)/C(D)

¶éÒ ÊÁÁØµÔ ÇèÒ

W (D)

ÁÕ ¤èÒ ¹éÍÂÁÒ¡ Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì ·Õ ãªé ¡ç

ÊÒÁÒÃ¶à» ¹ áºº§èÒÂæ ä´é àªè¹ Ç§¨ÃµÃÇ¨ËÒ¢Õ´ àÊé¹ áºè§ áººËÅÒÂÃÐ´Ñº (multi level threshold detector) à¾× Í ·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ

Y (D)

ÍÂèÒ§äÃ¡çµÒÁ ¢éÍàÊÕÂ ¢Í§¡ÒÃãªé ÍÕ¤ÇÍäÅà«ÍÃì áºº¼Å

µÍºÊ¹Í§àµçÁ ¡ç ¤×Í ÊÑÒ³Ãº¡Ç¹

W (D)

·Õ ËÅ§àËÅ×Í ÍÂÙè ÍÒ¨¨Ð¡èÍ ãËé à¡Ô´ »ÃÒ¡®¡ÒÃ³ì ¡ÒÃ¢ÂÒÂ

ÊÑÒ³Ãº¡Ç¹ ¹Ñ ¹¤×Í

W (D)

ÁÕ ¤èÒ à» ¹ ¤èÒ Í¹Ñ¹µì ¶éÒ ªèÍ§ÊÑÒ³

C(D)

ÁÕ Êà»¡µÃÑÁ ¤èÒ ÈÙ¹Âì

(spectral null) ·Õ ¤ÇÒÁ¶Õ ã´æ à¾ÃÒÐ©Ð¹Ñ ¹ ã¹·Ò§»¯ÔºÑµÔ ¨Ö§äÁè¹ÔÂÁ¹ÓÍÕ¤ÇÍäÅà«ÍÃìáºº¼ÅµÍºÊ¹Í§ àµçÁÁÒãªé§Ò¹ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

4.2.2

ÍÕ¤ÇÍäÅà«ÍÃìààºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹

ÍÕ¤ÇÍäÅà«ÍÃì áºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹ (partial response equalizer) ¤×Í ÍÕ¤ÇÍäÅà«ÍÃì ·Õ ÊÒÁÒÃ¶ à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìä´é´Ñ§¹Õ

F (D) =

â´Â·Õ

H(D)

H(D) C(D)

(4.5)

¤×Í ¼ÅµÍºÊ¹Í§·ÒÃìà¡çµ (target response) ·Õ µéÍ§¡ÒÃ áÅÐàÁ× Íá·¹¤èÒ

F (D)

¹Õ Å§

ã¹ÊÁ¡ÒÃ (4.3) ¨Ðä´é

H(D) C(D) H(D) = A(D)H(D) + N (D) | {z } C(D) | {z } wanted signal

Y (D) = {A(D)C(D) + N (D)}

(4.6)

W (D)

¹Ñ ¹¤×Í ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§ÍÕ¤ÇÍäÅà«ÍÃìáºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹¨Ð»ÃÐ¡Íºä»´éÇÂ ¢éÍÁÙÅ·Õ µéÍ§¡ÒÃ

A(D)H(D)

áÅÐÊÑÒ³Ãº¡Ç¹

W (D) = N (D)H(D)/C(D)

¨Ò¡ÊÁ¡ÒÃ (4.6) ¨ÐàËç¹ä´éÇèÒ

¢éÍÁÙÅ·Õ µéÍ§¡ÒÃ¨ÐÁÕ ISI á½§ÍÂÙè áµèà¹× Í§¨Ò¡ Ç§¨ÃÀÒ¤ÃÑº·ÃÒºÇèÒ ISI ¹Õ ¤×ÍÍÐäÃ (à¾ÃÒÐÇèÒà» ¹ ISI ·Õ à¡Ô´¨Ò¡·ÒÃìà¡çµ) ´Ñ§¹Ñ ¹ ISI ¹Õ ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡¨Ñ´¡ÒÃä´é´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ «Ö §¨ÐÍ¸ÔºÒÂµèÍä» ã¹ËÑÇ¢éÍ·Õ 4.3

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¹Í¡¨Ò¡¹Õ àÁ× Í ¾Ô¨ÒÃ³ÒÊèÇ¹¢Í§ÊÑÒ³Ãº¡Ç¹

W (D)

ã¹ÊÁ¡ÒÃ (4.6) ¨Ð¾ºÇèÒ ÊÒàËµØ ·Õ

ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì µéÍ§¡ÒÃ·Õ ¨Ðä´é ·ÒÃìà¡çµ àªÔ§ ¤ÇÒÁ¶Õ àËÁ×Í¹¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³ ·ÓãËé

W (D)

ÁÕ ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇ

H(D) = C(D)

áÅéÇ ¨Ðä´é ÇèÒ

W (D) = N (D)

C(D)

N (D)

H(D)

·Õ ÁÕ ¼ÅµÍºÊ¹Í§

ãËé ÁÒ¡·Õ ÊØ´ ¡ç à¾× Í ·Õ ÇèÒ¨Ðä´é

ãËé ÁÒ¡·Õ ÊØ´ ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ¶éÒ

«Ö § ¶×Í ÇèÒ à» ¹ à§× Í¹ä¢ËÅÑ¡ ·Õ ¨Ð·ÓãËé Ç§¨ÃµÃÇ¨ËÒ

ÇÕà·ÍÃìºÔÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ÊØ´ ËÃ×Í¡ÅèÒÇÍÕ¡¹ÑÂË¹Ö §¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ð¶Ù¡¾Ô¨ÒÃ³ÒÇèÒà» ¹ Ç§¨ÃµÃÇ¨ËÒ·Õ àËÁÒÐ·Õ ÊØ´ (opimal detector) ¶éÒÍ§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³ Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔà» ¹ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇ [15] ´Ñ§¹Ñ ¹ ÍÒ¨¨ÐÊÃØ» ä´éÇèÒ ¶éÒ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµàËÁ×Í¹¡Ñº¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³ÁÒ¡ à·èÒã´ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººã¹ÃÙ»¢Í§ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´ºÔµ (BER) ÇÑ´·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨ÃµÃÇ¨ËÒ ÇÕà·ÍÃìºÔ¡ç¨Ð´ÕÁÒ¡¢Ö ¹à·èÒ¹Ñ ¹

4.3

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¤×Í Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº (sequence detector) ·Õ ÊÃéÒ§â´Âãªé ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ (Viterbi algorithm) [15] à¾× Íãªéã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ·Õ ¶Ù¡à¢éÒÃËÑÊ´éÇÂ ÃËÑÊ¤Í¹âÇÅÙªÑ¹ (convo lutional code) [7] à·èÒ¹Ñ ¹ ã¹·Ò§»¯ÔºÑµÔáÅéÇ ªèÍ§ÊÑÒ³ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡¾Ô¨ÒÃ³ÒÇèÒà» ¹ÃËÑÊ¤Í¹ âÇÅÙªÑ¹»ÃÐàÀ·Ë¹Ö §·Õ ÁÕÍÑµÃÒÃËÑÊ (code rate) à·èÒ¡Ñº¤èÒË¹Ö § (¹Ñ ¹¤×Í ¢éÍÁÙÅÍÔ¹¾Øµ 1 ºÔµ àÁ× Íà¢éÒÃËÑÊ áÅéÇ¨Ðä´é¢éÍÁÙÅàÍÒµì¾ØµÍÍ¡ÁÒ 1 ºÔµàªè¹¡Ñ¹) Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕ¤ÇÒÁÊÒÁÒÃ¶·Õ ¨Ñ´¡ÒÃ¡Ñº ISI ·Õ á½§ÍÂÙèã¹¢éÍÁÙÅ·Õ ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ â´Â·Õ ¶éÒ ISI ÂÔ §ÁÒ¡ ¤ÇÒÁ«Ñº«éÍ¹¢Í§ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¡ç¨ÐÂÔ §ÁÒ¡ áÅÐ¶éÒ ISI ¹éÍÂ ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¡ç¨Ð¹éÍÂ à¹× Í§¨Ò¡ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÕ ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒáºº§èÒÂ (simple detector) àªè¹ Ç§¨ÃµÃÇ¨ËÒ¢Õ´ àÊé¹ áºè§ áººËÅÒÂÃÐ´Ñº ã¹¡ÒÃ·Õ ¨ÐµÑ´ÊÔ¹ã¨ÇèÒ ¨Ð¹ÓÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÒ ãªé §Ò¹ã¹ÃÐººËÃ×Í äÁè ¹Ñ ¹ ãËé ¾Ô¨ÒÃ³Ò¨Ò¡ÃÙ» ·Õ 4.3 ´Ñ§µèÍä»¹Õ ¨Ò¡ÃÙ» ·Õ 4.3(a) ¶éÒ ªèÍ§ÊÑÒ³äÁè ÁÕ ISI Ç§¨ÃÀÒ¤ÃÑº ¡ç ÊÒÁÒÃ¶¹ÓÇ§¨ÃµÃÇ¨ËÒáºº§èÒÂÁÒãªé §Ò¹ä´é àÅÂ ¶éÒ ªèÍ§ÊÑÒ³ÁÕ ISI ¹éÍÂ µÒÁÃÙ» ·Õ 4.3(b) Ç§¨ÃÀÒ¤ÃÑº ¡ç ÊÒÁÒÃ¶¹ÓÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÒãªé §Ò¹ä´é àÅÂ áµè ¶éÒ ªèÍ§ÊÑÒ³ ÁÕ ISI ¨Ó¹Ç¹ÁÒ¡µÒÁÃÙ» ·Õ 4.3(c) Ç§¨ÃÀÒ¤ÃÑº ¡ç ¤ÇÃ·Õ ¹ÓÍÕ¤ÇÍäÅà«ÍÃì ÁÒãªé §Ò¹ à¾× Í Å´¼Å¡ÃÐ·º

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

AWGN

(a)

simple detector

channel no ISI

âk

AWGN

(b)

channel with low ISI C(D)

Viterbi detector C(D)

âk

AWGN

ak (c)

channel with severe ISI C(D)

equalizer

Viterbi detector H(D)

âk

target H(D) ÃÙ»·Õ 4.3: µÑÇÍÂèÒ§áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅÅÑ¡É³ÐµèÒ§æ

¢Í§ ISI ãËé ¹éÍÂÅ§ ¨Ò¡¹Ñ ¹ ¨Ö§ ¤èÍÂÊè§ ¢éÍÁÙÅ àÍÒµì¾Øµ ·Õ ä´é ¨Ò¡ÍÕ¤ÇÍäÅà«ÍÃì ä»·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¶×ÍÇèÒà» ¹Ç§¨ÃµÃÇ¨ËÒ¢éÍÁÙÅ·Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ áÅÐ¶Ù¡¹ÓÁÒãªé§Ò¹ã¹ËÅÒÂæ §Ò¹»ÃÐÂØ¡µì ÃÇÁ·Ñ §ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì â´Â·Õ ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐÍÂÙè º¹¾× ¹°Ò¹¢Í§ á¼¹ÀÒ¾à·ÃÅÅÔÊ à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´

(trellis diagram) «Ö § ÊÃéÒ§ÁÒ¨Ò¡

(FSM: nite state machine) ´Ñ§¹Ñ ¹ ¡èÍ¹·Õ ¨ÐÍ¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§

ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ¼ÙéÍèÒ¹¤ÇÃ¨Ð·Ó¤ÇÒÁà¢éÒã¨à¡Õ ÂÇ¡Ñº ÇÔ¸Õ¡ÒÃÊÃéÒ§à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ áÅÐá¼¹ÀÒ¾ à·ÃÅÅÔÊ¡èÍ¹ «Ö §ÁÕÃÒÂÅÐàÍÕÂ´´Ñ§¹Õ

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

H(D)

{0,1} ÃÙ»·Õ 4.4: á¼¹ÀÒ¾ªèÍ§ÊÑÒ³áºº PR1,

µÒÃÒ§·Õ 4.1: ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§

4.3.1

áÅÐ

H(D) = 1 + D

¢Í§ªèÍ§ÊÑÒ³

ak−1

H(D) = 1 + D

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´

¾Ô¨ÒÃ³ÒªèÍ§ÊÑÒ³

H(D) = 1 + D

ã¹ÃÙ»·Õ 4.4 àÁ× Í ¢éÍÁÙÅºÔµÍÔ¹¾Øµ

ak ∈ {0, 1}

à¢éÒä»ã¹ªèÍ§ÊÑÒ³·ÓãËéä´éà» ¹¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³ (channel output) à¢ÕÂ¹µÒÃÒ§áÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾Øµ â´Â·Õ ¢éÍÁÙÅºÔµ

ak−1

áÅÐ¢éÍÁÙÅàÍÒµì¾Øµ

¶Ù¡Êè§¼èÒ¹

rk ∈ {0, 1, 2}

¶éÒ

¨Ðä´éµÒÁµÒÃÒ§·Õ 4.1

ÍÒ¨¨Ð¶Ù¡¾Ô¨ÒÃ³ÒÇèÒà» ¹¢éÍÁÙÅ·Õ ËÅ§àËÅ×ÍÍÂÙèã¹ àÃ¨ÔÊàµÍÃìáººàÅ× Í¹ (shift

¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§

áÅÐ

ã¹µÒÃÒ§·Õ 4.1 ÊÒÁÒÃ¶áÊ´§ãËéÍÂÙèã¹ÃÙ»¢Í§ à¤Ã× Í§Ê¶Ò¹Ð

¨Ó¡Ñ´ (FSM: nite state machine) «Ö § ¡ç ¤×Í áºº¨ÓÅÍ§¢Í§¡ÒÃ¤Ó¹Ç³·Õ áÊ´§ãËé àËç¹ ¶Ö§ ¡ÒÃ à»ÅÕ Â¹á»Å§¢Í§ ¢éÍÁÙÅÍÔ¹¾Øµ, Ê¶Ò¹ÐàÃÔ Áµé¹ (start state), Ê¶Ò¹ÐµèÍä» (next state), áÅÐ¢éÍÁÙÅ àÍÒµì¾ØµªèÍ§ÊÑÒ³ ´Ñ§áÊ´§ã¹ÃÙ»·Õ 4.5 â´Â·Õ ¢éÍÁÙÅºÔµ 0 áÅÐºÔµ 1 ·Õ ÍÂÙèã¹Ç§¡ÅÁ ¤×Í ¤èÒ·Õ ÍÂÙè

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

1/1 X/Y is denoted as:

0/0

1/2

ak Y = the output bit rk X = the input bit

0/1 ÃÙ»·Õ 4.5: à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ªèÍ§ÊÑÒ³ PR1,

ã¹àÃ¨ÔÊàµÍÃìáººàÅ× Í¹ ³ àÇÅÒ¢³Ð¹Ñ ¹, ªèÍ§ÊÑÒ³

¤×Í ¤èÒ¢éÍÁÙÅÍÔ¹¾Øµ

H(D) = 1 + D

ak ,

áÅÐ

¤×Í ¤èÒ¢éÍÁÙÅàÍÒµì¾Øµ

µÑÇÍÂèÒ§àªè¹ ÊÁÁØµÔÇèÒ ³ µÍ¹¹Õ ¤èÒ·Õ ÍÂÙèã¹àÃ¨ÔÊàµÍÃìáººàÅ× Í¹ ¤×Í ¤èÒ 1 ¶éÒ¢éÍÁÙÅ

ÍÔ¹¾Øµ ·Õ à¢éÒ ÁÒã¹ªèÍ§ÊÑÒ³ ¤×Í

ak = 0

¨Ðä´é ÇèÒ ¤èÒ ·Õ ÍÂÙè ã¹àÃ¨ÔÊàµÍÃì áººàÅ× Í¹àÁ× Í àÇÅÒ¼èÒ¹ä»

Ë¹Ö §Ë¹èÇÂ (ËÃ×Í Ê¶Ò¹ÐµèÍä») ¤×Í ¤èÒ 0 â´Â¨Ðä´é¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

rk = 1

ã¹·Ó¹Í§

à´ÕÂÇ¡Ñ¹ ¶éÒµÍ¹¹Õ ¤èÒ·Õ ÍÂÙèã¹àÃ¨ÔÊàµÍÃìáººàÅ× Í¹ ¤×Í ¤èÒ 0 áÅÐ¢éÍÁÙÅÍÔ¹¾Øµ·Õ à¢éÒÁÒã¹ªèÍ§ÊÑÒ³ ¤×Í

ak = 0

¨Ðä´é ÇèÒ ¤èÒ ·Õ ÍÂÙè ã¹àÃ¨ÔÊàµÍÃì áººàÅ× Í¹àÁ× Í àÇÅÒ¼èÒ¹ä»Ë¹Ö § Ë¹èÇÂ ¤×Í ¤èÒ 0 â´Â¨Ðä´é

rk = 0

¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

ËÁÒÂàËµØ

¶éÒ ¡ÓË¹´ãËé

|A|

à» ¹µé¹

¤×Í ¨Ó¹Ç¹¤èÒ ·Õ à» ¹ ä»ä´é ·Ñ §ËÁ´¢Í§¢éÍÁÙÅ ÍÔ¹¾Øµ

ak ,

áÅÐ

Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³ ´Ñ§¹Ñ ¹ ¨Ó¹Ç¹Ê¶Ò¹Ð (state) ·Ñ §ËÁ´ã¹à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ ¤×Í àªè¹ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ»·Õ 4.4 ¨Ðä´éÇèÒ

|A| = 2

¨Ó¡Ñ´¢Í§ªèÍ§ÊÑÒ³ PR1 ¨ÐÁÕ¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´

4.3.2

áÅÐ

21 = 2

ν=1

¤×Í

|A|ν

à¾ÃÒÐ©Ð¹Ñ ¹ à¤Ã× Í§Ê¶Ò¹Ð

Ê¶Ò¹Ð

àà¼¹ÀÒ¾à·ÃÅÅÔÊ

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´·Õ áÊ´§ã¹ÃÙ»·Õ 4.5 ÊÒÁÒÃ¶áÊ´§ãËéÍÂÙèã¹ÃÙ»¢Í§á¼¹ÀÒ¾à·ÃÅÅÔÊä´é ´Ñ§áÊ´§ã¹ ÃÙ»·Õ 4.6 â´Â·Õ ¨Ø´µèÍ (node) ·Ò§´éÒ¹«éÒÂÁ×Í ¤×Í Ê¶Ò¹ÐàÃÔ Áµé¹ («Ö §ÁÕ¤èÒà·èÒ¡Ñº ´éÒ¹¢ÇÒÁ×Í ¤×Í Ê¶Ò¹ÐµèÍä», ÅÙ¡ÈÃàÊé¹»Ðãªéá·¹¡ÒÃÊè§¢éÍÁÙÅÍÔ¹¾Øµ ¡ÒÃÊè§¢éÍÁÙÅÍÔ¹¾Øµ

ak = 1,

ak = 0,

ak−1 ),

¨Ø´µèÍ·Ò§

ÅÙ¡ÈÃàÊé¹·Öºãªéá·¹

áÅÐµÑÇàÅ¢·Õ áÊ´§ÍÂÙèã¹áµèÅÐàÊé¹ÊÒ¢Ò (branch) ¤×Í ¤èÒ¢éÍÁÙÅàÍÒµì¾Øµ

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

[ ak −1]

ak = 0

ak = 1

ÃÙ»·Õ 4.6: á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ PR1,

ªèÍ§ÊÑÒ³

µÑÇÍÂèÒ§àªè¹ ¶éÒÊ¶Ò¹ÐàÃÔ Áµé¹ ¤×Í¤èÒ 0 àÁ× Í¢éÍÁÙÅÍÔ¹¾Øµ

·ÓãËéä´é¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

rk = 1

àÃÔ Áµé¹ ¤×Í ¤èÒ 1 àÁ× Í ¢éÍÁÙÅ ÍÔ¹¾Øµ

ak = 1

rk = 2

H(D) = 1 + D

ak = 1

à¢éÒÁÒã¹ÃÐºº ¨Ð

áÅÐÊ¶Ò¹ÐµèÍä» ¤×Í¤èÒ 1 ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ¶éÒÊ¶Ò¹Ð à¢éÒ ÁÒã¹ÃÐºº ¨Ð·ÓãËé ä´é ¢éÍÁÙÅ àÍÒµì¾Øµ ªèÍ§ÊÑÒ³

áÅÐÊ¶Ò¹ÐµèÍä» ¤×Í¤èÒ 1

ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ÃÙ»·Õ 4.7 áÊ´§µÑÇÍÂèÒ§á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ EPR4 (extended PR4),

H(D) = 1 + D − D2 − D3 ,

àÁ× Í ¢éÍÁÙÅÍÔ¹¾Øµ

¢Í§á¼¹ÀÒ¾à·ÃÅÅÔÊ¨ÐÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

{ak } ∈ {0, 1}

|A|ν = 23 = 8

«Ö §ã¹¡Ã³Õ¹Õ ¨Ó¹Ç¹Ê¶Ò¹Ð

Ê¶Ò¹Ð à¹× Í§¨Ò¡ ªèÍ§ÊÑÒ³ EPR4 ÁÕ

¨Ó¹Ç¹Ë¹èÇÂ¤ÇÒÁ¨Óà·èÒ¡Ñº 3 Ë¹èÇÂ

µÑÇÍÂèÒ§·Õ 4.1

¡ÓË¹´ãËé¢éÍÁÙÅÍÔ¹¾Øµ

H(D) = 1 − D2 ,

ak ∈ {−1, 1}

áÅéÇä´é¢éÍÁÙÅàÍÒµì¾Øµà» ¹

¶Ù¡Êè§¼èÒ¹à¢éÒä»ÂÑ§ªèÍ§ÊÑÒ³áºº PR4,

rk ∈ {−2, 0, 2}

¨§

¡) ÇÒ´á¼¹ÀÒ¾ºÅçÍ¡¢Í§ªèÍ§ÊÑÒ³áºº PR4 ¹Õ (¤ÅéÒÂ¡ÑºÃÙ»·Õ 4.4)

¢) à¢ÕÂ¹ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾ØµáÅÐ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§ªèÍ§ÊÑÒ³¹Õ

¤) ÊÃéÒ§à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´

§) ÊÃéÒ§á¼¹ÀÒ¾à·ÃÅÅÔÊ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

[ak −1 ak −2 ak −3] (0)

000

(1)

100

(2)

010

(3)

110

(4)

001

(5)

101

1 2 -1 0 1 -1

0 0 0 1 -2

(6)

011

(7)

111

-1 -1

ak = 1 ak = 0

yk ÃÙ»·Õ 4.7: á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ EPR4,

H(D) = 1 + D − D2 − D3

ÇÔ¸Õ·Ó ¡)

¨Ò¡ªèÍ§ÊÑÒ³·Õ ¡ÓË¹´ãËé ÊÒÁÒÃ¶áÊ´§à» ¹á¼¹ÀÒ¾ºÅçÍ¡¢Í§ªèÍ§ÊÑÒ³áºº PR4 ä´é

´Ñ§ÃÙ»·Õ 4.8(a) ¢)

à¹× Í§¨Ò¡

H(D) =

P k

hk Dk = 1 − D2

´Ñ§¹Ñ ¹ ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ì ÃÐËÇèÒ§¢éÍÁÙÅ

ÍÔ¹¾ØµáÅÐ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§ªèÍ§ÊÑÒ³¹Õ ¤×Í

rk = ak ∗ hk = ak − ak−2 ¤)

¨Ò¡ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾ØµáÅÐ¢éÍÁÙÅàÍÒµì¾Øµ·Õ ä´éã¹¢éÍ ¢) à¤Ã× Í§Ê¶Ò¹Ð

¨Ó¡Ñ´ÊÒÁÒÃ¶áÊ´§ä´éµÒÁÃÙ»·Õ 4.8(b)

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

[ ak −1ak −2 ]

rk ak

{±1} (a) Block diagram: PR4

1 -11

1/2 -1/0

-1 - 1-1 -

1/0

-1/0

-1 -1

1 -1

1/2

-1 1 11

0 -2 0

1/0

-1/-2

0 2 -2

1 1

ak = -1 ak = 1

-1111

(b) FSM

ÃÙ»·Õ 4.8: (a) á¼¹ÀÒ¾ºÅçÍ¡, (b) à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, áÅÐ (c) á¼¹ÀÒ¾à·ÃÅÅÔÊ ¢Í§ªèÍ§ÊÑÒ³

H(D) = 1 − D2

§)

4.3.3

ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ

¨Ò¡à«µ¢Í§ªØ´µÑÇÍÑ¡ÉÃ

H(D) µÒÁÃÙ»·Õ 4.9 â´Â·Õ ak ¤×Í ¢éÍÁÙÅºÔµÍÔ¹¾Øµ·Õ ¶Ù¡àÅ×Í¡ÁÒ P A, H(D) = νk=0 hk Dk ¤×Í ªèÍ§ÊÑÒ³ÇÔÂØµ (discrete channel), hk

¤×Í ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô µÑÇ ·Õ

k, ν

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³

¤×Í Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³,

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ

¢ÒÇáºººÇ¡ (AWGN) ·Õ ÁÕ¤èÒà©ÅÕ Âà·èÒ¡Ñº¤èÒÈÙ¹Âì áÅÐ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ¡Ñº¤èÒ ä´é´éÇÂ

nk ∼ N (0, σ 2 ), rk

ÍÔ¹¾Øµ

{ak }

(â´Â·Ñ Çä»

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³, áÅÐ

L = 4096

σ2

ËÃ×Íà¢ÕÂ¹á·¹

¤×Í ¤ÇÒÁÂÒÇ¢Í§ÅÓ´Ñº¢éÍÁÙÅ

ºÔµ ÊÓËÃÑº ¢éÍÁÙÅ 1 à«¡àµÍÃì), áÅÐ

âk

¤×Í ¤èÒ »ÃÐÁÒ³¢Í§

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

nk ak

H(D)

ÃÙ»·Õ 4.9: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³

Viterbi detector

H(D)

time k

âk

¾ÃéÍÁÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

k+1

(u, q) q k-th stage

ÃÙ»·Õ 4.10: ¤ÓÍ¸ÔºÒÂá¼¹ÀÒ¾à·ÃÅÅÔÊ

¢éÍÁÙÅºÔµÍÔ¹¾Øµ

·Õ ä´é¨Ò¡¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅâ´ÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¡èÍ¹·Õ ¨ÐÍ¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ¨Ð¹ÔÂÒÁÊÑÅÑ¡É³ì µÒÁÃÙ» ·Õ 4.10 ´Ñ§¹Õ ãËé

Ψk = [ak ak−1 . . . ak−ν+1 ]

³ àÇÅÒ

k ), Q = |A|ν

¢Í§¢éÍÁÙÅ ÍÔ¹¾Øµ,

¤×Í Ê¶Ò¹Ð ³ àÇÅÒ

(ËÃ×Í¤èÒ·Õ ÍÂÙèã¹àÃ¨ÔÊàµÍÃìáººàÅ× Í¹·Ñ §ËÁ´

¤×Í ¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´·Õ à» ¹ä»ä´é,

|A|

¤×Í Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³, ÃÐÂÐ·Õ

ÊÒ¢Ò·Õ à» ¹ ä»ä´é ·Ñ §ËÁ´ ³ àÇÅÒ·Õ Ê¶Ò¹Ð

ä»ÂÑ§Ê¶Ò¹Ð

áÅÐ

(u, q)

k (k th

stage) ¤×Í ¡ÅØèÁ ¢Í§àÊé¹

¤×Í ÊÑÅÑ¡É³ì ·Õ ãªé á·¹¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡

¾Ô¨ÒÃ³Òá¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ PR4 ¹Ñ ¹¤×Í ÁÕ¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´

¤×Í ¨Ó¹Ç¹¤èÒ·Õ à» ¹ä»ä´é·Ñ §ËÁ´

Q = 22 = 4

H(D) = 1 − D2

µÒÁÃÙ»·Õ 4.11 «Ö §

Ê¶Ò¹Ð ·Õ áÊ´§´éÇÂÊÑÅÑ¡É³ì (0), (1), (2), áÅÐ (3) àÁ× Í

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

time k (0) -1 -1

k+1 0 2

(1) 1 -1

0 2 -2

(2) -1 1

λk (1, 2)

Φ + (2)

k 1

π k +1 (2)

-2

(3) 1 1

ak = 1 ak = -1

yk ÃÙ»·Õ 4.11: á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³ PR4,

¢éÍÁÙÅ ÍÔ¹¾Øµ

ak ∈ {−1, 1}

ã¹¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ÊÔ § ·Õ µéÍ§¤Ó¹Ç³·Ø¡ ªèÇ§àÇÅÒ ¤×Í

¤èÒ àÁµÃÔ¡ ÊÒ¢Ò (branch metric) ³ àÇÅÒ

λk (u, q),

¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð

k+1

¤èÒ àÁµÃÔ¡ àÊé¹·Ò§ (path metric) ³ àÇÅÒ

(predecessor) ÊÓËÃÑºÊ¶Ò¹Ð

H(D) = 1 − D2

³ àÇÅÒ

k + 1, πk+1 (q),

·Õ Ê¶Ò¹Ð

ä»ÂÑ§ Ê¶Ò¹Ð

q , Φk+1 (q),

áÅÐµÑÇ¹ÓË¹éÒ

«Ö §¨Ðà¡çº¤èÒÊ¶Ò¹ÐàÃÔ Áµé¹·Õ à» ¹¼Å·ÓãËé

à¡Ô´àÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ÊØ´ (best transition) àªè¹ ¾Ô¨ÒÃ³Ò·Õ Ê¶Ò¹Ð (2) ³ àÇÅÒ ¨ÐÁÕàÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð 2 àÊé¹·Ò§ ¤×Í

(1, 2)

áÅÐ

(3, 2)

¡ÒÃàÅ×Í¡àÊé¹·Ò§à¾ÕÂ§àÊé¹·Ò§à´ÕÂÇ·Õ ÁÒ¶Ö§Ê¶Ò¹Ð (2) ³ àÇÅÒ àÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ÊØ´ ¨Ðä´éÇèÒ

πk+1 (2)

k+1

ÊÁÁØµÔÇèÒ ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ¨Ð·Ó

k+1

ÊÁÁØµÔÇèÒ àÊé¹·Ò§

(1, 2)

¤×Í

= 1 ¹Ñ ¹àÍ§

à» ¹ ·Õ ·ÃÒº¡Ñ¹ ÇèÒ Ç§¨ÃµÃÇ¨ËÒ·Õ ·ÓãËé ¤ÇÒÁ¹èÒ¨Ðà» ¹ ¢Í§¢éÍ¼Ô´¾ÅÒ´¢Í§ÅÓ´Ñº ¢éÍÁÙÅ ·Ñ § ÅÓ´Ñº ÁÕ ¤èÒ¹éÍÂ·Õ ÊØ´ ¤×Í Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº·Õ ¤ÇÃ¨Ðà» ¹ÁÒ¡ÊØ´ (MLSD: maximum likelihood sequence detector) «Ö §ÊÒÁÒÃ¶ÊÃéÒ§ä´éâ´ÂãªéÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ ¨Ò¡áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ»·Õ 4.9 Ç§¨Ã µÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐàÅ×Í¡ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

{ak }

·Õ ·ÓãËé ¤ÇÒÁ¹èÒ¨Ðà» ¹ ¢Í§ÅÓ´Ñº ¢éÍÁÙÅ

{yk }

àÁ× Í

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ÓË¹´ÅÓ´Ñº¢éÍÁÙÅ

{ak }

ÁÒãËé ¹Ñ ¹¤×Í

(

L+ν−1 1 X exp − 2 |yk − rk |2 2σ

p(y|a) = ³√ ´L+ν 2πσ 2

(4.7)

k=0

ÁÕ¤èÒÁÒ¡·Õ ÊØ´ ÊÁ¡ÒÃ (4.7) ä´éÁÒ¨Ò¡¤ÇÒÁ¨ÃÔ§·Õ ÇèÒ ÊÑÒ³Ãº¡Ç¹ ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

)

nk ∼ N (0, σ 2 ) áÅÐàÁ× Í¡ÓË¹´

ÁÒãËé áÊ´§ÇèÒ ÃÐºº·ÃÒºÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ àÍÒµì¾Øµ

¤×Í ÍÐäÃ ´Ñ§¹Ñ ¹ ¢éÍÁÙÅ

¨ÐÁÕ¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹áººà¡ÒÊìà«ÕÂ¹ (Gaussian probability density function) àËÁ×Í¹¡Ñº

·Õ ÁÕ¤èÒà©ÅÕ Âà·èÒ¡Ñº¤èÒ

áÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ¡Ñº

σ2

àÁ× ÍãÊèÅÍ¡ÒÃÔ·ÖÁ¸ÃÃÁªÒµÔ (natural logarithm) ·Ñ §ÊÍ§¢éÒ§¢Í§ÊÁ¡ÒÃ (4.7) ¨Ðä´éà» ¹

   ln {p(y|a)} = ln

  

³√ ´L+ν     2πσ 2

−

L+ν−1 1 X |yk − rk |2 2σ 2

(4.8)

k=0

ÊÑ§à¡µ¨Ð¾ºÇèÒ ¡ÒÃ·ÓãËé ÊÁ¡ÒÃ (4.8) ÁÕ ¤èÒ ÁÒ¡·Õ ÊØ´ ÁÕ ¼Åà·ÕÂºà·èÒ ¡Ñº ¡ÒÃ·ÓãËé ¾¨¹ì ·Õ ÊÍ§·Ò§´éÒ¹ ¢ÇÒÁ×Í ¢Í§ÊÁ¡ÒÃ (4.8) ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ à¹× Í§¨Ò¡ ¾¨¹ì ·Õ Ë¹Ö § à»ÃÕÂºàÊÁ×Í¹¡Ñº ¤èÒ¤§·Õ à¾ÃÒÐ©Ð¹Ñ ¹ ¡ÒÃ·ÓãËéÊÁ¡ÒÃ (4.8) ÁÕ¤èÒÁÒ¡·Õ ÊØ´¨ÐÁÕ¤èÒà·èÒ¡Ñº¡ÒÃ·ÓãËéàÁµÃÔ¡ (metric)

L+ν−1 X

|yk − rk |2

(4.9)

k=0

ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ ´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨ÐàÅ×Í¡ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ ·ÓãËéÊÁ¡ÒÃ (4.9) ÁÕ¤èÒ¹éÍÂ ·Õ ÊØ´ ÊÑ§à¡µ¨Ò¡ÊÁ¡ÒÃ (4.9) ¨Ð¾ºÇèÒ ¾¨¹ì

|yk − rk |2

¡ç ¤×Í ¤èÒ ÃÐÂÐ·Ò§¡ÓÅÑ§ ÊÍ§à©ÅÕ Â

(MSD:

mean squared distance) [10] àÁµÃÔ¡ã¹ÊÁ¡ÒÃ (4.9) ÊÒÁÒÃ¶·ÓãËéÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ä´é â´Â¡ÒÃ¤é¹ËÒ àÊé¹·Ò§ (path) ·Õ ÁÕ ¤èÒ àÁµÃÔ¡ ¹éÍÂ·Õ ÊØ´ µÒÁá¼¹ÀÒ¾à·ÃÅÅÔÊ àÁ× Í àÁµÃÔ¡ àÊé¹·Ò§ÁÕ ¤èÒ à·èÒ ¡Ñº ¼ÅÃÇÁ ¢Í§àÁµÃÔ¡ÊÒ¢Ò â´Â·Õ àÁµÃÔ¡ÊÒ¢Ò¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð

λk (u, q) = |yk − r̂k (u, q)|2 1

ÈÖ¡ÉÒÃÒÂÅÐàÍÕÂ´à¾Ô ÁàµÔÁä´éã¹ËÑÇ¢éÍ·Õ 6.6.11 ã¹ [10]

ä»ÂÑ§Ê¶Ò¹Ð

¨Ð¹ÔÂÒÁâ´Â

(4.10)

4.3.

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

(A 1) ¡ÓË¹´¤èÒàÃÔ Áµé¹¢Í§àÁµÃÔ¡àÊé¹·Ò§ (A 2) For

k = 0, 1, . . . , L + ν − 1

(A 3)

For

Φ0 (p) = 0

ÊÓËÃÑº·Ø¡¤èÒ

q = 0, 1, . . . , Q − 1

(A 4)

λk (p, q) = |yk − r̂(p, q)|2

(A 5)

πk+1 (q) = arg minp {Φk (p) + λk (p, q)}

(A 6)

Φk+1 (q) = Φk (πk+1 (q)) + λk (πk+1 (q), q)

(A 7)

Sk+1 (q) = [Sk (πk+1 (q)) | πk+1 (q)]

(A 8)

for

∀p

End

(A 9) End (A 10) ¶Í´ÃËÑÊ¢éÍÁÙÅÍÔ¹¾Øµ

â

¨Ò¡àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè·Õ ÁÕ¤èÒ

ΦL+ν

¹éÍÂ·Õ ÊØ´

ÃÙ»·Õ 4.12: ¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ

àÁ× Í

r̂k (u, q)

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³·Õ ÊÍ´¤ÅéÍ§¡Ñº

(u, q)

áÅÐàÁµÃÔ¡àÊé¹·Ò§ÊÒÁÒÃ¶ËÒä´é

¨Ò¡

Φk+1 (q) =

k X

λi

(4.11)

i=0 ÃÙ» ·Õ 4.12 áÊ´§¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ¢Í§ªèÍ§ÊÑÒ³

H(D) = 1 − D2

µÑÇÍÂèÒ§àªè¹ ¨Ò¡á¼¹ÀÒ¾à·ÃÅÅÔÊ

ã¹ÃÙ»·Õ 4.11 ãËé¾Ô¨ÒÃ³ÒÃÐÂÐ·Õ

k (k th

à·ÃÅÅÔÊ ¨Ð¾ºÇèÒ ÁÕ ¡ÒÃàÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð 2 àÊé¹·Ò§·Õ ÁÒ¶Ö§ Ê¶Ò¹Ð ¹Ñ ¹¤×Í

(1, 2)

λk (3, 2)

áÅÐ

(3, 2)

stage) ¢Í§á¼¹ÀÒ¾

(2)

³ àÇÅÒ

ãËé ·Ó¡ÒÃ¤Ó¹Ç³¤èÒ àÁµÃÔ¡ ÊÒ¢Ò·Ñ § 2 àÊé¹·Ò§ ¹Ñ ¹¤×Í

k+1

λk (1, 2)

áÅÐ

µÒÁ¢Ñ ¹µÍ¹·Õ (A 4) ¨Ò¡¹Ñ ¹ Ê¶Ò¹ÐàÃÔ Áµé¹·Õ ÊÍ´¤¤ÅéÍ§¡ÑºàÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ

·Õ ØÊØ´·Õ ÁÒ¶Ö§Ê¶Ò¹Ð (2) ³ àÇÅÒ

k+1

¨Ð¶Ù¡àÅ×Í¡µÒÁ¢Ñ ¹µÍ¹·Õ (A 5) ÊÁÁØµÔÇèÒ

(1, 2)

¤×Í àÊé¹·Ò§

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ØÊØ´·Õ ÁÒ¶Ö§Ê¶Ò¹Ð (2) ³ àÇÅÒ ¹Ñ ¹ àÁµÃÔ¡àÊé¹·Ò§·Õ ÁÒ¶Ö§Ê¶Ò¹Ð (2) ³ àÇÅÒ áÅÐàÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè

k+1

´Ñ§¹Ñ ¹¨Ðä´éÇèÒ

k + 1, Φk+1 (2),

πk+1 (2) = 1

ËÅÑ§¨Ò¡

¨Ð¶Ù¡»ÃÑº¤èÒµÒÁ¢Ñ ¹µÍ¹·Õ (A 6)

(survivor path) ·Õ ÁÒ¶Ö§ Ê¶Ò¹Ð (2) ³ àÇÅÒ

k + 1, Sk+1 (2),

¨Ð¶Ù¡

»ÃÑº¤èÒµÒÁ¢Ñ ¹µÍ¹·Õ (A 7) ãËé·ÓµÒÁ¢Ñ ¹µÍ¹µèÒ§æ àËÅèÒ¹Õ µÒÁÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔä»¨¹ÊÔ ¹ÊØ´ÅÓ´Ñº ¢éÍÁÙÅ

{yk }

·Õ ä´éÃÑºÁÒ áÅÐ¢Ñ ¹µÍ¹ÊØ´·éÒÂ¡ç¤×Í ¡ÒÃµÑ´ÊÔ¹ã¨¨Ð¶Ù¡¡ÃÐ·Óâ´Â¡ÒÃàÅ×Í¡àÊé¹·Ò§·Õ ÂÑ§ÁÕ

ªÕÇÔµÍÂÙè·Õ ÁÕ¤èÒàÁµÃÔ¡àÊé¹·Ò§ ³ àÇÅÒ

4.3.4

L + ν , ΦL+ν ,

¹éÍÂ·Õ ÊØ´

¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

à¹× Í§¨Ò¡ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ð·Ó¡ÒÃ»ÃÐÁÇÅ¼ÅÅÓ´Ñº ¢éÍÁÙÅ ·Ñ §ËÁ´¡èÍ¹·Õ ¨ÐµÑ´ÊÔ¹ã¨ÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ·Õ ä´éÃÑº¤ÇÃ¨Ðà» ¹ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµã´ÁÒ¡·Õ ÊØ´ ´Ñ§¹Ñ ¹ ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ö§¢Ö ¹ÍÂÙè¡ÑºËÅÒÂ» ¨¨ÑÂ ´Ñ§¹Õ

1) ¨Ó¹Ç¹¤èÒ·Õ à» ¹ä»ä´é·Ñ §ËÁ´¢Í§¢éÍÁÙÅÍÔ¹¾Øµ

2) ¤ÇÒÁÂÒÇ¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

3) Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§·ÒÃìà¡çµ

|A|

|A|ν

(L + 1)|A|ν

{πk }

ÍÂèÒ§

Ë¹èÇÂ

¨ÐàËç¹ä´éÇèÒ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔáºº·Õ ãªé§Ò¹¡Ñ¹·Ñ Çä»äÁèÊÒÁÒÃ¶¹ÓÁÒãªé§Ò¹¨ÃÔ§ä´éã¹·Ò§»¯ÔºÑµÔ à¹× Í§¨Ò¡µéÍ§¡ÒÃË¹èÇÂ¤ÇÒÁ¨Óà» ¹¨Ó¹Ç¹ÁÒ¡ à¾ÃÒÐ©Ð¹Ñ ¹ÇÔ¸Õ¡ÒÃÅ´¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ ÇÕà·ÍÃìºÔ ¤×Í¡ÒÃãªé¾ÒÃÒÁÔàµÍÃì·Õ àÃÕÂ¡ÇèÒ ¤ÇÒÁÅÖ¡¡ÒÃ¶Í´ÃËÑÊ ÇÕà·ÍÃìºÔ àÁ× Í

(decoding depth) ã¹ÍÑÅ¡ÍÃÔ·ÖÁ

¤×Í ¤ÒºàÇÅÒ¢Í§ºÔµ (bit period) ¡ÅèÒÇ¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð·Ó¡ÒÃµÑ´ÊÔ¹ã¨

¢éÍÁÙÅ ·ÕÅÐºÔµ ËÅÑ§¨Ò¡·Õ àÇÅÒ¼èÒ¹ä»

Ë¹èÇÂ ´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Õ ÁÕ ¡ÒÃãªé ¤ÇÒÁÅÖ¡ ¡ÒÃ

¶Í´ÃËÑÊ¨ÐµéÍ§¡ÒÃ¨Ó¹Ç¹Ë¹èÇÂ¤ÇÒÁ¨Óã¹¡ÒÃà¡çº¢éÍÁÙÅµèÒ§æ ÍÂèÒ§¹éÍÂà·èÒ¡Ñº ·Ñ Çä»áÅéÇÁÑ¡¨Ðãªé

d ≥ 5(ν + 1)

[27]

(d+1)|A|ν

«Ö §â´Â

4.4.

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

(a) 0

ak = 1

0.5

(b) 1

ak = 0

1.5

ÃÙ»·Õ 4.13: á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ªèÍ§ÊÑÒ³

4.4

H(D) = 1 + 0.5D

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

ã¹ÊèÇ¹¹Õ ¨ÐáÊ´§µÑÇÍÂèÒ§¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÍÂèÒ§ÅÐàÍÕÂ´ ´Ñ§µèÍä»¹Õ

µÑÇÍÂèÒ§·Õ 4.2

{0,

¨Ò¡áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ» ·Õ 4.9 ¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

0, 1}, ªèÍ§ÊÑÒ³

hk = δk + 0.5δk−1

delta function), ÊÑÒ³Ãº¡Ç¹ ¢éÍÁÙÅ

ÇÔ¸Õ·Ó

{yk }

{nk }

àÁ× Í

{0.2,

δk

{ak }

¤×Í ¿ §¡ìªÑ¹â¤Ãà¹¤à¡ÍÃìà´ÅµÒ (Kronecker

0.5, 0,

−0.35}

¨§áÊ´§¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ

´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¨Ò¡·Õ â¨·Âì¡ÓË¹´ ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

ËÒä´é¨Ò¡

rk = ak ∗ hk = {r0 , r1 , r2 , r3 } = {0, 0, 1, 0.5} àÁ× Í

∗

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ¤Í¹âÇÅÙªÑ¹ (convolution operator) áÅÐ

yk = rk + nk = {0.2, 0.5, 1, 0.15} ¨Ò¡¹Ñ ¹ ãËéÊÃéÒ§á¼¹ÀÒ¾à·ÃÅÅÔÊ¨Ò¡ªèÍ§ÊÑÒ³

hk = δk + 0.5δk−1

¹Ñ ¹¤×Í

H(D) = 1 + 0.5D

«Ö § ¨Ð ä´é µÒÁ ÃÙ» ·Õ 4.13 â´Â ã¹ ·Õ ¹Õ á¼¹ÀÒ¾ à· ÃÅÅÔ ÊÁÕ ·Ñ §ËÁ´ 2 Ê¶Ò¹Ð ¤×Í Ê¶Ò¹Ð (a) áÅÐ Ê¶Ò¹Ð (b) ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅÊÒÁÒÃ¶áºè§ÍÍ¡à» ¹ªèÇ§àÇÅÒµèÒ§æ ´Ñ§áÊ´§ã¹ÃÙ»·Õ 4.14 «Ö § ÁÕÃÒÂÅÐàÍÕÂ´´Ñ§¹Õ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

0.04

Φ1 ( a ) = 0.04

0.64 0.09 0

1.69

Φ1 ( b ) = 0.64 0.04

0.25

Φ ( a ) = 0.29 2

0.25 0 0.64

Φ ( b ) = 0.29 2

0.29

0 0.25 0.29

0.25

Φ3 ( a ) = 0.54

Φ3 ( b ) = 0.29 0.54

0.02

Φ 4 ( a ) = 0.41

0.72 0.12 0.29

y 0 = 0.2

y1 = 0.5

y2 = 1

1.82

Φ 4 ( b ) = 1.26

y3 = 0.15

4.4.

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

ªèÇ§àÇÅÒ·Õ 0

àÁ× Í àÃÔ Áµé¹ ÃÑº ¢éÍÁÙÅ

y0 = 0.2

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ð·Ó¡ÒÃ¡ÓË¹´¤èÒ àÃÔ Áµé¹ ¢Í§

àÁµÃÔ¡àÊé¹·Ò§ãËéà·èÒ¡Ñº¤èÒÈÙ¹Âì µÒÁ¢Ñ ¹µÍ¹·Õ (A 1) ã¹ÃÙ»·Õ 4.12 ¹Ñ ¹¤×Í

Φ0 (a) = 0

áÅÐ

Φ0 (b) = 0

¨Ò¡¹Ñ ¹ ¡ç¨Ð·Ó¡ÒÃ¤Ó¹Ç³àÁµÃÔ¡ÊÒ¢Ò·Ø¡àÊé¹ÊÒ¢ÒµÒÁ¢Ñ ¹µÍ¹·Õ (A 4) ã¹ÃÙ»·Õ 4.12 ´Ñ§¹Õ

λ0 (a, a) = |0.2 − 0|2 = 0.04 λ0 (a, b) = |0.2 − 1|2 = 0.64 λ0 (b, a) = |0.2 − 0.5|2 = 0.09 λ0 (b, b) = |0.2 − 1.5|2 = 1.69 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹áµèÅÐàÊé¹ÊÒ¢Òã¹ÃÙ»·Õ 4.14 ¨Ò¡¹Ñ ¹ ·Õ áµèÅÐ¨Ø´µèÍ¡ç¨Ð·Ó¡ÒÃàÅ×Í¡àÊé¹·Ò§¡ÒÃ à»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ÊØ´ áÅéÇ¡ç·Ó¡ÒÃ»ÃÑº¤èÒàÁµÃÔ¡àÊé¹·Ò§ µÒÁ¢Ñ ¹µÍ¹·Õ (A 5) áÅÐ (A 6) ã¹ÃÙ»·Õ 4.12 ¹Ñ ¹¤×Í

Φ1 (a) = min{0 + 0.04, 0 + 0.09} = 0.04 Φ1 (b) = min{0 + 0.64, 0 + 1.69} = 0.64 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹¨Ø´µèÍã¹ÃÙ»·Õ 4.14 â´Â·Õ àÊé¹ÅÙ¡ÈÃÊÕ´Ó ¤×Í àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè (survivor path) ÊèÇ¹àÊé¹ÅÙ¡ÈÃÊÕà·Ò ¤×Í àÊé¹·Ò§·Õ ¶Ù¡µÑ´·Ô §

ªèÇ§àÇÅÒ·Õ 1

àÁ× Í ÃÑº ¢éÍÁÙÅ

y1 = 0.5

´Ñ§¹Õ

λ1 (a, a) = |0.5 − 0|2 = 0.25 λ1 (a, b) = |0.5 − 1|2 = 0.25 λ1 (b, a) = |0.5 − 0.5|2 = 0 λ1 (b, b) = |0.5 − 1.5|2 = 1

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹áµèÅÐàÊé¹ÊÒ¢Òã¹ÃÙ»·Õ 4.14 ¨Ò¡¹Ñ ¹ ·Õ áµèÅÐ¨Ø´µèÍ¡ç¨Ð·Ó¡ÒÃàÅ×Í¡àÊé¹·Ò§¡ÒÃ à»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ÊØ´ áÅéÇ¡ç·Ó¡ÒÃ»ÃÑº¤èÒàÁµÃÔ¡àÊé¹·Ò§ ¹Ñ ¹¤×Í

Φ2 (a) = min{0.04 + 0.25, 0.64 + 0} = 0.29 Φ2 (b) = min{0.04 + 0.25, 0.64 + 1} = 0.29 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹¨Ø´µèÍã¹ÃÙ»·Õ 4.14

ªèÇ§àÇÅÒ·Õ 2

àÁ× ÍÃÑº¢éÍÁÙÅ

y2 = 1

λ2 (a, a) = |1 − 0|2 = 1 λ2 (a, b) = |1 − 1|2 = 0 λ2 (b, a) = |1 − 0.5|2 = 0.25 λ2 (b, b) = |1 − 1.5|2 = 0.25 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹áµèÅÐàÊé¹ÊÒ¢Òã¹ÃÙ»·Õ 4.14 ¨Ò¡¹Ñ ¹ ·Õ áµèÅÐ¨Ø´µèÍ¡ç¨Ð·Ó¡ÒÃàÅ×Í¡àÊé¹·Ò§¡ÒÃ à»ÅÕ Â¹Ê¶Ò¹Ð·Õ ´Õ·Õ ÊØ´ áÅéÇ¡ç·Ó¡ÒÃ»ÃÑº¤èÒàÁµÃÔ¡àÊé¹·Ò§ ¹Ñ ¹¤×Í

Φ3 (a) = min{0.29 + 1, 0.29 + 0.25} = 0.54 Φ3 (b) = min{0.29 + 0, 0.29 + 0.25} = 0.29 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹¨Ø´µèÍã¹ÃÙ»·Õ 4.14

ªèÇ§àÇÅÒ·Õ 3

àÁ× Í ÃÑº ¢éÍÁÙÅ

y3 = 0.15

´Ñ§¹Õ

λ3 (a, a) = |0.15 − 0|2 = 0.02 λ3 (a, b) = |0.15 − 1|2 = 0.72 λ3 (b, a) = |0.15 − 0.5|2 = 0.12 λ3 (b, b) = |0.15 − 1.5|2 = 1.82

4.4.

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

Φ4 (a) = min{0.54 + 0.02, 0.29 + 0.12} = 0.41 Φ4 (b) = min{0.54 + 0.72, 0.29 + 1.82} = 1.26 µÒÁ·Õ à¢ÕÂ¹áÊ´§äÇéã¹¨Ø´µèÍã¹ÃÙ»·Õ 4.14

ËÅÑ§¨Ò¡·ÓµÒÁ¢Ñ ¹µÍ¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ¨¹ÊÔ ¹ÊØ´ÅÓ´Ñº¢éÍÁÙÅ·Õ ä´éÃÑº Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

â

¡ç ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ÍÔ¹¾Øµ ¨Ðä´éÇèÒ

Φ4 (a) = 0.41

¨Ò¡àÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè ·Õ ÁÕ ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§¹éÍÂ·Õ ÊØ´ ã¹·Õ ¹Õ

ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ à¾ÃÒÐ©Ð¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨ÐÁÍ§ÂéÍ¹¡ÅÑºä» (trace

back) µÒÁàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè·Õ ÁÒ¶Ö§¨Ø´µèÍ

Φ4 (a)

¡ç¨Ð¾ºÇèÒ ¢éÍÁÙÅÍÔ¹¾Øµ

{âk }

·Õ ÊÍ´¤ÅéÍ§¡Ñº

àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè¹Õ ¤×Í

{âk } = {â0 , â1 , â2 } = {0, 0, 1} «Ö §µÃ§¡Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak }

äÁèÁÕ¢éÍ¼Ô´¾ÅÒ´à¡Ô´¢Ö ¹ã¹ÃÐºº ËÁÒÂàËµØ

−1)

¢éÍÁÙÅ ÍÔ¹¾Øµ µÑÇ ÊØ´·éÒÂ·Õ ÊÒÁÒÃ¶¶Í´ÃËÑÊ ä´é ¨Ò¡Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ (ã¹·Õ ¹Õ ¤×Í

a3 =

äÁè¨Óà» ¹µéÍ§¶Í´ÃËÑÊ à¾ÃÒÐ¶×ÍÇèÒ à» ¹¢éÍÁÙÅºÔµÊèÇ¹à¡Ô¹·Õ ä´é¨Ò¡¡ÒÃ·Ó¤Í¹âÇÅÙªÑ¹¢Í§¢éÍÁÙÅ

ÍÔ¹¾Øµ ¡Ñº ªèÍ§ÊÑÒ³ áµè ¢éÍÁÙÅ

à» ¹ ¢éÍÁÙÅ ·Õ ¨Óà» ¹ ·Õ ¨ÐµéÍ§¹ÓÁÒãªé ã¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ¢Í§

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

µÑÇÍÂèÒ§·Õ 4.3

{−1, −1,

¨Ò¡áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ» ·Õ 4.9 ¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

−1},

ÊÑÒ³Ãº¡Ç¹

{nk }

ªèÍ§ÊÑÒ³ =

hk = δk − δk−1

{0.5, −0.4,

0.1, 0.7,

¡) ÇÒ´á¼¹ÀÒ¾ºÅçÍ¡¢Í§ªèÍ§ÊÑÒ³

−0.3}

àÁ× Í

δk

{ak }

¤×Í ¿ §¡ìªÑ¹ â¤Ãà¹¤à¡ÍÃìà´ÅµÒ,

¨§

¢) à¢ÕÂ¹ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ì ÃÐËÇèÒ§¢éÍÁÙÅ ÍÔ¹¾Øµ áÅÐ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§ªèÍ§ÊÑÒ³ áÅÐ ¤Ó¹Ç³ËÒ¤èÒ

{yk }

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

rk ak

0 2

-1

(a) Block diagram

-2

1/2

--1 1-

-1/0

-1

111

ak = 1 ak = -1

1/0

(b) FSM ÃÙ»·Õ 4.15: (a) á¼¹ÀÒ¾ºÅçÍ¡, (b) à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, áÅÐ (c) á¼¹ÀÒ¾à·ÃÅÅÔÊ ¢Í§ªèÍ§ÊÑÒ³

H(D) = 1 − D

§) ¶Í´ÃËÑÊ¢éÍÁÙÅ

{yk }

´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

ÇÔ¸Õ·Ó ¡)

¨Ò¡ªèÍ§ÊÑÒ³·Õ ¡ÓË¹´ÁÒãËé

hk = δk − δk−1

¹Ñ ¹¤×Í

H(D) = 1 − D

ÊÒÁÒÃ¶áÊ´§à» ¹

á¼¹ÀÒ¾ºÅçÍ¡¢Í§ªèÍ§ÊÑÒ³ä´éµÒÁÃÙ»·Õ 4.15(a) ¢)

à¹× Í§¨Ò¡

àÍÒµì¾Øµ

H(D) = 1 − D

´Ñ§¹Ñ ¹ ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾Øµ

áÅÐ¢éÍÁÙÅ

¢Í§ªèÍ§ÊÑÒ³¹Õ ¤×Í

rk = ak − ak−1 «Ö §¨Ðä´éÇèÒ

{−1,

0, 2,

−2, 1}

´Ñ§¹Ñ ¹

yk = rk + nk

{−0.5, −0.4,

2.1,

−1.3,

0.7}

4.4.

µÑÇÍÂèÒ§¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

-1

0.25

0.41

0.16

4.41

0.91

4.82 0.49

0.25

0.16

0.41

0.42

1.69

1.40

1.69

0.01

0.49

2.11

0.49

2.60

ÃÙ»·Õ 4.16: á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¤)

¨Ò¡ÊÁ¡ÒÃáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾ØµáÅÐ¢éÍÁÙÅàÍÒµì¾Øµ·Õ ä´éã¹¢éÍ ¢) à¤Ã× Í§Ê¶Ò¹Ð

¨Ó¡Ñ´áÅÐá¼¹ÀÒ¾à·ÃÅÅÔÊ ÊÒÁÒÃ¶áÊ´§ä´éµÒÁÃÙ»·Õ 4.15(b) áÅÐ 4.15(c) µÒÁÅÓ´Ñº §)

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔãªéá¼¹ÀÒ¾à·ÃÅÅÔÊã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ

{yk } â´Â·Õ ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ

¢éÍÁÙÅ ÊÒÁÒÃ¶ÊÃØ» ä´é µÒÁÃÙ» ·Õ 4.16 àÁ× Í µÑÇàÅ¢·Õ áÊ´§ÍÂÙè º¹¨Ø´µèÍ áµèÅÐ¨Ø´ ¤×Í ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§ ·Õ ÁÒ¶Ö§ ³ ¨Ø´µèÍ ¹Ñ ¹ áÅÐµÑÇàÅ¢·Õ áÊ´§ÍÂÙè º¹àÊé¹ ÊÒ¢ÒáµèÅÐàÊé¹ ¤×Í ¤èÒ àÁµÃÔ¡ ÊÒ¢Ò¢Í§áµèÅÐàÊé¹ ÊÒ¢Ò·Õ ´Õ ·Õ ÊØ´ ·Õ ÁÒ¶Ö§ ·Õ ¨Ø´µèÍ ¹Ñ ¹æ ¨Ò¡ÃÙ» ·Õ 4.16 ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§·Õ ¹éÍÂ·Õ ÊØ´ ¤×Í ¤èÒ 1.40 ´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð¶Í´ÃËÑÊ¢éÍÁÙÅâ´Â¡ÒÃÁÍ§ÂéÍ¹¡ÅÑºä»µÒÁàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè·Õ ÁÒ¶Ö§¨Ø´µèÍ ·Õ ÁÕ¤èÒàÁµÃÔ¡àÊé¹·Ò§à·èÒ¡Ñº 1.40 «Ö §¨Ð¾ºÇèÒ ¤èÒ»ÃÐÁÒ³¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{âk }

·Õ ÊÍ´¤ÅéÍ§

¡ÑºàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè¹Õ ¤×Í

{âk } = {â0 , â1 , â2 , â3 } = {−1, −1, 1, −1} «Ö §ÁÕ¤èÒµÃ§¡ÑºÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak }

µÃÇ¨ËÒÇÕà·ÍÃìºÔã¹µÑÇÍÂèÒ§¢éÍ¹Õ ¨Ö§äÁèÁÕ¢éÍ¼Ô´¾ÅÒ´à¡Ô´¢Ö ¹

4.4.1

ÊÃØ»Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ð·Ó§Ò¹ä´é ÍÂèÒ§ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡·Õ ÊØ´ ¡ç µèÍàÁ× Í Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³ Ãº¡Ç¹·Õ á½§ÍÂÙèã¹¢éÍÁÙÅ·Õ ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹ à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN) [15] ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ä´é ÁÒ¨Ò¡ÊÁÁØµÔ°Ò¹·Õ ÇèÒ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

H(D)

·ÒÃìà¡çµáºº PR PR4

[1 0

EPR4 EEPR4

−1]

[1 1

−1 −1]

[1 2 0

−2 −1]

Ë¹èÇÂ¤ÇÒÁ¨Ó

¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´

(1 − D)(1 + D)

22 = 4

(1 − D)(1 + D)2

23 = 8

(1 − D)(1 + D)3

24 = 16

Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔà» ¹ÊÑÒ³Ãº¡Ç¹áººà¡ÒÊì ÊÕ¢ÒÇáºººÇ¡ Ë¹éÒ·Õ ËÅÑ¡ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¤×Í ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ â´ÂãËé ÁÕ ¤èÒ¤ÇÒÁ¹èÒ¨Ðà» ¹ ¢Í§ ¢éÍ ¼Ô´¾ÅÒ´ÅÓ´Ñº (probability of sequence error) ¹éÍÂ·Õ ÊØ´ áÅÐâ´Â·Ñ Çä»¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨Ã µÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð¢Ö ¹ÍÂÙè¡Ñº¨Ó¹Ç¹Ê¶Ò¹Ð·Õ ãªéã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ ´Ñ§áÊ´§ã¹µÒÃÒ§·Õ 4.2 ¨Ð¾ºÇèÒ àÁ× Í ·ÒÃìà¡çµ ·Õ ãªé ÁÕ ¨Ó¹Ç¹á·ç» (ËÃ×Í Ë¹èÇÂ¤ÇÒÁ¨Ó) ÁÒ¡¢Ö ¹ ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¡ç ¨ÐÁÒ¡¢Ö ¹ à¹× Í§¨Ò¡ ¨Ó¹Ç¹Ê¶Ò¹Ð·Õ ãªé ã¹á¼¹ÀÒ¾à·ÃÅÅÔ ÊÁÕ ÁÒ¡¢Ö ¹ ÍÂèÒ§äÃ¡çµÒÁ àÁ× Í ¤ÇÒÁ¨Ø ¢éÍÁÙÅ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§¢Ö ¹ ·ÒÃìà¡çµ·Õ ¨Ð¹ÓÁÒãªé¡ç¤ÇÃ·Õ ¨ÐµéÍ§ÁÕ¨Ó¹Ç¹á·ç»ÁÒ¡¢Ö ¹ à¾× Í·ÓãËé¼Å µÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§·ÒÃìà¡çµ ÊÍ´¤ÅéÍ§¡Ñº ¼ÅµÍºÊ¹Í§àªÔ§ ¤ÇÒÁ¶Õ ¢Í§ªèÍ§ÊÑÒ³ ´Ñ§¹Ñ ¹ã¹ ¡ÒÃ¾Ô¨ÒÃ³ÒÇèÒ ¨Ð¹Ó·ÒÃìà¡çµ ·Õ ÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡ÁÒãªé §Ò¹ËÃ×Í äÁè ¹Ñ ¹ ¨ÐµéÍ§»ÃÐ¹Õ»ÃÐ¹ÍÁÃÐËÇèÒ§ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ¨Ðä´éÃÑº áÅÐ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

4.5

ÊÃØ»·éÒÂº·

à·¤¹Ô¤ PRML à» ¹ ¡ÒÃãªé §Ò¹ÃèÇÁ¡Ñ¹ ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃì áºº PR áÅÐÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ «Ö § à» ¹·Õ ¹ÔÂÁãªé§Ò¹¡Ñ¹ÁÒ¡ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ÊÒàËµØË¹Ö §ÍÒ¨¨Ðà» ¹ à¾ÃÒÐÇèÒÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¶×Íä´éÇèÒà» ¹Ç§¨ÃµÃÇ¨ËÒ¢éÍÁÙÅ·Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡ â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í Í§¤ì »ÃÐ¡Íº¢Í§ÊÑ Ò³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÁÕ ÅÑ¡É³Ðà» ¹ ÊÑÒ³ Ãº¡Ç¹áººà¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ ËÅÑ¡ ¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐÍÂÙè º¹¾× ¹ °Ò¹¢Í§á¼¹ ÀÒ¾à·ÃÅÅÔÊ«Ö §ÍÒ¨¨ÐÊÃéÒ§ä´é¨Ò¡à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ áÅÐâ´Â·Ñ Çä»áÅéÇ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ

4.6.

ààºº½ ¡ËÑ´·éÒÂº·

ÇÕà·ÍÃìºÔ¨Ð¢Ö ¹ÍÂÙè¡Ñº¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´·Õ µéÍ§ãªéã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ «Ö §¨Ó¹Ç¹Ê¶Ò¹Ð·Õ ãªéã¹á¼¹ ÀÒ¾à·ÃÅÅÔÊ¨Ð¢Ö ¹ÍÂÙè¡Ñº ¨Ó¹Ç¹¤èÒ·Õ à» ¹ä»ä´é·Ñ §ËÁ´¢Í§¢éÍÁÙÅÍÔ¹¾Øµ áÅÐË¹èÇÂ¤ÇÒÁ¨Ó¢Í§·ÒÃìà¡çµ ´Ñ§¹Ñ ¹ ¡ÒÃ¨Ð¹Ó·ÒÃìà¡çµ ã´ÁÒãªé §Ò¹ã¹ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ¨ÐµéÍ§»ÃÐ¹Õ»ÃÐ¹ÍÁÃÐËÇèÒ§»ÃÐÊÔ·¸ÔÀÒ¾ ¢Í§ÃÐºº·Õ ¨Ðä´éÃÑº áÅÐ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

4.6

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§Í¸ÔºÒÂ¢éÍáµ¡µèÒ§ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃìáºº¼ÅµÍºÊ¹Í§àµçÁ (full response) áÅÐáºº¼Å µÍºÊ¹Í§ºÒ§ÊèÇ¹ (partial response) 2. ¡ÓË¹´ãËé¢éÍÁÙÅÍÔ¹¾Øµ

ak ∈ {−1, 1}

¨§ÇÒ´á¼¹ÀÒ¾ºÅçÍ¡ (block diagram), à¤Ã× Í§Ê¶Ò¹Ð

¨Ó¡Ñ´ (FSM), áÅÐá¼¹ÀÒ¾à·ÃÅÅÔÊ (Trellis diagram) ¢Í§ªèÍ§ÊÑÒ³ 2.1)

H(D) = 1 − 0.5D

2.2)

H(D) = 1 + 2D + D2

2.3)

H(D) = 1 − D3

2.4)

H(D) = 1 + 3D + 3D2 + D3

3. ¨Ò¡áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ» ·Õ 4.9 ¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

−1,

1} ¶Ù¡ Êè§ ¼èÒ¹ªèÍ§ÊÑÒ³

−0.4,

0.1, 0.7,

−0.3,

H(D)

{ak }

«Ö § ¶Ù¡ Ãº¡Ç¹´éÇÂÊÑÒ³Ãº¡Ç¹

0.4} ¨§¶Í´ÃËÑÊ¢éÍÁÙÅ

{yk }

µèÍä»¹Õ

{1, −1,

{nk }

{0.5,

â´ÂãªéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÓËÃÑºªèÍ§

ÊÑÒ³µèÍä»¹Õ 3.1)

H(D) = 1 + 2D + D2

3.2)

H(D) = 1 − D2

4. ¨Ò¡áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ» ·Õ 4.9 ¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ 0} ¶Ù¡Êè§¼èÒ¹ªèÍ§ÊÑÒ³ 0.2, 0.6,

−0.4, −0.3,

ÊÑÒ³µèÍä»¹Õ

H(D)

«Ö §¶Ù¡Ãº¡Ç¹´éÇÂÊÑÒ³Ãº¡Ç¹

0.5} ¨§¶Í´ÃËÑÊ¢éÍÁÙÅ

{yk }

{ak }

{nk }

{1,

0, 1,

{0.3, −0.5,

â´ÂãªéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÓËÃÑºªèÍ§

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

4.1)

H(D) = 1 + 3D + 3D2 + D3

4.2)

H(D) = 1 + D − D2 − D3

º··Õ 5

¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ËÅÑ¡¡ÒÃÇÔà¤ÃÒÐËì àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´ (error event) «Ö § à» ¹ ¡ÒÃ¤é¹ËÒÃÙ»áºº ¢Í§¢éÍ¼Ô´¾ÅÒ´·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ áÅÐ àÁ× Í ÊÒÁÒÃ¶ÇèÒ ¢éÍ¼Ô´¾ÅÒ´ÃÙ»áººã´·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ ¹Ñ¡ÍÍ¡áººÃÐºº¡ç ÊÒÁÒÃ¶·Õ ¨Ð·Ó¡ÒÃÍÍ¡áºº ÃËÑÊ RLL (run length limited)

[9] ËÃ×Í Ç§¨Ãà¢éÒÃËÑÊ¡èÍ¹

(precoder) [47] à¾× Íãªéà¢éÒÃËÑÊ¢éÍÁÙÅ

¢èÒÇÊÒÃ¡èÍ¹·Õ ¨Ð·Ó¡ÒÃà¢ÕÂ¹Å§ä»ã¹Ê× ÍºÑ¹·Ö¡ à¾× ÍËÅÕ¡àÅÕ Â§¡ÒÃà¡Ô´¢éÍ¼Ô´¾ÅÒ´àËÅèÒ¹Ñ ¹ÃÐËÇèÒ§¡ÒÃ ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ «Ö § ¨ÐÊè§ ¼Å·ÓãËé »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººã¹ÃÙ» ¢Í§ÍÑµÃÒ¢éÍ ¼Ô´¾ÅÒ´ºÔµ (BER) ¹éÍÂÅ§ÁÒ¡ ¹Í¡¨Ò¡¹Õ ¶éÒ·ÃÒºÇèÒ¢éÍ¼Ô´¾ÅÒ´ÃÙ»áººã´·Õ à¡Ô´¢Ö ¹ºèÍÂã¹ÃÐºº ¡çÊÒÁÒÃ¶·Õ ¨Ð¹Ó¢éÍÁÙÅ¹Õ ÁÒãªéã¹¡ÒÃÇÔà¤ÃÒÐËìáÅÐà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§·ÒÃìà¡çµáººµèÒ§æ ä´é â´Âãªé ¾ÒÃÒÁÔàµÍÃì ·Õ àÃÕÂ¡ÇèÒ SNR »ÃÐÊÔ·¸Ô¼Å (e ective SNR) [48] «Ö § ÁÕ ¼ÅÅÑ¾¸ì à·ÕÂºà·èÒ ¡Ñº ¡ÒÃ ãªé¾ÒÃÒÁÔàµÍÃì BER ã¹¡ÒÃà»ÃÕÂºà·ÕÂº áµèãªéàÇÅÒã¹¡ÒÃ¤Ó¹Ç³ËÒ¤èÒ SNR »ÃÐÊÔ·¸Ô¼Å¹Õ ¹éÍÂ¡ÇèÒ ÁÒ¡ ´Ñ§ÃÒÂÅÐàÍÕÂ´·Õ ¨ÐÍ¸ÔºÒÂµèÍä»ã¹º·¹Õ

5.1

º·¹Ó

µÒÁ·Õ Í¸ÔºÒÂã¹ËÑÇ¢éÍ·Õ 4.3 ¾ºÇèÒÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð·Ó§Ò¹ÍÂÙèº¹¾× ¹°Ò¹¢Í§á¼¹ÀÒ¾à·ÃÅÅÔÊ (trellis diagram) «Ö §ã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅºÒ§¤ÃÑ § ÁÕ¤ÇÒÁà» ¹ä»ä´é·Õ ¨Ðà¡Ô´àËµØ¡ÒÃ³ìµÒÁÃÙ»·Õ 5.1 91

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

D F #1

-1

Error 0 sequence

-2

ÃÙ»·Õ 5.1: µÑÇÍÂèÒ§¡ÒÃ·Ó§Ò¹ÀÒÂã¹à·ÃÅÅÔÊ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¹Ñ ¹¤×Í ã¹¢³Ð·Õ ·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ¼èÒ¹á¼¹ÀÒ¾à·ÃÅÅÔÊ ¨¹ÊÔ ¹ÊØ´ ÅÓ´Ñº ¢éÍÁÙÅ ·Õ ä´é ÃÑº »ÃÒ¡®ÇèÒ àÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè (survivor path) ·Õ ´Õ ·Õ ÊØ´ à» ¹ ä»µÒÁÃÙ» ·Õ 5.1 ¡ÅèÒÇ¤×Í àÁ× Í ¤Ó¹Ç³ËÒ¤èÒ àÁµÃÔ¡àÊé¹·Ò§ (path metric) ·Õ ¨Ø´ E à¾× Í·Ó¡ÒÃàÅ×Í¡àÊé¹·Ò§·Õ ´Õ·Õ ÊØ´·Õ ÁÒ¶Ö§¨Ø´ E ¾ºÇèÒÁÕàÊé¹·Ò§ 2 àÊé¹·Ò§ ¤×Í àÊé¹·Ò§ #1 (àÊé¹·Ò§ ABCEF) áÅÐàÊé¹·Ò§ #2 (àÊé¹·Ò§ ABDEF) ·Õ ÁÕ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§ ³ ¨Ø´ E à·èÒ¡Ñ¹ (àÊé¹·Ò§·Ñ §ÊÍ§ÁÕ¤ÇÒÁà» ¹ä»ä´éà·èÒ¡Ñ¹·Õ ¨Ð¶Ù¡àÅ×Í¡â´ÂÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ) à¾ÃÒÐ©Ð¹Ñ ¹ ã¹¡Ã³Õ ¹Õ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÒÁÒÃ¶·Õ ¨ÐµÑ´ÊÔ¹ã¨àÅ×Í¡àÊé¹·Ò§ã´¡çä´é à¾× Í ãªé à» ¹ ÊèÇ¹Ë¹Ö § ¢Í§àÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè ·Õ ´Õ ·Õ ÊØ´ ÊÓËÃÑº ¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ µÑÇÍÂèÒ§àªè¹ ¶éÒ Ç§¨ÃµÃÇ¨ËÒ ÇÕà·ÍÃìºÔàÅ×Í¡àÊé¹·Ò§ #1 ¡ç¨Ðä´é¶Í´ÃËÑÊ¢éÍÁÙÅä´éà» ¹ àÊé¹·Ò§ #2 ¡ç¨Ðä´é¼ÅÅÑ¾¸ìà» ¹ ¨ÃÔ§ ¤×Í

{−1,

¢éÍÁÙÅà» ¹

{−1,

−1, 1, 1,

{−1,

−1, −1,

−1,

1, 1,

−1,

{−1,

−1,

−1, −1,

1, 1} áµè¶éÒàÅ×Í¡

1, 1} ´Ñ§¹Ñ ¹¶éÒÊÁÁØµÔÇèÒ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

1, 1} ¡çËÁÒÂ¤ÇÒÁÇèÒ âÍ¡ÒÊ·Õ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð¶Í´ÃËÑÊ 1, 1} ¡çÁÕ¤ÇÒÁà» ¹ä»ä´éÊÙ§ (ËÃ×Íã¹·Ò§¡ÅÑº¡Ñ¹) à¾ÃÒÐ©Ð¹Ñ ¹

¶éÒ¹ÓàÍÒÅÓ´Ñº¢éÍÁÙÅ·Ñ §ÊÍ§ (ÅÓ´Ñº·Õ #1 áÅÐ #2) ÁÒÅº¡Ñ¹ àªè¹ ÅÓ´Ñº¢éÍÁÙÅ #1 Åº´éÇÂÅÓ´Ñº¢éÍÁÙÅ #2 ¡ç ¨Ðä´é ¼ÅÅÑ¾¸ì à» ¹

{0,

−2,

0, 0, 0} ËÃ×Í ¶éÒ ¹ÓàÍÒÅÓ´Ñº ¢éÍÁÙÅ #2 Åº´éÇÂÅÓ´Ñº

5.2.

¤ÇÒÁËÁÒÂ¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

W(D) A(D)

H(D)

X(D)

Y(D)

Viterbi detector

Aˆ ( D )

ÃÙ»·Õ 5.2: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ GPR áººÊÁÁÙÅ

¢éÍÁÙÅ #1 ¡ç¨Ðä´é¼ÅÅÑ¾¸ìà» ¹

{2, −2, 2}

{0,

0, 2,

−2,

2, 0, 0, 0} ´Ñ§¹Ñ ¹ ¼ÅÅÑ¾¸ì·Õ ä´é

{−2,

−2}

ËÃ×Í

¨ÐàÃÕÂ¡¡Ñ¹ ÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ (error sequence) [15, 49, 50] «Ö § àÍÒäÇé ãªé ã¹¡ÒÃ

¤Ó¹Ç³ËÒàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº ¡ÒÃÇÔà¤ÃÒÐËì àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¨ÐªèÇÂ·ÓãËé ·ÃÒºÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ ÃÙ»áººã´·Õ ¨ÐÊè§ ¼Å¡ÃÐ·º·ÓãËé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ à¡Ô´ ¤ÇÒÁÊÑºÊ¹ã¹ÃÐËÇèÒ§·Õ ·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ (à¡Ô´ »ÃÒ¡®¡ÒÃ³ìµÒÁÃÙ»·Õ 5.1) ´Ñ§¹Ñ ¹ ¶éÒÊÒÁÒÃ¶·Õ ¨ÐËÅÕ¡àÅÕ Â§¡ÒÃÊè§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾ØµÃÙ»áººàËÅèÒ¹Ñ ¹ à¢éÒä»ã¹ÃÐººä´é ¡ç¨ÐªèÇÂ·ÓãËéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔà¡Ô´¢éÍ¼Ô´¾ÅÒ´ã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ¹éÍÂÅ§ «Ö § ¨ÐÊè§¼Å·ÓãËé»ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐºº´ÕÂÔ §¢Ö ¹ [49, 50]

5.2

¤ÇÒÁËÁÒÂ¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

áºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµã¹ÃÙ»·Õ 3.2 ÊÒÁÒÃ¶·Õ ¨Ð¨Ñ´ãËéÍÂÙèã¹ÃÙ»¢Í§áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ GPR (generalized partial response) áººÊÁÁÙÅ ´Ñ§áÊ´§ã¹ÃÙ»·Õ 5.2 àÁ× Í ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ ã¹ÃÙ» ·Õ 3.2 ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡ ¾Ô¨ÒÃ³ÒÇèÒ à» ¹ ÊÑÒ³Ãº¡Ç¹

W (D)

·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒ

ÇÕà·ÍÃìºÔ µÒÁÃÙ»·Õ 5.2 ã¹·Ò§»¯ÔºÑµÔ (â´Âà©¾ÒÐÍÂèÒ§ÂÔ § ·Õ ¤ÇÒÁ¨Ø¢éÍÁÙÅ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ND ÊÙ§) ÊÑÒ³Ãº¡Ç¹

¹Õ ÁÑ¡¨ÐÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹áººÊÕ (colored noise) ·Õ ÁÕ¤èÒà©ÅÕ Âà·èÒ

¡Ñº¤èÒÈÙ¹ÂìáÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ¡Ñº

2 σw

¨Ò¡áºº¨ÓÅÍ§ã¹ÃÙ» ·Õ 5.2 ÊÑÒ³ÍÔ¹¾Øµ ·Õ ´éÒ¹¢Òà¢éÒ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ã¹ÃÙ»ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìã¹â´àÁ¹

ä´é´Ñ§¹Õ

Y (D) = A(D)H(D) + W (D) = X(D) + W (D) â´Â·Õ

A(D) ¤×Í ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ, H(D) =

¢Í§·ÒÃìà¡çµ,

X(D)

A(D)H(D)

PL−1

hk Dk

k=0

(5.1)

¤×Í ·ÒÃìà¡çµ,

L ¤×Í ¨Ó¹Ç¹á·ç»·Ñ §ËÁ´

¤×Í ¢éÍÁÙÅ àÍÒµì¾Øµ ªèÍ§ÊÑÒ³, áÅÐ

Ãº¡Ç¹áººÊÕ·Õ ÁÕ¤èÒà©ÅÕ Âà·èÒ¡Ñº¤èÒÈÙ¹Âì áÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ¡Ñº ãËé ¾Ô¨ÒÃ³ÒÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ 2 áºº ¤×Í

A1 (D)

áÅÐ

W (D)

¤×Í ÊÑÒ³

2 σw

A2 (D)

«Ö § à» ¹ ÅÓ´Ñº ¢éÍÁÙÅ ·Õ ·ÓãËé

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ à¡Ô´ ¤ÇÒÁÊÑºÊ¹ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ÁÒ¡·Õ ÊØ´ â´Â·Õ ÊÁÒªÔ¡ áµèÅÐ µÑÇã¹ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾ØµÁÕ¤èÒ·Õ à» ¹ä»ä´é ¤×Í

{−1, 1}

´Ñ§¹Ñ ¹ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ÊÍ´¤ÅéÍ§¡Ñº

àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ ¨Ð¹ÔÂÒÁâ´Â

εa (D) = A1 (D) − A2 (D) àÁ× Í ÊÁÒªÔ¡áµèÅÐµÑÇã¹

εa (D)

à» ¹ÊÁÒªÔ¡¢Í§

{−2,

(5.2)

0, 2} ¶éÒ¡ÓË¹´ãËéÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾ØµÁÕ

ÃÙ»¢Í§¾ËØ¹ÒÁ (polynomial) ¤×Í

εa (D) =

p−1 X

εa,k Dk

k=0

= εa,0 + εa,1 D + · · · + εa,p−1 Dp−1

(5.3)

ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§ (valid input error sequence) ¨ÐµéÍ§ÊÍ´¤ÅéÍ§¡Ñº ¤Ø³ÊÁºÑµÔ 2 ¢éÍ ´Ñ§µèÍä»¹Õ

1) ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¾¨¹ìáÃ¡áÅÐ¾¨¹ìÊØ´·éÒÂ¢Í§

áÅÐ

εa (D)

µéÍ§ÁÕ¤èÒäÁèà·èÒ¡Ñº¤èÒÈÙ¹Âì ¹Ñ ¹¤×Í

εa,0 6=

εa,p−1 6= 0

2) ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

εa (D)

·Õ ¶Ù¡µéÍ§¨ÐµéÍ§äÁè Á¤ Õ èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ·Õ ÁÕ ¤èÒ à·èÒ ¡Ñº ¤èÒ ÈÙ¹Âì ã¹

L−1

µÑÇ ÁÔ©Ð¹Ñ ¹áÅéÇ ¼ÅÅÑ¾¸ì·Õ

5.2.

¤ÇÒÁËÁÒÂ¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

{ 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 1 -1 1 } A2 ( D ) = { 1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 1 1 -1 1 1 } A1 ( D ) =

ε a ( D) =

{ 0 2 -2 2 0 0 2 -2 0 2 0 0 2 -2 0 0 -2 2 -2 0 } ÃÙ»·Õ 5.3: µÑÇÍÂèÒ§¡ÒÃ¤Ó¹Ç³ËÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

àÁ× Í ä´é ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ ¶Ù¡µéÍ§áÅéÇ àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´ (error event) ¢Í§ÃÐºº¨Ð ¹ÔÂÒÁâ´Â

εx (D) = εa (D)H(D)

µÑÇÍÂèÒ§·Õ 5.1

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR4,

H(D) = 1 − D2 ,

ÍÔ¹¾ØµÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº 20 ºÔµ â´Â·Õ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ Ë¹Ö §

−1, −1, −1,

1, 1,

−1,

−1, −1,

−1,

1, 1,

−1,

−1, −1,

−1, 1}

−1, −1,

(5.4)

A1 (D)

¶éÒ¡ÓË¹´ãËéÅÓ´Ñº¢éÍÁÙÅ

¤×Í

{1,

1, 1, 1,

áÅÐÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ ÊÍ§ 1, 1, 1, 1,

−1,

A2 (D)

1, 1,

¤×Í

{1,

1, 1} ¨§ËÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§·Ñ §ËÁ´·Õ ¾ºã¹ÃÐºº¹Õ

ÇÔ¸Õ ·Ó

àÃÔ Áµé¹ ãËé ¤Ó¹Ç³ËÒÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´

εa (D)

¨Ò¡ÊÁ¡ÒÃ (5.2) «Ö § ¨Ðä´é ¼ÅÅÑ¾¸ì ´Ñ§ áÊ´§

ã¹ÃÙ» ·Õ 5.3 ¨Ò¡¹Ñ ¹ ãËé ·Ó¡ÒÃËÒÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ ¶Ù¡µéÍ§ «Ö § ¨Ò¡ÃÙ» ·Õ 5.3 ¨Ðä´é ÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§ÁÕ·Ñ §ËÁ´ 4 µÑÇ ¤×Í

{2, −2, 2},

{2, −2},

{2, −2, 2}

áÅÐ

{−2,

A1 (D) − A2 (D)

ËÃ×Í

A2 (D) − A1 (D)

áµè ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ ¨Ð¾Ô¨ÒÃ³Ò¨Ò¡

{2, −2, 0, 2}, 2,

−2}

{−2, 2, −2}

¶×Í ÇèÒ à» ¹ µÑÇ à´ÕÂÇ¡Ñ¹ à¹× Í§¨Ò¡¢Ö ¹ ÍÂÙè ¡Ñº ÇèÒ à¾ÃÒÐ©Ð¹Ñ ¹ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ

¶Ù¡µéÍ§ã¹ÃÐºº¨Ð¶×ÍÇèÒÁÕ·Ñ §ËÁ´ 3 áºº ¤×Í

{2, −2, 2},

{2, −2, 0, 2},

{2, −2}

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ËÃ×ÍÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ¤³ÔµÈÒÊµÃìã¹â´àÁ¹

2D3 ,

áÅÐ

ËÁÒÂàËµØ

2 − 2D

ä´é ¤×Í

2 − 2D + 2D2 , 2 − 2D +

µÒÁÅÓ´Ñº

¨ÐàËç¹ä´éÇèÒ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§

¢Ö ¹ÍÂÙè¡ÑºÇèÒ¨Ð¾Ô¨ÒÃ³Ò¨Ò¡

µÑÇÍÂèÒ§·Õ 5.2

A1 (D) − A2 (D)

ËÃ×Í

εa (D)

¨ÐÁÕ¼ÅÅÑ¾¸ìà·èÒ¡Ñº

−εa (D)

·Ñ §¹Õ

{−1, 1}

à» ¹

A2 (D) − A1 (D)

·Õ ·ÃÒº¡Ñ¹ÇèÒ ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ (longitudinal recording) ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¤×Í ¤Ó¹Ç³ËÒàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¹Õ àÁ× ÍÃÐººãªé·ÒÃìà¡çµáºº PR4,

ÇÔ¸Õ·Ó

¨Ò¡·Õ â¨·Âì¡ÓË¹´ãËé ¨Ðä´éÇèÒ

εa (D) = 2 − 2D + 2D2

{2, −2, 2}

[19] ¨§

H(D) = 1 − D2

´Ñ§¹Ñ ¹ àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

εx (D)

ÊÒÁÒÃ¶ËÒä´é¨Ò¡ÊÁ¡ÒÃ (5.4) ¹Ñ ¹¤×Í

εx (D) = εa (D)H(D) = (2 − 2D + 2D2 )(1 − D2 ) = 2 − 2D + 2D3 − 2D4 à¾ÃÒÐ©Ð¹Ñ ¹ àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ ·Õ ãªé ·ÒÃìà¡çµ áºº PR4 ¤×Í

εx (D) = 2 − 2D + 2D3 − 2D4

µÑÇÍÂèÒ§·Õ 5.3

{−1, 1}

à» ¹

·Õ ·ÃÒº¡Ñ¹ ÇèÒ ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § (perpendicular recording) ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ à¡Ô´¢Ö ¹ºèÍÂã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¤×Í ¤Ó¹Ç³ËÒàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¹Õ àÁ× ÍÃÐººãªé·ÒÃìà¡çµáºº PR2,

ÇÔ¸Õ ·Ó

¨Ò¡·Õ â¨·Âì ¡ÓË¹´ãËé ¨Ðä´é ÇèÒ

εa (D) = 2 − 2D

{2, −2}

[18] ¨§

H(D) = 1 + 2D + D2

´Ñ§¹Ñ ¹ àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´

εx (D)

5.3.

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´

ÊÒÁÒÃ¶ËÒä´é¨Ò¡ÊÁ¡ÒÃ (5.4) ¹Ñ ¹¤×Í

εx (D) = εa (D)H(D) = (2 − 2D)(1 + 2D + D2 ) = 2 + 2D − 2D2 − 2D3 à¾ÃÒÐ©Ð¹Ñ ¹ àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ·Õ ãªé·ÒÃìà¡çµáºº PR2 ¤×Í =

εx (D)

2 − 2D + 2D3 − 2D4

5.3

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´

¨Ò¡ÃÙ» ·Õ 5.2 ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´¢Í§ÊÑÒ³·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ËÃ×Í ·Õ àÃÕÂ¡¡Ñ¹ ÇèÒ àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ (error event) ¢Í§ÃÐºº ¤×Í

εx (D) = [A1 (D) − A2 (D)] H(D) = X1 (D) − X2 (D)

(5.5)

¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ â´Âãªé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡ Í¸ÔºÒÂâ´Âãªé ÃÙ»ÀÒ¾ÊÍ§ÁÔµÔ µÒÁÃÙ»·Õ 5.4 àÁ× Í

X1 (D)

¤×Í ÊÑÒ³·Õ ¶Ù¡µééÍ§ áÅÐ

X2 (D)

X2 (D)

ÃÐËÇèÒ§

ÁÕ¤èÒÁÒ¡¡ÇèÒ

X1 (D)

áÅÐ

d/2

â´Â·Õ

¤×Í ÊÑÒ³·Õ ¼Ô´¾ÅÒ´ Ç§¨ÃµÃÇ¨ËÒ

W (D) (¹Ñ ¹¤×Í ϕ) ã¹·ÔÈ·Ò§¨Ò¡ X1 (D)

¤×Í ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ (Euclidean distance)

εx (D)

·Õ ÇÑ´

X2 (D)

εx (D) =

n X

εx,k Dk

k=0

= εx,0 + εx,1 D + · · · + εx,n Dn ´Ñ§¹Ñ ¹ÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§ (squared Euclidean distance) ¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´,

(5.6)

d2 {εa (D)},

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Y ( D) W ( D)

X 1 ( D)

X 2 ( D)

d Decision boundary ÃÙ»·Õ 5.4: ÀÒ¾ÊÍ§ÁÔµÔáÊ´§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅâ´ÂãªéÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¨Ð¶Ù¡¹ÔÂÒÁãËéÁÕ¤èÒà·èÒ¡Ñº ¤èÒ¾ÅÑ§§Ò¹¢Í§

εx (D)

[15] ¹Ñ ¹¤×Í

d2 {εa (D)} = kεx (D)k2 n X ε2x,k = k=0

= ε Tε â´Â·Õ

k·k

·Õ ÁÕÊÁÒªÔ¡

¤×Í ¡ÒÃËÒ¤èÒ¹ÍÃìÁ (norm) áÅÐ

¤×Í àÇ¡àµÍÃìá¹ÇµÑ §¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

n+1 µÑÇ µÑÇÍÂèÒ§àªè¹ ¶éÒ εx (D) = 2−3D+4D3 −5D4

µÑÇÍÂèÒ§·Õ 5.4

(5.7)

¨Ðä´éÇèÒ

εx (D)

ε = [2, −3, 0, 4, −5]T

¨Ò¡¢éÍÁÙÅ ã¹µÑÇÍÂèÒ§·Õ 5.3 ¨§¤Ó¹Ç³ËÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ¡ÓÅÑ§ ÊÍ§¢Í§àËµØ¡ÒÃ³ì

¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº

ÇÔ¸Õ·Ó

¨Ò¡µÑÇÍÂèÒ§·Õ 5.3 ¨Ðä´éÇèÒ

2D + 2D3 − 2D4

εa (D) = 2 − 2D, H(D) = 1 + 2D + D2 ,

áÅÐ

εx (D) = 2 −

d2 {εa (D)}

ËÒä´é¨Ò¡ÊÁ¡ÒÃ (5.7) ´Ñ§µèÍä»¹Õ

d {εa (D)} =

n X i=0

ε2x,i = (2)2 + (−2)2 + (0)2 + (2)2 + (−2)2 = 16

ÊÒÁÒÃ¶

5.4.

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å

ËÃ×ÍÍÒ¨¨ÐËÒä´é¨Ò¡

d2 {εa (D)} = ε Tε = [2, −2, 0, 2, −2] · [2, −2, 0, 2, −2]T = 16 à¾ÃÒÐ©Ð¹Ñ ¹ ÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

εx (D) = 2 − 2D + 2D3 − 2D4

ÁÕ¤èÒà·èÒ¡Ñº 16

¶éÒÊÁÁØµÔÇèÒ ÊÑÒ³Ãº¡Ç¹ ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹¢Í§

W (D)

à» ¹ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºººÇ¡ (AWGN) ¨Ðä´éÇèÒ

εx (D)

εa (D)

·Õ à» ¹¼Å

·Õ ÁÕ¤èÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§·Õ ¹éÍÂÊØ´ [15] «Ö §¹ÔÂÒÁâ´Â

d2min =

min

valid εa (D)

£ 2 ¤ d {εa (D)}

(5.8)

à¾ÃÒÐ©Ð¹Ñ ¹ ¤ÇÒÁ¹èÒ¨Ðà» ¹ ¢Í§¢éÍ¼Ô´¾ÅÒ´ (probability of error) ËÃ×Í BER ·Õ ´éÒ¹¢ÒÍÍ¡¢Í§ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÒÁÒÃ¶»ÃÐÁÒ³¤èÒä´é´Ñ§¹Õ [15]

µ Pe ≈ K1 Q àÁ× Í

¤×Í ¤èÒ¤§µÑÇ·Õ äÁè¢Ö ¹¡Ñº¤èÒ

σw

áÅÐ

Q(x) =

dmin 2σw

√1 2π

R∞ x

(5.9)

e−

u2 2

du ´Ñ§¹Ñ ¹ ã¹¡Ã³Õ·Õ Í§¤ì»ÃÐ¡Íº

¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔà» ¹ÊÑÒ³Ãº¡Ç¹ AWGN ¤èÒ ÃÐÂÐ·Ò§ ÂØ¤ÅÔ´·Õ ¹éÍÂÊØ´

dmin

ÊÒÁÒÃ¶·Õ ¨Ð¹ÓÁÒãªéã¹¡ÒÃ»ÃÐÁÒ³¤èÒ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº

ä´é â´Â·Õ ¼ÅÅÑ¾¸ì ·Õ ä´é ¨ÐÁÕ ¤ÇÒÁ¹èÒ àª× Í¶×Í ÁÒ¡ÂÔ § ¢Ö ¹ ¶éÒ ÃÐººÁÕ àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´·Õ â´´à´è¹ (dominant error event) à¾ÕÂ§µÑÇà´ÕÂÇ ¹Ñ ¹¤×ÍÁÕ¤èÒ

d2 {εa (D)} ¹éÍÂÁÒ¡ àÁ× Íà·ÕÂº¡Ñº¤èÒ d2 {εa (D)}

¢Í§ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´Í× ¹æ ·Õ ¾ºã¹ÃÐºº

5.4

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å

¶éÒÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

W (D)

à» ¹ÊÑÒ³Ãº¡Ç¹áººÊÕ («Ö §ã¹

·Ò§»¯ÔºÑµÔáÅéÇÁÑ¡¨Ðà» ¹àªè¹¹Õ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §·Õ ND ÊÙ§) ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´¨Ð¢Ö ¹ÍÂÙè

100

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

dmin

X1 (D)

ä»ÂÑ§

X2 (D)

W (D)

àÇ¡àµÍÃì á¹ÇµÑ § ¢Í§ÊÑÒ³Ãº¡Ç¹ ¨Ðä´éÇèÒ

W (D)

(5.10)

εx (D)

·Õ ÁÕ ÊÁÒªÔ¡

n+1

µÑÇ àªè¹ ¶éÒ

µÑÇ, áÅÐ

W (D) = 0.82 −

ÊÒÁÒÃ¶ËÒä´é¨Ò¡ [48]

σϕ2 = E[ϕ2 ] · T T T ¸ (w ε ) (w ε ) = E kεεk2 £ ¤ ε T E wwT ε = ε Tε T ε Rwwε = ε Tε E[·]

¤×Í

w = [0.82, −1.3, 0, 0.2]T

´Ñ§¹Ñ ¹ ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹¢Í§

àÁ× Í

Å§º¹àÇ¡àµÍÃìË¹Ö §Ë¹èÇÂ (unit vector)

w Tε kεεk

¤×Í àÇ¡àµÍÃì á¹ÇµÑ § ¢Í§àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´

1.3D + 0.2D3

[48, 49]

¹Ñ ¹¤×Í

ϕ= àÁ× Í

deff {εa (D)}

ÊÓËÃÑº¡ÒÃ»ÃÐÁÒ³¤èÒ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº ¨Ò¡ÃÙ»·Õ 5.4 ¤èÒ

ÁÕ¤èÒà·èÒ¡Ñº¡ÒÃ©ÒÂ (projection) ÊÑÒ³Ãº¡Ç¹ ·Õ ÁÕ·ÔÈ·Ò§¨Ò¡

´Ñ§¹Ñ ¹

¨Ö§äÁèÊÒÁÒÃ¶¹ÓÁÒãªéã¹¡ÒÃ»ÃÐÁÒ³¤èÒ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´·Õ à¡Ô´¢Ö ¹ã¹

ÃÐººä´é ´Ñ§¹Ñ ¹ ¨Ö§ä´éÁÕ¡ÒÃ¹Ó ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å (e ective distance) ÁÒãªéá·¹

εx (D), ϕ,

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ¤èÒ¤Ò´ËÁÒÂ (expectation operator),

(auto correlation matrix) ¢Í§

W (D)

ËÒä´é¨Ò¡

Rww (i, j) = E

â´Â·Õ ÊÁÒªÔ¡á¶Ç·Õ

"S−1 X

(5.11)

Rww

¤×Í àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì

áÅÐá¹ÇµÑ §·Õ

¢Í§àÁ·ÃÔ¡«ì

Rww

# wk−i wk−j ,

0 ≤ i, j ≤ n + 1

(5.12)

k=0 àÁ× Í

¤×Í ¤ÇÒÁÂÒÇ¢Í§ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

SNRevent {εa (D)},

{ak }

ã¹ [49] ¤èÒ SNR ¢Í§àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´,

¨Ð¹ÔÂÒÁâ´Â

SNRevent {εa (D)} =

d2 {εa (D)} 2 σw

(5.13)

5.4.

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å

áÅÐ SNR »ÃÐÊÔ·¸Ô¼Å,

101

SNReff ,

¢Í§àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ ¤×Í

d2 {εa (D)} σϕ2

SNReff {εa (D)} =

(5.14)

à¾× ÍãËéÊÒÁÒÃ¶»ÃÐÁÒ³¤èÒ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´·Õ à¡Ô´¢Ö ¹ã¹ÃÐººä´éÍÂèÒ§¹èÒàª× Í¶×ÍÁÒ¡ ¡ÇèÒ ¡ÒÃãªé ¾ÒÃÒÁÔàµÍÃì

dmin

µÒÁÊÁ¡ÒÃ (5.9) ¨Ö§ ä´é ÁÕ ¡ÒÃ¹ÔÂÒÁ¤èÒ ÃÐÂÐ·Ò§áººãËÁè ¢Ö ¹ ÁÒ·Õ àÃÕÂ¡

ÇèÒ ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å (e ective distance), á»Ã»ÃÇ¹

σϕ2

à¢éÒä»´éÇÂáÅéÇ ´Ñ§¹Ñ ¹ àÁ× Íá·¹¤èÒ

áÅéÇ ¨Ðà» ¹¼Å·ÓãËé

SNRevent {εa (D)}

deff {εa (D)}, d2 {εa (D)}

ÁÕ¤èÒà·èÒ¡Ñº

SNReff {εa (D)} =

«Ö § ¨ÐÃÇÁ¼Å¡ÃÐ·º¢Í§¤èÒ ¤ÇÒÁ

d2eff {εa (D)}

´éÇÂ

SNReff {εa (D)}

ã¹ÊÁ¡ÒÃ (5.13)

¹Ñ ¹¤×Í

d2eff {εa (D)} d2 {εa (D)} = 2 σw σϕ2

(5.15)

¨Ò¡ÊÁ¡ÒÃ (5.15) ¨Ðä´éÇèÒ ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§ (squared e ective distance) ÁÕ¤èÒà·èÒ¡Ñº

2 d2eff {εa (D)} = σw 2 = σw

d2 {εa (D)} σϕ2 (εεTε )2 ε T Rwwε

(5.16)

àªè¹à´ÕÂÇ¡Ñ¹ ¤èÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§·Õ ¹éÍÂÊØ´ ¨Ð¹ÔÂÒÁâ´Â

d2effmin =

min

valid εa (D)

¤ d2eff {εa (D)}

(5.17)

áÅÐ¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´ã¹ (5.9) ¨Ðà»ÅÕ Â¹ä»à» ¹ [15]

µ Pe ≈ K2 Q àÁ× Í

¤×Í ¤èÒ¤§µÑÇ·Õ äÁè¢Ö ¹¡Ñº¤èÒ

σw

deffmin 2σw

¨Ò¡¡ÒÃ·´ÅÍ§¾ºÇèÒ

(5.18)

deffmin

ÊÒÁÒÃ¶¹Óãªéã¹¡ÒÃ»ÃÐÁÒ³

¤èÒ ¤ÇÒÁ¹èÒ¨Ðà» ¹ ¢Í§¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐººä´é ÍÂèÒ§¹èÒ àª× Í¶×Í ÁÒ¡¡ÇèÒ ¡ÒÃãªé

deffmin

dmin

·Ñ §¹Õ à¹× Í§ÁÒ¨Ò¡

ä´éÃÇÁ¼Å¡ÃÐ·º·Õ à¡Ô´¨Ò¡ÊÑÒ³Ãº¡Ç¹áººÊÕäÇéáÅéÇ

µÑÇÍÂèÒ§·Õ 5.5

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ã¹ÃÙ» ·Õ 3.2 ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ áºº

á¹ÇµÑ § ·Õ ND = 2 áÅÐ SNR = 22 dB â´Â·Õ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

ak ∈ {−1, 1}

áÅÐ»ÃÒ¡®ÇèÒ·Ó

102

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ãËéä´é ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

−12.72}

{wk }

{−3.64, −4.34,

¶éÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

áºº PR2,

H(D) = 1 + 2D + D2

εa (D)

2.96,

−1.56, −3.70,

·Õ à¡Ô´¢Ö ¹ºèÍÂÃÐºº ¤×Í

0.80, 8.52,

{2, −2}

−3.76,

6.10,

áÅÐÃÐººãªé·ÒÃìà¡çµ

¨§¤Ó¹Ç³ËÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§

d2eff {εa (D)}

¢Í§

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

ÇÔ¸Õ·Ó

¨Ò¡·Õ â¨·Âì¡ÓË¹´ àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

εx (D)

¢Í§ÃÐºº¹Õ ËÒä´é¨Ò¡

εx (D) = εa (D)H(D) = (2 − 2D)(1 + 2D + D2 ) = 2 + 2D − 2D2 − 2D3 ¹Ñ ¹¤×Í

ε = [2, 2, −2, −2]T

¨Ò¡ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´

{wk }

·Õ ¡ÓË¹´ãËé ¨Ðä´é ÇèÒ àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì

Rww

ÊÒÁÒÃ¶ËÒä´é

¨Ò¡ÊÁ¡ÒÃ (5.12) «Ö §ÁÕ¤èÒà·èÒ¡Ñº



 34.33 −13.84

Rww

áÅÐ

6.13 −11.25

     −13.84 34.33 −13.84 6.13    =   6.13 −13.84 34.33 −13.84    −11.25 6.13 −13.84 34.33

2 = R σw ww (0, 0) = 34.33

´Ñ§¹Ñ ¹ ¤èÒ ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ ÊÍ§

d2eff {εa (D)}

ËÒä´é ¨Ò¡

ÊÁ¡ÒÃ (5.16) ¹Ñ ¹¤×Í

(εεTε )2 ε T Rwwε µ ¶ 256 = 34.33 430.48 = 20.41

2 d2eff {εa (D)} = σw

à¾ÃÒÐ©Ð¹Ñ ¹ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

(5.19)

εa (D) = {2, −2} ã¹ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §·Õ ãªé·ÒÃìà¡çµ

áºº PR2 ¨ÐÁÕ¤èÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§à·èÒ¡Ñº 20.41 Ë¹èÇÂ

5.5.

¼Å¡ÒÃ·´ÅÍ§

103

ËÅÑ§¨Ò¡¤Ó¹Ç³ËÒ¤èÒ

deffmin

ä´é áÅéÇ ´Ñ§¹Ñ ¹ ¤èÒ SNR »ÃÐÊÔ·¸Ô¼Å

¨Ð¹ÔÂÒÁâ´Â

SNReff =

SNReff

d2effmin (εεTε )2 = 2 σw ε T Rwwε

¨Ò¡¡ÒÃ·´ÅÍ§·Õ ¨ÐáÊ´§ã¹ËÑÇ¢éÍ·Õ 5.5 ¨Ð¾ºÇèÒ

SNReff

·Õ ÊÍ´¤ÅéÍ§¡Ñº

(5.20)

ÊÒÁÒÃ¶¹ÓÁÒãªéã¹¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸Ô

ÀÒ¾¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áººµèÒ§æ ä´é ÍÂèÒ§¹èÒ àª× Í¶×Í àªè¹à´ÕÂÇ¡Ñ¹ ¡Ñº ¡ÒÃãªé ¾ÒÃÒÁÔàµÍÃì BER ã¹ ¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº â´Â¼ÅÅÑ¾¸ì ·Õ ä´é ¨ÐÁÕ ¤ÇÒÁ¹èÒ àª× Í¶×Í ÁÒ¡ÂÔ § ¢Ö ¹ ¶éÒ ã¹ÃÐººÁÕ àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´·Õ â´´à´è¹ à¾ÕÂ§µÑÇ à´ÕÂÇà·èÒ¹Ñ ¹ ¹Ñ ¹¤×Í àÁ× Í ÃÐºº·Ó§Ò¹ ³ ÃÐ´Ñº SNR ·Õ ÊÙ§ à¾ÕÂ§¾Í àªè¹ àÁ× ÍÃÐººÁÕ BER

5.5

< 10−4

¼Å¡ÒÃ·´ÅÍ§

ã¹¡ÒÃ·´ÅÍ§à¾× Í ·Ó¡ÒÃÇÔà¤ÃÒÐËì àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç µÑ § (perepdicular recording) à·èÒ¹Ñ ¹ ÊÓËÃÑº¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ (longitudinal recording) ÊÒÁÒÃ¶ÈÖ¡ÉÒä´é¨Ò¡ [49] ãËé¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ÃÐººã¹ ÃÙ»·Õ 3.2 â´Â·Õ ÊÑÒ³ read back ¨Ðà» ¹ä»µÒÁÊÁ¡ÒÃ (3.26) ¹Ñ ¹¤×Í

p(t) =

S−1 X

bk g(t − kT + ∆tk ) + n(t)

(5.21)

k=0 àÁ× Í

bk = (ak − ak−1 )/2

Ê¶Ò¹ÐºÇ¡ËÃ×ÍÅº áÅÐ ·Õ

·Õ ÁÕ¨Ó¹Ç¹·Ñ §ËÁ´

¤×Í ºÔµ à»ÅÕ Â¹Ê¶Ò¹Ð (àÁ× Í

bk = 0

bk = ±1

¤×ÍäÁèÁÕ¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹Ð),

S = 4096

ºÔµ (1 à«¡àµÍÃì),

¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § µÒÁÊÁ¡ÒÃ (1.2),

n(t)

g(t)

ÊÍ´¤ÅéÍ§¡Ñº ¡ÒÃà»ÅÕ Â¹á»Å§

ak ∈ ±1

¤×Í ¢éÍÁÙÅÍÔ¹¾ØµºÔµµÑÇ

¤×Í ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð¢Í§ÃÐºº

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN)

·Õ ÁÕ¤ÇÒÁË¹Òá¹è¹Êà»¡µÃÑÁ¡ÓÅÑ§áººÊÍ§´éÒ¹à·èÒ¡Ñº

N0 /2,

áÅÐ

∆t

¤×Í ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì

¢Í§Ê× ÍºÑ¹·Ö¡ (media jitter noise) ·Õ ¶Ù¡¨ÓÅÍ§ãËéÁÕÅÑ¡É³Ðà» ¹ ¡ÒÃàÅ× Í¹µÓáË¹è§¢Í§¡ÒÃà»ÅÕ Â¹ Ê¶Ò¹ÐáººÊØèÁ «Ö §ÁÕ¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹áººà¡ÒÊìà«ÕÂ¹·Õ ÁÕ¤èÒà©ÅÕ Âà·èÒ¡Ñº¤èÒÈÙ¹Âì áÅÐ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ ¡Ñº

|bk |σj2

áÅÐ¶Ù¡ ¨Ó¡Ñ´ ãËé ÁÕ ¤èÒ äÁè à¡Ô¹

¨Ó¹Ç¹à»ÍÃìà«ç¹µì¢Í§ºÔµà«ÅÅì

|bk |

áÅÐ

¤×Í ¤èÒÊÑÁºÙÃ³ì¢Í§

T /2

àÁ× Í

σj

¨Ð¶Ù¡ ¡ÓË¹´à» ¹

104

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊÑÒ³ read back ¨Ð¶Ù¡ Êè§ ¼èÒ¹ä»ÂÑ§ Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó ºÑµà·ÍÃìàÇÔÃìµ ÍÑ¹´Ñº ·Õ 7 áÅÐ¶Ù¡ ·Ó

1/T

¡ÒÃªÑ¡ µÑÇÍÂèÒ§´éÇÂÍÑµÃÒ¤ÇÒÁ¶Õ à·èÒ ¡Ñº

â´ÂÊÁÁØµÔ ÇèÒ Ç§¨Ã¡ÒÃªÑ¡ µÑÇÍÂèÒ§ÁÕ ¡ÒÃà¢éÒ ¨Ñ§ËÇÐáºº

ÊÁºÙÃ³ì (perfect synchronization) ¨Ò¡¹Ñ ¹ ÅÓ´Ñº¢éÍÁÙÅ·Õ ä´é

{sk }

¨Ð¶Ù¡Êè§ä»ÂÑ§ÍÕ¤ÇÍäÅà«ÍÃì à¾× Í

»ÃÑº ÃÙ»ÃèÒ§¢Í§ÊÑÒ³ãËé à» ¹ ä»µÒÁ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ ¹Ñ ¹¤×Í ÍÕ¤ÇÍäÅà«ÍÃì ¨Ð¾ÂÒÂÒÁ·ÓãËé ÅÓ´Ñº ¢éÍÁÙÅàÍÒµì¾Øµ

{yk }

·Õ ä´éÁÕ¤èÒã¡Åéà¤ÕÂ§¡ÑºÅÓ´Ñº¢éÍÁÙÅ·Õ µéÍ§¡ÒÃ

µÃÇ¨ËÒÇÕà·ÍÃìºÔ¡ç¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ

{yk }

{dk }

ãËéÁÒ¡·Õ ÊØ´ ËÅÑ§¨Ò¡¹Ñ ¹ Ç§¨Ã

à¾× ÍËÒÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak }

·Õ à» ¹ä»ä´éÁÒ¡·Õ ÊØ´

ã¹¡ÒÃ·´ÅÍ§ ¤èÒ SNR ¨Ð¹ÔÂÒÁµÒÁÊÁ¡ÒÃ (3.27) ¹Ñ ¹¤×Í

Ã SNR = 10 log10

â´Â·Õ

Vp = g(∞) = 1

pulse) ³ àÇÅÒ

∞

Vp2 σ2

! (dB)

¤×Í ¢¹Ò´¢Í§ÊÑÒ³¾ÑÅÊì à»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È

áÅÐ

σ2

N0 /(2T )

¤×Í ¡ÓÅÑ§¢Í§ÊÑÒ³Ãº¡Ç¹

(isolated transition

n(t)

ã¹¡ÒÃ·´ÅÍ§¹Õ ·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì¨Ð¶Ù¡ÍÍ¡áºº·Õ ND = 2.5 áÅÐ SNR = 22 dB ³ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡ µèÒ§æ àªè¹

2, d2effmin , σw

áÅÐ

SNReff

σj

µÒÁ·Õ ¡ÓË¹´ÁÒãËé ÊèÇ¹¾ÒÃÒÁÔàµÍÃì

à» ¹µé¹ ¨Ð¶Ù¡¤Ó¹Ç³ËÒâ´Âãªé¢éÍÁÙÅà¾ÕÂ§ 1 à«¡àµÍÃì (4096

ºÔµ) ÊÓËÃÑº áµèÅÐ SNR áÅÐ ND ã¹·Õ ¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐ·ÒÃìà¡çµ ·Õ ¶Ù¡ ÍÍ¡áººâ´Âà§× Í¹ä¢ºÑ§¤Ñº áººâÁ¹Ô¡ (´ÙÃÒÂÅÐàÍÕÂ´ã¹ËÑÇ¢éÍ·Õ 3.2.1) áÅÐà¾× ÍãËé§èÒÂµèÍ¡ÒÃÍ¸ÔºÒÂ ÊÑÅÑ¡É³ì GPRn ¨Ðãªé á·¹·ÒÃìà¡çµáººâÁ¹Ô¡·Õ ÁÕ¨Ó¹Ç¹á·ç»à·èÒ¡Ñº

n á·ç» ¹Í¡¨Ò¡¹Õ

ã¹¡ÒÃ·´ÅÍ§ à¤Ã× Í§ËÁÒÂ − ¨Ð

ãªéá·¹¢éÍÁÙÅ −2, à¤Ã× Í§ËÁÒÂ + ¨Ðãªéá·¹¢éÍÁÙÅ +2, áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Ø¡µÑÇ¨ÐÁÕ¤Ø³ÊÁºÑµÔÊÁÁÒµÃ¡Ñ¹ ¹Ñ ¹¤×Í

5.5.1

εa (D)

εa (D) = −εa (D)

¡ÒÃÇÔà¤ÃÒÐËìÃÐÂÐ·Ò§·Õ ¹éÍÂÊØ´

¨Ò¡áºº¨ÓÅÍ§áÅÐà§× Í¹ä¢·Õ ¡ÓË¹´ãËé ¨Ðä´éÇèÒ ·ÒÃìà¡çµáºº GPR3 ·Õ ¶Ù¡ÍÍ¡áººÊÓËÃÑºÃÐºº¡ÒÃ ºÑ¹·Ö¡áººá¹ÇµÑ §·Õ ND = 2.5 áÅÐ

σj = 0%

¤×Í

H(D) = 1 + 1.3022D + 0.6623D2

¨Ò¡¹Ñ ¹

ãËé ãªé ·ÒÃìà¡çµ ¹Õ ã¹¡ÒÃ·Ó¡ÒÃ¨ÓÅÍ§ÃÐºº (system simulation) à¾× Í ¤Ó¹Ç³ËÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ¡ÓÅÑ§ ÊÍ§

d2 {εa (D)},

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§

d2eff {εa (D)},

áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

εa (D)

µèÒ§æ ·Õ à¡Ô´¢Ö ¹ ã¹ÃÐºº (·Õ ´éÒ¹¢ÒÍÍ¡¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ) ³ SNR = 22 dB «Ö §¨Ðä´éµÒÁ·Õ

5.5.

¼Å¡ÒÃ·´ÅÍ§

105

µÒÃÒ§·Õ 5.1: ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ¡ÓÅÑ§ ÊÍ§ áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

εa (D)

d2 {εa (D)},

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ ÊÍ§

d2eff {εa (D)},

¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáºº GPR3 ·Õ ND = 2.5 áÅÐ SNR =

22 dB

¤ÇÒÁÂÒÇ (ºÔµ) ¢Í§

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ (Euclidean distance)

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å (E ective distance)

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

¨Ó¹Ç¹¤ÃÑ §

εa (D)

·Õ à¡Ô´¢Ö ¹

¢éÍ¼Ô´¾ÅÒ´ 1

12.5375

7.7579

8.2764

d2eff

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

¨Ó¹Ç¹¤ÃÑ §

εa (D)

·Õ à¡Ô´¢Ö ¹

17.0522

127

6.7243

10.0266

8.7950

+ +

11.2688

+ +

9.3135

+ +

7.0754

+ 0 +

9.8321

+ + +

9.5535

+ 0 +

10.3507

+ + +

10.6952

+ + 0 +

10.8692

+ + + +

7.8234

+ 0 + 0 +

Í× ¹æ

127

áÊ´§ã¹µÒÃÒ§·Õ 5.1 ¶éÒãªéËÅÑ¡¤ÇÒÁ¨ÃÔ§·Õ ÇèÒ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ÁÕ¤èÒÃÐÂÐ·Ò§·Õ ¹éÍÂÊØ´¨Ðà» ¹ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ ÍÔ¹¾Øµ ·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ·Õ ÊØ´ ´Ñ§¹Ñ ¹ ¨Ò¡µÒÃÒ§·Õ 5.1 ¶éÒ ãªé ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ¡ÓÅÑ§ ÊÍ§ à¡³±ì ã¹¡ÒÃ¾Ô¨ÒÃ³Ò ¨Ðä´é ÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ ¤×Í

{

+ +} à¹× Í§¨Ò¡ ÁÕ ¤èÒ

d2 {εa (D)}

ãªéÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§ ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂ ¤×Í

+},

{

à» ¹

+ }, áÅÐ

à·èÒ ¡Ñº 7.7579, 8.2764, áÅÐ 8.7950 µÒÁÅÓ´Ñº áµè ¶éÒ

d2eff {εa (D)}

{ +}, {

{

d2 {εa (D)}

à» ¹à¡³±ìã¹¡ÒÃ¾Ô¨ÒÃ³Ò ¨Ðä´éÇèÒ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

+ 0 +}, áÅÐ

{

+ 0 + 0 +} à¹× Í§¨Ò¡ ÁÕ¤èÒ

d2eff {εa (D)}

à·èÒ¡Ñº 6.7243, 7.0754, áÅÐ 7.8234 µÒÁÅÓ´Ñº à¾× Íà» ¹¡ÒÃµÃÇ¨ÊÍº´ÙÇèÒ à¡³±ìã´ (ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ËÃ×ÍÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å) ÁÕ¤ÇÒÁ¹èÒàª× Í¶×Í ÁÒ¡¡ÇèÒ¡Ñ¹ ÊÓËÃÑºãªéã¹¡ÒÃ·Ó¹ÒÂÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂã¹ÃÐºº ¨Ö§ä´é·Ó¡ÒÃ¨ÓÅÍ§ ÃÐººÍÕ¡ ¤ÃÑ § Ë¹Ö § â´Â¡ÒÃÊè§ ¢éÍÁÙÅ ËÅÒÂæ à«¡àµÍÃì à¢éÒ ä»ã¹ÃÐºº (µÒÁáºº¨ÓÅÍ§ã¹ÃÙ» ·Õ 3.2) ·Õ

106

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

SNR = 22 dB ¨¹¡ÃÐ·Ñ § ¢éÍ¼Ô´¾ÅÒ´ (error) ÊÐÊÁ·Õ à¡Ô´ ·Ñ §ËÁ´ÁÕ à» ¹ ¨Ó¹Ç¹ 500 ºÔµ ¨Ò¡¹Ñ ¹ ·Ó¡ÒÃÇÔà¤ÃÒÐËìÇèÒ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾ØµáµèÅÐáººà¡Ô´¢Ö ¹·Ñ §ËÁ´¡Õ ¤ÃÑ § áÅÐàÁ× ÍÊÔ ¹ÊØ´¡ÒÃ·´ÅÍ§ ¨Ð¾ºÇèÒ ÃÐººÁÕ BER =

5.1945 × 10−4 ,

ºÔµ·Õ ¼Ô´¾ÅÒ´ÁÕ¨Ó¹Ç¹ 500 ºÔµ, áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

ÍÔ¹¾Øµ ·Ñ §ËÁ´ÁÕ ¨Ó¹Ç¹ 180 µÑÇ (ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ áµèÅÐáºº ÍÒ¨¨Ðà¡Ô´ ¢Ö ¹ ä´é ËÅÒÂ¤ÃÑ § ËÃ×Í ËÅÒÂµÑÇ) ¨Ò¡µÒÃÒ§·Õ 5.1 ¨Ð¾ºÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ ¤×Í +}, áÅÐ

{

+ 0 + 0 +} µÒÁÅÓ´Ñº «Ö § ÊÍ´¤ÅéÍ§¡Ñº ¡ÒÃãªé à¡³±ì

·Ó¹ÒÂ¼Å à¾ÃÒÐ©Ð¹Ñ ¹

d2eff {εa (D)}

{

+},

{

d2eff {εa (D)}

+ 0

ã¹¡ÒÃ

à¡Ô´¢Ö ¹ºèÍÂã¹ÃÐººä´é¶Ù¡µéÍ§ÁÒ¡¡ÇèÒ¡ÒÃãªé

d2 {εa (D)}

ÍÂèÒ§äÃ¡çµÒÁ ¢éÍÊÃØ»¹Õ ¨ÐÁÕ¤ÇÒÁ¹èÒàª× Í¶×Í

ÁÒ¡¢Ö ¹ ¡çµèÍàÁ× Í ã¹ÃÐººÁÕÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ â´´à´è¹à¾ÕÂ§µÑÇà´ÕÂÇ ¹Ñ ¹¤×Í àÁ× ÍÃÐºº·Ó§Ò¹ ·Õ ÃÐ´Ñº SNR ¤èÍ¹¢éÒ§ÊÙ§ (ËÃ×Í·Õ ÃÐ´Ñº BER

< 10−4 )

ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ µÒÃÒ§·Õ 5.2 áÊ´§¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ÊÓËÃÑºÃÐºº·Õ ãªé·ÒÃìà¡çµ áºº PR2,

H(D) = 1 + 2D + D2 ,

·Õ ND = 2.5 áÅÐ SNR = 22 dB «Ö §ã¹¡Ã³Õ¹Õ ¢éÍÁÙÅËÅÒÂæ

à«¡àµÍÃì¨Ð¶Ù¡Êè§à¢éÒä»ã¹ÃÐºº ¨¹¡ÃÐ·Ñ §ä´é BER =

1.4251 × 10−3 ,

ºÔµ·Õ ¼Ô´¾ÅÒ´ÁÕ¨Ó¹Ç¹ 502

ºÔµ, áÅÐÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Ñ §ËÁ´ÁÕ ¨Ó¹Ç¹ 179 µÑÇ ¨ÐàËç¹ ä´é ÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ à¡Ô´ ¢Ö ¹ ºèÍÂã¹ÃÐºº¹Õ ¤×Í

d2eff {εa (D)}

{

+} áÅÐ

{

+ 0 +} µÒÁÅÓ´Ñº «Ö § ÊÍ´¤ÅéÍ§¡Ñº ¡ÒÃãªé à¡³±ì

ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂ ¤×Í ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ÁÕ ÍÔ¹¾Øµ·Õ ÁÕ

d2 {εa (D)}

d2eff {εa (D)}

¹éÍÂ·Õ ÊØ´ (äÁèãªèÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

d2eff {εa (D)}

d2 {εa (D)}

ã¹ÊèÇ¹µèÍä»¹Õ ¨Ð·Ó¡ÒÃÇÔà¤ÃÒÐËì¼Å¡ÃÐ·º¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡µèÍ¡ÒÃà¡Ô´ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµã¹ÃÐºº ãËé¾Ô¨ÒÃ³ÒÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §·Õ ND = 2.5 â´Âãªé·ÒÃìà¡çµ áºº GPR5 (¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§áµèÅÐá·ç» ¢Í§·ÒÃìà¡çµ ÊÓËÃÑº áµèÅÐ ã¹ÃÙ» ·Õ 3.7(b)) µÒÃÒ§·Õ 5.3 áÊ´§ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ àËÅèÒ¹Ñ ¹ ³ ¨Ø´ ·Õ ÃÐººÁÕ BER = ¢Í§

σj /T

¹éÍÂ (0%

áººá¹ÇµÑ § ¤×Í

− 3%)

{2, −2}

10−4

εa (D)

σj /T

ÊÒÁÒÃ¶´Ù ä´é ¨Ò¡¢éÍÁÙÅ

áÅÐ¤ÇÒÁ¶Õ ã¹¡ÒÃà¡Ô´ ÅÓ´Ñº

¨Ò¡µÒÃÒ§·Õ 5.3 àÁ× Í ÃÐ´Ñº ¤ÇÒÁÃØ¹áÃ§

¹Í¡¨Ò¡¹Õ ¨Ó¹Ç¹¢Í§ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´·Õ â´´à´è¹ ¨ÐÁÕ à¾Ô Á ¢Ö ¹ àÁ× Í ÃÐ´Ñº

5.5.

¼Å¡ÒÃ·´ÅÍ§

107

µÒÃÒ§·Õ 5.2: ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ ¡ÓÅÑ§ ÊÍ§ áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ¤ÇÒÁÂÒÇ (ºÔµ) ¢Í§

εa (D)

d2 {εa (D)},

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ ÊÍ§

¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáºº PR2 ·Õ ND=2.5 áÅÐ SNR=22 dB

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´ (Euclidean distance)

d2eff {εa (D)},

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å (E ective distance)

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

¨Ó¹Ç¹¤ÃÑ §

d2eff

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

¨Ó¹Ç¹¤ÃÑ §

εa (D)

·Õ à¡Ô´¢Ö ¹

{εa (D)}

εa (D)

·Õ à¡Ô´¢Ö ¹

34.0001

127

12.7191

¢éÍ¼Ô´¾ÅÒ´

{εa (D)}

16.1802

+ +

19.3624

+ +

13.6519

+ 0 +

+ + +

16.6625

+ 0 +

+ + +

16.8916

+ + +

+ + + +

15.5885

+ 0 + 0 +

Í× ¹æ

¤ÇÒÁÃØ¹áÃ§¢Í§

σj /T

0 127

ÁÒ¡¢Ö ¹ ÊÓËÃÑº ¡ÒÃÇÔà¤ÃÒÐËì àËµØ¡ÒÃ³ì ¢éÍ¼Ô´¾ÅÒ´¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áºº

{2, −2, 2}

[19]

»ÃÐâÂª¹ì·Õ ä´é¨Ò¡¡ÒÃÈÖ¡ÉÒ¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´ ¤×Í àÁ× Í·ÃÒºÇèÒÃÐºº·Õ ãªéÁÕÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ ÍÔ¹¾Øµ ·Õ â´´à´è¹ áºº ã´ ¹Ñ¡ÇÔ¨ÑÂ ÊÒÁÒÃ¶ ·Õ ¨Ð à¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾ ÃÇÁ ¢Í§ ÃÐºº ä´é â´Â ¡ÒÃ ÍÍ¡áººÃËÑÊ RLL (run length limited) [9] ËÃ×ÍÇ§¨Ãà¢éÒÃËÑÊ¡èÍ¹ (precoder) [47] à¾× Íãªéà¢éÒÃËÑÊ ¢éÍÁÙÅ¢èÒÇÊÒÃ¡èÍ¹·Õ ¨Ð·Ó¡ÒÃà¢ÕÂ¹Å§ä»ã¹Ê× ÍºÑ¹·Ö¡ à¾× ÍËÅÕ¡àÅÕ Â§¡ÒÃà¡Ô´ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ â´´à´è¹àËÅèÒ¹Ñ ¹ ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

5.5.2

¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§

ã¹ËÑÇ¢éÍ¹Õ ¨ÐáÊ´§ãËéàËç¹ÇèÒ

SNReff

ààÅÐ BER

áÅÐ BER ÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¡Ñ¹¤èÍ¹¢éÒ§ÁÒ¡ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §

àÁ× Í¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡

σj /T

ÁÕ¤èÒ¹éÍÂ áÅÐÃÐºº·Ó§Ò¹·Õ ÃÐ´Ñº

SNR ÊÙ§à¾ÕÂ§¾Í(¹Ñ ¹¤×Í àÁ× Íã¹ÃÐººÁÕàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´·Õ â´´à´è¹à¾ÕÂ§µÑÇà´ÕÂÇ)

108

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

µÒÃÒ§·Õ 5.3: ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ÃÐººÁÕ BER =

εa (D)

¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáÅÐ

σj /T

áººµèÒ§æ ³ ¨Ø´·Õ

10−4

ÅÓ´Ñº

PR2

¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

σj /T

GPR5

= 0%

σj /T

GPR5

= 0%

σj /T

GPR5

= 3%

σj /T

= 6%

σj /T

= 9%

4.90%

3.19%

3.36%

5.84%

41.53%

67.54%

83.25%

79.66%

35.21%

9.62%

+ +

5.79%

0.35%

1.98%

38.31%

21.53%

+ +

0.51%

0.58%

1.14%

6.66%

15.73%

+ + +

0.13%

0.23%

0.48%

2.66%

6.31%

+ 0 +

15.53%

8.75%

8.94%

3.03%

0.00%

+ 0 + 0 +

1.34%

0.73%

0.84%

0.22%

0.00%

Í× ¹æ

4.26%

2.72%

3.60%

8.06%

5.28%

ÃÙ»·Õ 5.5 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õ ãªé·ÒÃìà¡çµáºº GPR5 ³ ÃÐ´Ñº ÃÙ»¢Í§ BER áÅÐ

SNReff

σj /T

·Õ ND = 2.5 ¨ÐàËç¹ä´éÇèÒ »ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ»¢Í§ BER áÅÐ

¼ÅÅÑ¾¸ìà» ¹ä»µÒÁ·Õ ¤Ò´ËÇÑ§äÇé ¡ÅèÒÇ¤×Í àÁ× Í ¤èÒ

GPR5

σj /T

µèÒ§æ ã¹

SNReff

ÁÕ

ÁÕ¤èÒà¾Ô Á¢Ö ¹ ¤èÒ BER ¢Í§ÃÐºº¡ç¨Ðà¾Ô Á¢Ö ¹ áÅÐ

¢Í§ÃÐºº¡ç¨ÐÅ´¹éÍÂÅ§ ¹Í¡¨Ò¡¹Õ ÃÙ»·Õ 5.5(a) áÊ´§ãËéàËç¹ÇèÒ ³ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§

¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡µ Ó ¤èÒ

SNReff

ÊÒÁÒÃ¶¹ÓÁÒãªéã¹¡ÒÃ·Ó¹ÒÂ¤èÒ BER ä´é

¨Ò¡ÊÁ¡ÒÃ (5.18) áÅÐ (5.20) ¨Ðä´éÇèÒ [19]

BER ≈ K2 Q â´Â·Õ

¤×Í ¤èÒ¤§µÑÇ·Õ äÁè¢Ö ¹¡Ñº

2 σw

µ p ¶ 1 SNReff 2

µÑÇÍÂèÒ§àªè¹ àÁ× Í

σj /T = 0%

(5.22)

¤èÒ BER ·Õ ·Ó¹ÒÂä´é¨ÐáÊ´§

´éÇÂàÊé¹ Q(·) ã¹ÃÙ» «Ö §ÊÍ´¤ÅéÍ§¡Ñº¤èÒ BER ¨ÃÔ§·Õ ä´é¨Ò¡¡ÒÃ¨ÓÅÍ§ÃÐºº àÁ× Í ÃÙ»·Õ 5.6(a) áÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§ BER áÅÐ áººã´¡çµÒÁ ¶éÒÃÐººÁÕ¤èÒ àÁ× Í

σj /T

SNReff

ÁÕ ¤èÒ ¹éÍÂ ´Ñ§¹Ñ ¹ ¤èÒ

SNReff

K2 = 2.3

¨ÐàËç¹ä´éÇèÒ äÁèÇèÒÃÐºº¨Ðãªé·ÒÃìà¡çµ

à·èÒ¡Ñ¹áÅéÇ ÃÐºº¡ç¨ÐÁÕ¤èÒ BER ·Õ ã¡Åéà¤ÕÂ§¡Ñ¹ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §

SNReff

¨Ö§ ÊÒÁÒÃ¶¹ÓÁÒãªé ã¹¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§

·ÒÃìà¡çµ áººµèÒ§æ ä´é àªè¹à´ÕÂÇ¡Ñº ¡ÒÃãªé ¤èÒ BER ÍÂèÒ§äÃ¡çµÒÁ ¤ÇÃµÃÐË¹Ñ¡ äÇé ÇèÒ ÃÐººµèÒ§æ ¨Ð

5.5.

¼Å¡ÒÃ·´ÅÍ§

109

−1

−2

BER

−3

jitter = 0% jitter = 3% jitter = 6% jitter = 9% Q(⋅) with jitter = 0%

−4

−5

(a)

Electronics SNR (dB)

SNReff (dB)

jitter = 0% jitter = 3% jitter = 6% jitter = 9%

9 14

(b)

Electronics SNR (dB)

ÃÙ»·Õ 5.5: »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººã¹ÃÙ» (a) BER áÅÐ (b)

SNReff

¢Í§·ÒÃìà¡çµáºº GPR5

ãªé »ÃÔÁÒ³ SNR ·Õ µèÒ§¡Ñ¹ ã¹¡ÒÃ·ÓãËé à¡Ô´ ¤èÒ BER áÅÐ¤èÒ

SNReff

·Õ à·èÒ ¡Ñ¹ ´Ñ§·Õ áÊ´§ã¹ÃÙ» ·Õ

5.6(b)

110

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

−1

−2

BER

−3

PR2 [1 2 1], jitter=0% GPR5, jitter=0% GPR5, jitter=3% GPR5, jitter=6%

−4

−5

(a)

Effective SNR (dB)

−1

−2

BER

−3

−4

PR2 [1 2 1], jitter=0% GPR5, jitter=0% GPR5, jitter=3% GPR5, jitter=6%

−5

(b)

ÃÙ»·Õ 5.6:

(a) ¡ÃÒ¿ BER áÅÐ

SNReff ,

Electronics SNR (dB)

(b) ¡ÃÒ¿ BER áÅÐ SNR ¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áºº

µèÒ§æ ³ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡·Õ à¢ÕÂ¹ÇèÒ jitter µèÒ§æ ·Õ ND = 2.5

5.6.

ÊÃØ»·éÒÂº·

5.6

111

ÊÃØ»·éÒÂº·

ã¹¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ µÒÁà§× Í¹ä¢ºÑ§¤Ñº áººâÁ¹Ô¡ (monic constraint) â´Âãªé áºº¨ÓÅÍ§ã¹ÃÙ» ·Õ 3.2 ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´

ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡ ¾Ô¨ÒÃ³Òä´é ÇèÒ à» ¹ ÊÑÒ³Ãº¡Ç¹ã¹áºº¨ÓÅÍ§ªèÍ§

ÊÑÒ³ GPR áººÊÁÁÙÅ µÒÁÃÙ»·Õ 5.2 ¶éÒÊÑÒ³Ãº¡Ç¹

à» ¹ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºº

ºÇ¡áÅéÇ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¨Ð¢Ö ¹ÍÂÙè¡Ñº ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ÁÕ¤èÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´·Õ ¹éÍÂÊØ´

dmin

ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ

ÁÑ¡¨ÐÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹áººÊÕ â´Âà©¾ÒÐÍÂèÒ§ÂÔ §

·Õ ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ìÊÙ§æ ´Ñ§¹Ñ ¹ ã¹¡Ã³Õ ¹Õ »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¨Ð¢Ö ¹ ÍÂÙè ¡Ñº ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´·Õ ÁÕ¤èÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å·Õ ¹éÍÂÊØ´

deffmin

¼Å¡ÒÃ·´ÅÍ§áÊ´§ãËéàËç¹ÇèÒ ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂ ¤×Í ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ ÁÕ

d2eff {εa (D)}

·Õ ¹éÍÂÊØ´ (äÁè ãªè ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ ÁÕ

d2 {εa (D)}

·Õ ¹éÍÂÊØ´) ¹Í¡¨Ò¡¹Õ

¨Ó¹Ç¹¢Í§ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ â´´à´è¹¨ÐÁÕà¾Ô Á¢Ö ¹ àÁ× ÍÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹ ¨Ôµ àµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ à´ÕÂÇ (àÁ× Í ÃÐººÁÕ

σj /T

ÁÒ¡¢Ö ¹ ã¹¡Ã³Õ ·Õ ÃÐººÁÕ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ â´´à´è¹ à¾ÕÂ§µÑÇ

¹éÍÂ áÅÐ·Ó§Ò¹·Õ ÃÐ´Ñº SNR ÊÙ§ à¾ÕÂ§¾Í) ¹Ñ¡ÇÔ¨ÑÂ ÊÒÁÒÃ¶ãªé»ÃÐâÂª¹ì

¨Ò¡¢éÍÁÙÅ¢Í§¡ÒÃÇÔà¤ÃÒÐËìàËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´¹Õ ÁÒãªéã¹¡ÒÃÍÍ¡áººÃËÑÊ RLL ËÃ×ÍÇ§¨Ãà¢éÒÃËÑÊ ¡èÍ¹ à¾× Íãªéà¢éÒÃËÑÊ¢éÍÁÙÅ¢èÒÇÊÒÃ¡èÍ¹·Õ ¨Ð·Ó¡ÒÃà¢ÕÂ¹Å§ä»ã¹Ê× ÍºÑ¹·Ö¡ à¾× ÍËÅÕ¡àÅÕ Â§¡ÒÃà¡Ô´ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ â´´à´è¹ àËÅèÒ¹Ñ ¹ ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ «Ö §¨ÐªèÇÂ·ÓãËé»ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐºº´ÕÁÒ¡¢Ö ¹ ÊØ´·éÒÂä´éáÊ´§ãËéàËç¹ÇèÒ

SNReff

ãªéã¹¡ÒÃÇÑ´»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººä´é àªè¹à´ÕÂÇ¡Ñº¡ÒÃãªé BER ¹Ñ ¹¤×Í ÃÐºº·Õ ÁÕ

ÊÒÁÒÃ¶¹ÓÁÒ

SNReff

¤èÒ BER µ Ó áÅÐ¶Ö§áÁéÇèÒ ÃÐººáµèÅÐÃÐºº¨Ðãªé·ÒÃìà¡çµµèÒ§¡Ñ¹ áµè¶éÒÃÐººàËÅèÒ¹Ñ ¹ÁÕ

ÊÙ§ ¡ç¨ÐÁÕ

SNReff

à·èÒ

¡Ñ¹ ÃÐºº¡ç¨ÐÁÕ BER ã¡Åéà¤ÕÂ§¡Ñ¹´éÇÂ

5.7

ààºº½ ¡ËÑ´·éÒÂº·

1. ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR2,

H(D) = 1 + 2D + D2 ,

ÍÔ¹¾ØµÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº 25 ºÔµ â´Â·Õ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ·Õ Ë¹Ö §

−1,

1, 1,

−1, −1,

1, 1,

−1,

1, 1,

−1,

1, 1,

¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ

A1 (D) −1,

¤×Í

1, 1,

{1, −1, −1}

1, 1,

áÅÐÅÓ´Ñº

112

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¢éÍÁÙÅÍÔ¹¾Øµ·Õ ÊÍ§ 1, 1,

−1,

1, 1,

A2 (D)

−1, −1,

¤×Í

{1,

1, 1,

−1}

−1,

1, 1,

−1, −1,

−1,

¨§ËÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§·Ñ §ËÁ´·Õ ¾ºã¹

ÃÐºº¹Õ

2. ¡ÓË¹´ãËé ÊÁÒªÔ¡ áµèÅÐµÑÇ ¢Í§ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ ÁÕ ¤èÒ ·Õ à» ¹ ä»ä´é ¤×Í ºÑ¹·Ö¡ áººá¹Ç¹Í¹

(longitudinal

recording)

{−1,

1} ã¹ÃÐºº¡ÒÃ

ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ ·Õ à¡Ô´ ¢Ö ¹ ºèÍÂ

{2, −2, 2}

ã¹ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¤×Í

¨§¤Ó¹Ç³

2.1)

H(D) = 1 − D

2.2)

H(D) = 1 + D − D2 − D3

2.3)

H(D) = 1 + 2D − 2D3 − D4

2.4)

H(D) = 1 − 0.04D − 0.64D2

2.5)

H(D) = 1 + 0.22D − 0.65D2 − 0.36D3

2.6)

H(D) = 1 + 0.24D − 0.50D2 − 0.40D3 − 0.21D4

3. ¡ÓË¹´ãËé ÊÁÒªÔ¡ áµèÅÐµÑÇ ¢Í§ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ ÁÕ ¤èÒ ·Õ à» ¹ ä»ä´é ¤×Í ºÑ¹·Ö¡áººá¹ÇµÑ §

(perpendicular

recording)

{−1,

1} ã¹ÃÐºº¡ÒÃ

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ à¡Ô´¢Ö ¹ºèÍÂã¹

ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ

¤×Í

3.1)

H(D) = 1 + D

3.2)

H(D) = 1 + 3D + 3D2 + D3

3.3)

H(D) = 1 + 4D + 6D2 + 4D3 + D4

3.4)

H(D) = 1 + 1.30D + 0.66D2

3.5)

H(D) = 1 + 1.19D + 0.60D2 + 0.12D3

3.6)

H(D) = 1 + 1.21D + 0.62D2 + 0.16D3 + 0.01D4

{2, −2}

¨§¤Ó¹Ç³ËÒ

5.7.

ààºº½ ¡ËÑ´·éÒÂº·

113

4. ¨§¾ÔÊÙ¨¹ì¤èÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§

d2 {εa (D)}

·Õ áÊ´§ã¹µÒÃÒ§·Õ 5.1

5. ¨§¾ÔÊÙ¨¹ì¤èÒÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§

d2 {εa (D)}

·Õ áÊ´§ã¹µÒÃÒ§·Õ 5.2

6. ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµã¹ÃÙ»·Õ 3.2 ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ ·Õ

ak ∈ {−1, 1}

ND = 2 áÅÐ SNR = 22 dB â´Â·Õ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{wk } = {−1.95,

1.66, 0.36,

·Õ à¡Ô´¢Ö ¹ºèÍÂÃÐºº ¤×Í

−0.63,

{2, −2, 2}

¶éÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

1.90, 0.10, 2.12} áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

¨§¤Ó¹Ç³ËÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§

¢Í§ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ¹Õ àÁ× ÍÃÐººãªé·ÒÃìà¡çµ

6.1)

H(D) = 1 − D

6.2)

H(D) = 1 − D2

6.3)

H(D) = 1 + D − D2 − D3

H(D)

εa (D)

d2eff {εa (D)}

´Ñ§µèÍä»¹Õ

7. ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ ã¹ÃÙ» ·Õ 3.2 ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § ·Õ ND = 2 áÅÐ SNR = 22 dB â´Â·Õ ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{wk }

εa (D)

{−5.37, −4.65,

0.56, 5.60,

·Õ à¡Ô´ ¢Ö ¹ ºèÍÂÃÐºº ¤×Í

−2.40, −8.26,

{2, −2}

H(D) = 1 + D

7.2)

H(D) = 1 + 2D + D2

7.3)

H(D) = 1 + 3D + 3D2 + D3

¶éÒÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

4.85} áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

¨§ËÒÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ ÊÍ§

¢Í§ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ¹Õ àÁ× ÍÃÐººãªé·ÒÃìà¡çµ

7.1)

ak ∈ {−1, 1}

H(D)

´Ñ§µèÍä»¹Õ

d2eff {εa (D)}

114

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

º··Õ 6

Ç§¨ÃµÃÇ¨ËÒ NPML

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹áÅÐ»ÃÐâÂª¹ì ¢Í§ Ç§¨ÃµÃÇ¨ËÒ NPML (noise predictive maxi mum likelihood) [51, 52] «Ö §à» ¹Ç§¨ÃµÃÇ¨ËÒ·Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML (par tial response maximum likelihood) â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í ÃÐºº·Ó§Ò¹·Õ ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÊÙ§ ã¹·Ò§»¯ÔºÑµÔ Ç§¨ÃµÃÇ¨ËÒ NPML »ÃÐÂØ¡µì ÁÒ¨Ò¡Ç§¨ÃµÃÇ¨ËÒ PRML â´Â¡ÒÃ¹Ó ¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ (noise prediction process) á½§à¢éÒ ä»ÍÂÙè ã¹áµèÅÐàÊé¹ ÊÒ¢Ò (branch) ¢Í§á¼¹ÀÒ¾à·ÃÅÅÔÊ (trellis diagram) ´Ñ§·Õ ¨ÐÍ¸ÔºÒÂµèÍä»ã¹º·¹Õ ¾ÃéÍÁ·Ñ §áÊ´§ ¼Å¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾ÃÐËÇèÒ§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐÇ§¨ÃµÃÇ¨ËÒ NPML

6.1

º·¹Ó

à·¤¹Ô¤ PRML ¤×Í ¡ÒÃãªé §Ò¹ÃèÇÁ¡Ñ¹ ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃì áºº PR (partial response) áÅÐÇ§¨Ã µÃÇ¨ËÒÇÕà·ÍÃìºÔ (Viterbi detector) «Ö § à» ¹ ·Õ ¹ÔÂÁãªé §Ò¹ÁÒ¡ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì µÒÁ·Õ Í¸ÔºÒÂã¹º··Õ 4 ãËé ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁè µèÍà¹× Í§·Ò§àÇÅÒ áººÊÁÁÙÅ ã¹â´àÁ¹

µÒÁÃÙ» ·Õ 6.1 àÁ× Í

A(D)

N (D) ¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºººÇ¡ ¤×Í ·ÒÃìà¡çµ (target),

¤×Í ¢éÍÁÙÅ ºÔµ ÍÔ¹¾Øµ,

(AWGN),

C(D)

¤×Í ªèÍ§ÊÑÒ³,

F (D) ¤×Í ÍÕ¤ÇÍäÅà«ÍÃìáºº

PR,

H(D)

Y (D) ¤×Í ¢éÍÁÙÅ·Õ ¨Ð¶Ù¡Êè§à¢éÒä»·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ, 115

116

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

N(D)

F(D)

channel

H ( D) Y(D) C ( D)

A(D) C(D)

Aˆ ( D )

Viterbi detector

ÃÙ»·Õ 6.1: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ

áÅÐ

Â(D)

¤×Í ¤èÒ»ÃÐÁÒ³¢Í§¢éÍÁÙÅºÔµÍÔ¹¾Øµ

A(D)

¨Ò¡ÃÙ» ·Õ 6.1 ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì

Y (D)

ÊÒÁÒÃ¶à¢ÕÂ¹à» ¹ ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃì

ä´éµÒÁÊÁ¡ÒÃ (4.6) ¹Ñ ¹¤×Í

H(D) Y (D) = A(D)H(D) + N (D) | {z } C(D) | {z } wanted signal

(6.1)

W (D)

â´Â·Õ

W (D)

¤×Í ÊÑÒ³Ãº¡Ç¹·Õ ¨Ðà¢éÒä»ã¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ (µÒÁ·Õ Í¸ÔºÒÂã¹ËÑÇ¢éÍ·Õ 4.2.2)

W (D)

ÁÕÅÑ¡É³Ð

à» ¹ ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ áÅéÇ (â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í ÃÐºº·Ó§Ò¹·Õ ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ìÊÙ§æ) ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ (tap) ¹éÍÂ ãËéÁÕ¼ÅµÍºÊ¹Í§àËÁ×Í¹¡ÑºªèÍ§ÊÑÒ³ 1

¨ÐÁÕ ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹áººÊÕ

C(D)

H(D)

·Õ ÁÕ ¨Ó¹Ç¹á·ç»

·Óä´éÂÒ¡ÁÒ¡ ´Ñ§¹Ñ ¹â´Â·Ñ Çä»

W (D)

(colored noise) [25] «Ö § ¨ÐÊè§ ¼Å·ÓãËé »ÃÐÊÔ·¸ÔÀÒ¾¡ÒÃ

·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ Å´Å§ à¾ÃÒÐ©Ð¹Ñ ¹ ¶éÒ µéÍ§¡ÒÃãËé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÊÒÁÒÃ¶·Õ ¨Ð ·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÊÙ§ÊØ´àËÁ×Í¹à´ÔÁ ¹Ñ¡ÇÔ¨ÑÂ¨ÐµéÍ§ËÒÇÔ¸Õ¡ÒÃã´ÇÔ¸Õ¡ÒÃË¹Ö §ã¹¡ÒÃ·ÓãËéÍ§¤ì »ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹ã¹¢éÍÁÙÅ

Y (D)

(¹Ñ ¹¤×Í

W (D))

ÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹à¡ÒÊì

ÊÕ¢ÒÇáºººÇ¡ ¡èÍ¹·Õ ¨ÐÊè§¼ÅÅÑ¾¸ì·Õ ä´éà¢éÒä»·Ó¡ÒÃ¶Í´ÃËÑÊ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ´Ñ§¹Ñ ¹ÍÒ¨¨Ð¡ÅèÒÇä´éÇèÒ à·¤¹Ô¤ NPML [51, 52] ¤×Í ¡ÒÃãªé§Ò¹ÃèÇÁ¡Ñ¹ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃìáºº PR áÅÐÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ·Õ ÁÕ¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ ËÃ×Í ¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ ·ÓãËé ÊÑÒ³Ãº¡Ç¹à» ¹ ÊÕ ¢ÒÇ (noise whitening process) á½§ÍÂÙè ¢éÒ§ã¹ÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ´Ñ§ 1

¢éÍÁÙÅá«Áà» Å¢Í§ÊÑÒ³Ãº¡Ç¹

W (D)

áµèÅÐá«Áà» Å¨ÐÁÕÊËÊÑÁ¾Ñ¹¸ì (correlation) ¡Ñ¹

6.2.

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹

117

wk target

H(D)

âk Viterbi algorithm

predictor

P(D) ÃÙ»·Õ 6.2: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¾ÃéÍÁÇ§¨ÃµÃÇ¨ËÒ NPML

áÊ´§ã¹ÃÙ»·Õ 6.2 à¾ÃÒÐ©Ð¹Ñ ¹ àÁ× ÍÃÐºº·Ó§Ò¹·Õ ¤ÇÒÁ¨Ø¢éÍÁÙÅ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§æ Ç§¨ÃµÃÇ¨ËÒ NPML ¨Ö§ ¤ÇÃ·Õ ¨Ð¶Ù¡ ¹ÓÁÒãªé §Ò¹ÁÒ¡¡ÇèÒ ¡ÒÃãªé Ç§¨ÃµÃÇ¨ËÒ PRML à¾× Í·Õ ¨Ðä´é »ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ ¢Í§ÃÐºº·Õ ´Õ¡ÇèÒ

6.2

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹

Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ (predictor lter) ·Õ ãªé§Ò¹·Ñ Çä»ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³´Ô¨Ô·ÑÅ¨ÐÁÕÅÑ¡É³Ð ·Ñ §·Õ à» ¹ áºº¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì ¨Ó¡Ñ´ (FIR: nite impulse response) áÅÐáºº¼ÅµÍºÊ¹Í§ ÍÔÁ¾ÑÅÊìäÁè¨Ó¡Ñ´ (IIR: in nite impulse response) ¹Í¡¨Ò¡¹Õ Õ ¤Ø³ÊÁºÑµÔ·Ñ Çä»¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ ¤×Í ¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ (prediction error) ¨Ð¤èÍÂæ Å´Å§ àÁ× Í¨Ó¹Ç¹á·ç»¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ à¾Ô Á¢Ö ¹ ã¹Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº FIR à·èÒ¹Ñ ¹ ¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ ã¹ÃÙ»·Õ 6.3 àÁ× Í ÊÑÒ³Ãº¡Ç¹áººÊÕ, áÅÐ

P (D)

ŵk

¤×Í ¤èÒ»ÃÐÁÒ³¢Í§

wk , ek = wk − ŵk

¤×Í ¿ §¡ìªÑ¹¶èÒÂâÍ¹¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂã¹â´àÁ¹

P (D) =

N X k=1

¤×Í

¤×Í ¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ,

«Ö §ÁÕÃÙ»ÊÁ¡ÒÃ ¤×Í

pk Dk = p1 D + p2 D2 + . . . + pN DN

(6.2)

118

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ek predictor

wˆ k

P(D)

ÃÙ»·Õ 6.3: áºº¨ÓÅÍ§¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ

â´Â·Õ

¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô µÑÇ·Õ

¡ÃÍ§·Ó¹ÒÂ ´Ñ§¹Ñ ¹

ŵk

¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ áÅÐ

¤×Í ¨Ó¹Ç¹á·ç»·Ñ §ËÁ´¢Í§Ç§¨Ã

ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìä´é ¤×Í

ŵk =

N X

pi wk−i

(6.3)

i=1 ÊÁ¡ÒÃ (6.3) ¨ÐÃÙé¨Ñ¡¡Ñ¹ã¹ª× Í¢Í§ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂË¹Ö §¢Ñ ¹áººàªÔ§àÊé¹ (linear one step predic tor) àªè¹à´ÕÂÇ¡Ñ¹ ¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ

ÊÒÁÒÃ¶¨Ñ´ ãËé ÍÂÙè ã¹ÃÙ» ¢Í§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃì ä´é

´Ñ§¹Õ

ek = wk − ŵk = wk −

N X

pi wk−i

(6.4)

i=1 ËÃ×Íà¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§â´àÁ¹

ä´é ¤×Í

E(D) = [1 − P (D)]W (D) â´Â·Õ ¾¨¹ì

[1 − P (D)]

(6.5)

¨ÐàÃÕÂ¡¡Ñ¹ ·Ñ Çä»ÇèÒ Ç§¨Ã¡ÃÍ§¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ (prediction error

lter)

6.3

¡ÒÃËÒ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

¨Ø´»ÃÐÊ§¤ì ã¹¡ÒÃÍÍ¡áººÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ ·Ó¹ÒÂ) ¤×Í ¡ÒÃ·ÓãËé¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ

P (D) ek

(¹Ñ ¹¤×Í ¡ÒÃËÒ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§

ÁÕ¤èÒ¹éÍÂ·Õ ÊØ´ ËÃ×ÍÍÕ¡¹ÑÂË¹Ö §¡ç¤×Í ¡ÒÃ·ÓãËé

ÁÕ

6.3.

¡ÒÃËÒ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

119

ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹ÊÕ ¢ÒÇãËé ÁÒ¡·Õ ÊØ´ ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ¢éÍÁÙÅ

¶×Í ÇèÒ à» ¹ Í§¤ì»ÃÐ¡Íº

¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ËÅ§àËÅ×Í ÍÂÙè ã¹¢éÍÁÙÅ ·Õ ¨ÐÊè§ à¢éÒ ä»·Ó¡ÒÃ¶Í´ÃËÑÊ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ´Ñ§¹Ñ ¹ ÇÔ¸Õ¡ÒÃËÒ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ·Õ ´Õ·Õ ÊØ´ ¡ç¤×Í ¡ÒÃ·ÓãËé¤èÒ¢éÍ¼Ô´¾ÅÒ´¡ÓÅÑ§ÊÍ§ à©ÅÕ Â

(MSE: mean squared error) [51, 52]

£ ¤ £ ¤ E e2k = E (wk − ŵk )2 ÁÕ ¤èÒ ¹éÍÂ·Õ ÊØ´ â´Â·Õ

E[·]

(6.6)

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ¤èÒ ¤Ò´ËÁÒÂ «Ö § ÊÒÁÒÃ¶·Óä´é â´Â¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì ¢Í§

ÊÁ¡ÒÃ (6.6) à·ÕÂº¡Ñº¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

áµèÅÐµÑÇ áÅéÇãËé¼ÅÅÑ¾¸ì·Õ ä´éÁÕ¤èÒà·èÒ

¡Ñº¤èÒÈÙ¹Âì ¨Ò¡¹Ñ ¹ ·Ó¡ÒÃá¡éÃÐººÊÁ¡ÒÃàªÔ§àÊé¹¡ç¨Ðä´é¤ÓµÍºÍÍ¡ÁÒ ËÃ×Í ÍÒ¨¨ÐÍÒÈÑÂ ËÅÑ¡¡ÒÃ àªÔ§µÑ §©Ò¡

(orthogonality principle) ·Õ ÇèÒ

E [(wk − ŵk )wm ] = 0 ÊÓËÃÑº

m = 1, 2, . . . , N

(6.7)

â´Â¡ÒÃá¡éÊÁ¡ÒÃ (6.7) ¨Ðä´éÇèÒ

E[wk wm ] −

N X

pi E[wk−i wm ] = 0

i=1

E[wk wm ] = Rww (k − m) =

N X i=1 N X

pi E[wk−i wm ] pi Rww (k − i − m)

(6.8)

i=1 àÁ× Í

Rww (i)

¤×Í ¤èÒÍÑµÊËÊÑÁ¾Ñ¹¸ì (auto correlation) ÅÓ´Ñº·Õ

â´Â

Rww (i) = E[wk+i wk ] = E

"S−1 X

¢Í§ÊÑÒ³Ãº¡Ç¹

«Ö §¹ÔÂÒÁ

# wk+i wk

(6.9)

k=0 â´Â·Õ

¤×Í ¤ÇÒÁÂÒÇËÃ×Í¨Ó¹Ç¹ºÔµ¢Í§ÅÓ´Ñº¢éÍÁÙÅ

{wk }

¶éÒá·¹¤èÒ

k−m=j

ã¹ÊÁ¡ÒÃ (6.8)

¨Ðä´é¼ÅÅÑ¾¸ìà» ç¹ ÊÁ¡ÒÃ¹ÍÃìÁÍÅ (normal equation) ¹Ñ ¹¤×Í

Rww (j) =

N X i=1

pi Rww (j − i)

(6.10)

120

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊÓËÃÑº

j = 1, 2, . . . , N 

 Rww (1)

   Rww (2)   . .  .  Rww (N ) | {z





      =       }

«Ö §ÊÒÁÒÃ¶¨Ñ´ãËéÍÂÙèã¹ÃÙ»¢Í§àÁ·ÃÔ¡«ìä´é ¤×Í

Rww (0)

Rww (1)

Rww (0)

. . .

Rww (N − 1)

···

Rww (N − 1)

 p1

  Rww (N − 2)   p2    .. . . . .  . . .  Rww (1) Rww (0) pN {z } | {z ···

      

(6.11)

}

ËÃ×Í

r = Rp à¹× Í§¨Ò¡

(6.12)

à» ¹àÁ·ÃÔ¡«ì¨ÑµØÃÑÊ (square matrix) ´Ñ§¹Ñ ¹ ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

ÊÒÁÒÃ¶ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ (6.12) ¹Ñ ¹¤×Í

p = R−1 r áÅÐ¤èÒ ¢éÍ¼Ô´¾ÅÒ´¡ÓÅÑ§ ÊÍ§à©ÅÕ Â ·Õ ¹éÍÂÊØ´

(6.13)

(MMSE: minimum mean squared error) ¢Í§Ç§¨Ã

¡ÃÍ§·Ó¹ÒÂ¨ÐÁÕ¤èÒà·èÒ¡Ñº [52]

N X £ 2¤ pi Rww (i) E ek = Rww (0) −

(6.14)

i=1

6.4

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

à¾× ÍãËé§èÒÂµèÍ¡ÒÃÍ¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ãËé¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR4 µÒÁÃÙ»·Õ 6.4 â´Â·Õ ¢éÍÁÙÅ·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»ÊÁ¡ÒÃ ·Ò§¤³ÔµÈÒÊµÃìä´é ¤×Í

yk = rk + wk = ak − ak−2 + wk àÁ× Í

rk = ak − ak−2

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³ áÅÐ

(6.15)

¤×Í ÊÑÒ³Ãº¡Ç¹áººÊÕ

6.4.

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

121

wk ak

PR4 target

1− D

NPML detector

aˆk

ÃÙ»·Õ 6.4: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ PR4

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ¨ÐµèÒ§¨Ò¡ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ã¹ àÃ× Í§¢Í§¡ÒÃ¤Ó¹Ç³àÁµÃÔ¡ÊÒ¢Ò (branch metric) ¡ÅèÒÇ¤×Í àÁµÃÔ¡ÊÒ¢Ò¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ¨Ð ÁÕ¾¨¹ì·Õ à» ¹¤èÒ·Ó¹ÒÂ¢Í§ÊÑÒ³Ãº¡Ç¹

ŵk

à¢éÒÁÒÃèÇÁ´éÇÂ ¹Ñ ¹¤×Í

λk (u, q) = |yk − r̂k (u, q) − ŵk |2 àÁ× Í

r̂k (u, q)

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³·Õ äÁèÁÕÊÑÒ³Ãº¡Ç¹ (noiseless channel output) ·Õ

ÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð ³ àÇÅÒ·Õ

(6.16)

ä»Ê¶Ò¹Ð

¶éÒ¡ÓË¹´ãËé

·Õ ÊÍ´¤ÅéÍ§¡ÑºàÊé¹·Ò§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð

ak (q)

ä»Ê¶Ò¹Ð

¤×Í ¢éÍÁÙÅºÔµÍÔ¹¾Øµ

´Ñ§¹Ñ ¹ ÊÓËÃÑºªèÍ§

ÊÑÒ³ PR4 ¨Ðä´éÇèÒ

r̂k (u, q) = ak (q) − ak−2 (q) ¹Í¡¨Ò¡¹Õ ¤èÒ ·Ó¹ÒÂ¢Í§ÊÑÒ³Ãº¡Ç¹

ŵk

¤×Í

ŵk =

(6.17)

ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè ã¹ÃÙ» ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃì ä´é

N X

pi wk−i

(6.18)

i=1 á·¹¤èÒ

wk = yk − ak + ak−2

¨Ò¡ÊÁ¡ÒÃ (6.15) Å§ã¹ÊÁ¡ÒÃ (6.18) ¨Ðä´é

ŵk =

N X

pi (yk−i − ak−i + ak−i−2 )

(6.19)

i=1 á·¹¤èÒ

r̂k (u, q)

¨Ò¡ÊÁ¡ÒÃ (6.17) áÅÐ

ŵk

¨Ò¡ÊÁ¡ÒÃ (6.19) Å§ã¹ÊÁ¡ÒÃ (6.16) ¨Ðä´éà» ¹

¯2 ¯ N ¯ ¯ X ¯ ¯ pi (yk−i − âk−i (q) + âk−i−2 (q))¯ λk (u, q) = ¯yk − ak (q) + ak−2 (q) − ¯ ¯ i=1

(6.20)

122

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

â´Â·Õ

âk (q)

¤×Í ¤èÒ»ÃÐÁÒ³¢Í§¢éÍÁÙÅºÔµÍÔ¹¾Øµ ³ àÇÅÒ·Õ

(survivor path) ·Õ ÁÒ¶Ö§Ê¶Ò¹Ð

·Õ ÊÍ´¤ÅéÍ§¡ÑºàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè

àÁµÃÔ¡ÊÒ¢Òã¹ÊÁ¡ÒÃ (6.20) äÁèàËÁÒÐÊÓËÃÑº¡ÒÃ¹ÓÁÒãªé¡Ñº§Ò¹»ÃÐÂØ¡µì (application) ·Õ µéÍ§ ¡ÒÃ¤ÇÒÁàÃçÇ ã¹¡ÒÃ»ÃÐÁÇÅ¼ÅÊÙ§ àªè¹ ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì à¹× Í§¨Ò¡ ¡ÒÃ¤Ó¹Ç³àÁµÃÔ¡ ÊÒ¢ÒÁÕ ¿ §¡ìªÑ¹ ¡ÒÃ¤Ù³ (ÊÓËÃÑº¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹) à¾Ô Á¢Ö ¹ÁÒ á·¹·Õ ¨ÐÁÕà©¾ÒÐ¿ §¡ìªÑ¹¡ÒÃºÇ¡ ¡ÒÃà»ÃÕÂº à·ÕÂº ¡ÒÃàÅ×Í¡ (ACS: add compare select) àËÁ×Í¹¡Ñº·Õ ãªéã¹ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔáºº¸ÃÃÁ´Ò ´Ñ§¹Ñ ¹ à¾× ÍãËéÇ§¨ÃµÃÇ¨ËÒ NPML ÊÒÁÒÃ¶¹ÓÁÒãªé¡Ñº§Ò¹»ÃÐÂØ¡µì·Õ µéÍ§¡ÒÃ¤ÇÒÁàÃçÇã¹¡ÒÃ»ÃÐÁÇÅ¼ÅÊÙ§ ä´é ÊÁ¡ÒÃ (6.20) ¨ÐµéÍ§¶Ù¡¨Ñ´ÃÙ»ãËÁèãËéà» ¹

¯ ¯2 N +2 K ¯ ¯ X X ¯ ¯ λk (u, q) = ¯zk − ak−i (q)gi − ak (q)¯ âk−i (q)gi + ¯ ¯ i=1

i=K+1

àÁ× Í

(6.21)

¤×Í ¾ÒÃÒàµÍÃì·Õ ãªéã¹¡ÒÃ»ÃÐ¹Õ»ÃÐ¹ÍÁÃÐËÇèÒ§¤ÇÒÁ«Ñº«éÍ¹ (complexity) áÅÐ»ÃÐÊÔ·¸ÔÀÒ¾

¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ¡ÅèÒÇ¤×Í ¶éÒ

(áÅÐã¹·Ò§µÃ§¡Ñ¹¢éÒÁ),

zk = yk −

N X

yk−i pi

(6.22)

i=1 ¤×Í ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§Ç§¨Ã¡ÃÍ§¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ ¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§ ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

[1 − P (D)]

´Ñ§áÊ´§ã¹ÃÙ»·Õ 6.5, áÅÐ

(e ective target) ã¹â´àÁ¹

«Ö §¹ÔÂÒÁâ´Â

Heff (D) = 1 − g1 D − g2 D2 − . . . − gN +2 DN +2 = (1 − D2 )[1 − P (D)]

(6.23)

â´ÂÊÃØ»áÅéÇ ¡ÒÃÊÃéÒ§Ç§¨ÃµÃÇ¨ËÒ NPML ã¹·Ò§»¯ÔºÑµÔ ·Óä´é´Ñ§µèÍä»¹Õ

1) ¤Ó¹Ç³ËÒÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ

2) ¤Ó¹Ç³ËÒÅÓ´Ñº ¢éÍÁÙÅ

{yk }

{zk }

·Õ ÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ

P (D)]

µÒÁÃÙ»·Õ 6.5

P (D)

â´ÂãªéÊÁ¡ÒÃ (6.13)

¨Ò¡ÊÁ¡ÒÃ (6.22) â´Â¹ÓÅÓ´Ñº ¢éÍÁÙÅ àÍÒµì¾Øµ ¢Í§ÍÕ¤ÇÍäÅà«ÍÃì

H(D)

·Õ µéÍ§¡ÒÃ ÁÒ¼èÒ¹Ç§¨Ã¡ÃÍ§¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ

[1 −

6.4.

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

123

âk

zk Viterbi algorithm predictor

P(D) G(D)

ÃÙ»·Õ

6.5:

â¤Ã§ÊÃéÒ§ ¢Í§ Ç§¨Ã µÃÇ¨ËÒ

NPML

·Õ ãªé ¡Ñº §Ò¹ »ÃÐÂØ¡µì ·Õ µéÍ§¡ÒÃ ¤ÇÒÁ àÃçÇ ã¹ ¡ÒÃ

»ÃÐÁÇÅ¼ÅÊÙ§

3) ¹ÓÅÓ´Ñº ¢éÍÁÙÅ

{zk }

·Õ ä´é ä»·Ó¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ áºº¸ÃÃÁ´Ò áµè

á¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ãªé ã¹¡ÒÃ¤Ó¹Ç³µÒÁÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ (µÒÁ·Õ Í¸ÔºÒÂã¹ËÑÇ¢éÍ ·Õ 4.3.3) ¨ÐµéÍ§ÊÃéÒ§¨Ò¡·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

Heff (D)

«Ö §ËÒä´é¨Ò¡

Heff (D) = H(D)[1 − P (D)] àÁ× Í

H(D)

(6.24)

¤×Í ·ÒÃìà¡çµ·Õ ÊÍ´¤ÅéÍ§¡Ñº ÍÕ¤ÇÍäÅà«ÍÃì ·Õ ãªé ã¹ÃÐºº ¨ÐàËç¹ä´éÇèÒ ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§

·ÒÃìà¡çµ »ÃÐÊÔ·¸Ô¼Å¨Ðà» ¹ àÅ¢¨Ó¹Ç¹¨ÃÔ§ ¡ÅèÒÇ¤×Í ¶Ö§áÁéÇèÒ ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§ ¨Ó¹Ç¹àµçÁ áµè ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§

P (D)

H(D)

à» ¹ àÅ¢ ¨Ó¹Ç¹¨ÃÔ§ ´Ñ§¹Ñ ¹ ¼ÅÅÑ¾¸ì ·Õ ä´é

¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô à» ¹ àÅ¢¨Ó¹Ç¹¨ÃÔ§ à¾ÃÒÐ©Ð¹Ñ ¹ ÍÒ¨¨Ð¡ÅèÒÇä´é ÇèÒ ·ÒÃìà¡çµ »ÃÐÊÔ·¸Ô¼Å

¨Ðà» ¹ àÅ¢

Heff (D) Heff (D)

¨ÐÁÕ ¤×Í

·ÒÃìà¡çµáºº GPR áººË¹Ö §¡çä´é

µÑÇÍÂèÒ§·Õ 6.1

¨Ò¡¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì µÒÁáºº¨ÓÅÍ§ã¹ÃÙ»·Õ 3.2 ÊÓËÃÑºÃÐºº

¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ ·Õ ND = 2 áÅÐ SNR = 15 dB â´Â¡ÓË¹´ãËé ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ ¤×Í

H(D) = 1 − D −0.66}

»ÃÒ¡®ÇèÒ

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

{wk }

·Õ ä´é ¤×Í

{0.86, −0.26, −0.13, −0.14, 0.35,

¨§¤Ó¹Ç³ËÒ

¡) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

P (D)

áºº 2 á·ç» áÅÐ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

Heff (D)

124

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¢) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ

ÇÔ¸Õ·Ó

P (D)

¨Ò¡ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

áºº 4 á·ç» áÅÐ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

{wk }

Heff (D)

·Õ ¡ÓË¹´ãËé ¤èÒÍÑµÊËÊÑÁ¾Ñ¹¸ì¢Í§

ÊÒÁÒÃ¶ËÒä´é¨Ò¡ÊÁ¡ÒÃ

(6.9) ´Ñ§¹Õ

Rww (i) = {0.2336, −0.0903, −0.0071, −0.0419, 0.2363, −0.5676} ÊÓËÃÑº

i = 0, 1, 2, . . . , 5

µÒÁÅÓ´Ñº

¡) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» ÊÒÁÒÃ¶ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ (6.11) ¹Ñ ¹¤×Í

 

 −0.0903



=

−0.0071

 0.2336

−0.0903

0.2336



 p1



¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ ÁÕ¤èÒà·èÒ¡Ñº

 

 p1 p2



 = 

−1  0.2336

−0.0903





 −0.0903



0.2336 −0.0071   5.0323 1.9454 −0.0903   =  1.9454 5.0323 −0.0071   −0.4684  =  −0.2116 

−0.0903

´Ñ§¹Ñ ¹ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» ¤×Í

P (D) = −0.4684D − 0.2116D2 áÅÐ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å·Õ ÊÍ´¤ÅéÍ§¡ÑºÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ¹Õ ¤×Í

£ ¤ Heff (D) = (1 − D) 1 − (−0.4684D − 0.2116D2 ) = 1 − 0.5316D − 0.2568D2 − 0.2116D3 â´Â¨Ó¹Ç¹Ê¶Ò¹Ðã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ·Õ ãªéã¹Ç§¨ÃµÃÇ¨ËÒ NPML ¨ÐÁÕ·Ñ §ËÁ´

23 = 8

Ê¶Ò¹Ð

6.4.

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

125

¢) ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 4 á·ç» ¡çÊÒÁÒÃ¶ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ (6.11) ¹Ñ ¹¤×Í



 −0.0903



 0.2336

−0.0903 −0.0071 −0.0419

 p1

           −0.0071   −0.0903 0.2336 −0.0903 −0.0071   p2   =         −0.0419   −0.0071 −0.0903 0.2336 −0.0903   p3       0.2363 −0.0419 −0.0071 −0.0903 0.2336 p4 ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ ÁÕ¤èÒà·èÒ¡Ñº



 p1



−1  0.2336

−0.0903 −0.0071 −0.0419

           p2   −0.0903 0.2336 −0.0903 −0.0071     =          p3   −0.0071 −0.0903 0.2336 −0.0903        p4 −0.0419 −0.0071 −0.0903 0.2336   5.9512 3.2140 2.2035 2.0163 −0.0903      3.2140 7.0038 3.6575 2.2035   −0.0071   =    2.2035 3.6575 7.0038 3.2140   −0.0419   2.0163 2.2035 3.2140 5.9512 0.2363   −0.1762      0.0274    =    0.2412    1.0739

 −0.0903

  −0.0071    −0.0419   0.2363        

´Ñ§¹Ñ ¹ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 4 á·ç» ¤×Í

P (D) = −0.1762D + 0.0274D2 + 0.2412D3 + 1.0739D4 áÅÐ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å·Õ ÊÍ´¤ÅéÍ§¡ÑºÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ¹Õ ¤×Í

£ ¤ Heff (D) = (1 − D) 1 − (−0.1762D + 0.0274D2 + 0.2412D3 + 1.0739D4 ) = 1 − 0.8238D − 0.2036D2 − 0.2138D3 − 0.8327D4 + 1.0739D5

126

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

target

H(D)

NPML

Viterbi

âk

G(D)

P(D) PRML

âk

Viterbi H(D)

ÃÙ»·Õ 6.6: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³áººÊÁÁÙÅ ¾ÃéÍÁ·Ñ §Ç§¨ÃµÃÇ¨ËÒ NPML áÅÐ PRML

25 = 32

Ê¶Ò¹Ð

ÊÑ§à¡µ¨Ð¾ºÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ¨ÐÁÕ ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ·ÒÃìà¡çµ »ÃÐÊÔ·¸Ô¼Å

Heff (D)

¨ÐÁÕ ¨Ó¹Ç¹á·ç» ÁÒ¡¢Ö ¹ ¡ÇèÒ ·ÒÃìà¡çµ »¡µÔ

H(D)

«Ö § à» ¹ ¼Å

¨Ó¹Ç¹Ê¶Ò¹Ð =

àÁ× Í »¡µÔ

|A|

|A|ν+N

á·¹¨Ó¹Ç¹¢éÍÁÙÅ ºÔµ ÍÔ¹¾Øµ ·Õ à» ¹ ä»ä´é ·Ñ §ËÁ´,

H(D),

áÅÐ

¤×Í ¨Ó¹Ç¹Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§·ÒÃìà¡çµ

µÃÇ¨ËÒ NPML ÊÒÁÒÃ¶·ÓãËéÅ´Å§ä´éµÒÁ·Õ àÊ¹Íã¹ [53]

µÑÇÍÂèÒ§·Õ 6.2

áºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áÅÐÍÕ¤ÇÍäÅà«ÍÃì ã¹ÃÙ» ·Õ 3.2 ÊÓËÃÑº ÃÐºº¡ÒÃ

ºÑ¹·Ö¡áººá¹Ç¹Í¹ ·Õ ND = 2 áÅÐ SNR = 15 dB ÊÒÁÒÃ¶Å´ÃÙ»ä´éà» ¹ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ áººÊÁÁÙÅ µÒÁÃÙ» ·Õ 6.6 àÁ× Í ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ ¤×Í

H(D) = 1 − D

¶éÒ ¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ

6.4.

ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

ÍÔ¹¾Øµ

{ak } = {−1, 1, 1, 1}

¨§¶Í´ÃËÑÊ¢éÍÁÙÅ

127

áÅÐÊÑÒ³Ãº¡Ç¹

{wk } = {0.46, −1.20, 1.02, −0.59, −0.98}

´éÇÂ

¡) Ç§¨ÃµÃÇ¨ËÒ PRML

¢) Ç§¨ÃµÃÇ¨ËÒ NPML àÁ× ÍãªéÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 1 á·ç» ¤×Í

ÇÔ¸Õ·Ó

¨Ò¡ÃÙ»·Õ 6.6 ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

P (D) = −0.753D

ËÒä´é¨Ò¡

rk = ak ∗ hk = {−1, 2, 0, 0, −1} ´Ñ§¹Ñ ¹ ¢éÍÁÙÅ·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐ NPML ¤×Í

yk = rk + wk = {−0.54, 0.80, 1.02, −0.59, −1.98} ¡)

ÊÓËÃÑº ÃÐºº PRML Ç§¨Ã µÃÇ¨ËÒ ÇÕà·ÍÃìºÔ ¨Ð ·Ó ¡ÒÃ ¶Í´ÃËÑÊ ¢éÍÁÙÅ

à·ÃÅÅÔÊ ·Õ ÊÃéÒ§¨Ò¡·ÒÃìà¡çµ ¢éÍÁÙÅ

{yk }

H(D) = 1 − D

{yk }

â´Â ãªé á¼¹ÀÒ¾

µÒÁ·Õ áÊ´§ã¹ÃÙ» ·Õ 6.7(a) «Ö § ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ

ÊÒÁÒÃ¶ÊÃØ»ä´é µÒÁÃÙ»·Õ 6.8 â´Â·Õ µÑÇàÅ¢·Õ áÊ´§ÍÂÙèº¹¨Ø´µèÍ (node) áµèÅÐ¨Ø´ ¤×Í ¤èÒ

àÁµÃÔ¡àÊé¹·Ò§·Õ ÁÒ¶Ö§ ³ ¨Ø´µèÍ¹Ñ ¹ áÅÐµÑÇàÅ¢·Õ áÊ´§ÍÂÙèº¹àÊé¹ÊÒ¢ÒáµèÅÐàÊé¹ ¤×Í ¤èÒàÁµÃÔ¡ÊÒ¢Ò ¢Í§áµèÅÐàÊé¹ ÊÒ¢Ò·Õ ´Õ ·Õ ÊØ´ ·Õ ÁÒ¶Ö§ ·Õ ¨Ø´µèÍ ¹Ñ ¹æ à¾ÃÒÐ©Ð¹Ñ ¹ ¨Ò¡ÃÙ» ·Õ 6.8 ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§·Õ ¹éÍÂ ·Õ ÊØ´ ¤×Í ¤èÒ 2.24 ´Ñ§¹Ñ ¹Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð¶Í´ÃËÑÊ¢éÍÁÙÅâ´Â¡ÒÃÁÍ§ÂéÍ¹¡ÅÑºä»µÒÁàÊé¹·Ò§ ·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè (survivor path) ·Õ ÁÒ¶Ö§ ³ ¨Ø´µèÍ ·Õ ÁÕ ¤èÒ àÁµÃÔ¡ àÊé¹·Ò§à·èÒ ¡Ñº 2.24 «Ö § ¨Ð¾ºÇèÒ ¤èÒ »ÃÐÁÒ³¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{âk }

·Õ ÊÍ´¤ÅéÍ§¡ÑºàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè¹Õ ¤×Í

{âk } = {â0 , â1 , â2 , â3 } = {−1, −1, 1, 1} «Ö §ÁÕ¤èÒäÁèµÃ§¡ÑºÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak } = {−1, 1, 1, 1}

·Õ Êè§ÁÒ¨Ò¡µé¹·Ò§ ´Ñ§¹Ñ ¹ ¡ÒÃ¶Í´ÃËÑÊ

¢)

ÊÓËÃÑºÃÐºº NPML ÅÓ´Ñº¢éÍÁÙÅ

{yk }

¨Ð¶Ù¡Êè§¼èÒ¹à¢éÒä»ã¹Ç§¨Ã¡ÃÍ§ã¹¡ÒÃ·ÓãËéÊÑÒ³

Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ (noise whitening lter) â´Â¨Ðä´é¼ÅÅÑ¾¸ìÍÍ¡ÁÒà» ¹ ËÃ×ÍáÊ´§à» ¹ÅÓ´Ñº¢éÍÁÙÅ

{zk }

Z(D) = Y (D)[1 − P (D)]

ã¹â´àÁ¹àÇÅÒ ä´é´Ñ§¹Õ

{zk } = {−0.5400, 0.3934, 1.6224, 0.1781, −2.4243, −1.4910}

128

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

-1

-1 -1

2 -2

-1.5061

1 -1 0

0.4939

(a)

-0.4939

-1 1

ak = -1

1.5061

-2

ak = 1

1 1

(b) ÃÙ»·Õ 6.7: á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§ (a) ·ÒÃìà¡çµ =

1 − 0.247D − 0.753D2

-1

0.29

H(D)

1−D

áÅÐ (b) ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

·Õ ãªéã¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ¢Í§ÃÐºº PRML áÅÐ NPML µÒÁÅÓ´Ñº

0.64

0.93

1.04

1.97

0.35

2.32

0.96

0.29

Heff (D)

0.64

0.93

2.24 0

1.89

0.35

2.24

3.92

6.16

ÃÙ»·Õ 6.8: á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÓËÃÑºÃÐºº PRML

¨Ò¡¹Ñ ¹ ÅÓ´Ñº ¢éÍÁÙÅ

{zk }

¨Ð¶Ù¡ ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Õ ·Ó§Ò¹â´Âãªé á¼¹ÀÒ¾

à·ÃÅÅÔÊ·Õ ÊÃéÒ§¨Ò¡·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

Heff (D) = H(D)[1 − P (D)] = 1 − 0.247D − 0.753D2

µÒÁ·Õ áÊ´§ã¹ÃÙ» ·Õ 6.6(b) â´Â·Õ ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ

{zk }

ÊÒÁÒÃ¶ÊÃØ» ä´é µÒÁÃÙ» ·Õ 6.9

6.5.

-1 -1

¼Å¡ÒÃ·´ÅÍ§

0.29

129

0.29

0.15

0.45

2.63

3.08

0.03

3.11

0.24

1.88

0.14 0.84

1 -1

1.07 0

0.59

0.01 0.79

4.59

9.56

4.18

0.45 4.48

-1 1

0 1.07

1.86

0.01

0.29

0.15

0.45

6.19 1.04

0.01 0.03

0.03

3.94

8.52

4.49 0.10

0.06

0.18 5.88

0.24

5.93

0.26

2.22

8.16

ÃÙ»·Õ 6.9: á¼¹ÀÒ¾ÊÃØ»¢Ñ ¹µÍ¹¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÊÓËÃÑºÃÐºº NPML

à¹× Í§¨Ò¡ ¤èÒàÁµÃÔ¡ àÊé¹·Ò§·Õ ¹éÍÂ·Õ ÊØ´ ¤×Í ¤èÒ 0.24 à¾ÃÒÐ©Ð¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨Ð¶Í´ÃËÑÊ ¢éÍÁÙÅâ´Â¡ÒÃÁÍ§ÂéÍ¹¡ÅÑºä»µÒÁàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè·Õ ÁÒ¶Ö§ ³ ¨Ø´µèÍ·Õ ÁÕ¤èÒàÁµÃÔ¡àÊé¹·Ò§à·èÒ¡Ñº 0.24 «Ö §¨Ð¾ºÇèÒ ¤èÒ»ÃÐÁÒ³¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{âk }

·Õ ÊÍ´¤ÅéÍ§¡ÑºàÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè¹Õ ¤×Í

{âk } = {â0 , â1 , â2 , â3 } = {−1, 1, 1, 1} «Ö §ÁÕ¤èÒµÃ§¡ÑºÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

{ak } = {−1, 1, 1, 1}

·Õ Êè§ÁÒ¨Ò¡µé¹·Ò§ ´Ñ§¹Ñ ¹ ¡ÒÃ¶Í´ÃËÑÊ´éÇÂ

Ç§¨ÃµÃÇ¨ËÒ NPML ã¹µÑÇÍÂèÒ§¢éÍ¹Õ ¨Ö§äÁèÁÕ¢éÍ¼Ô´¾ÅÒ´à¡Ô´¢Ö ¹

6.5

¼Å¡ÒÃ·´ÅÍ§

ã¹ÊèÇ¹¹Õ ¨Ð·Ó¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐ NPML â´Âãªéáºº¨ÓÅÍ§ ªèÍ§ÊÑÒ³¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹Ç¹Í¹ (longitudinal recording) µÒÁÃÙ» ·Õ 6.10 â´Â·Õ

130

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

n(t)

1− D {±1} 2

p(t)

g(t)

s(t) LPF

equalizer

detector

âk

t k = kT ÃÙ»·Õ 6.10: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áÁèàËÅç¡

ÊÑÒ³ read back ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ¤³ÔµÈÒÊµÃìä´é ¤×Í

p(t) =

S−1 X

bk g(t − kT ) + n(t)

(6.25)

k=0

bk = (ak − ak−1 )/2

àÁ× Í

ºÇ¡ËÃ×ÍÅº áÅÐ ·Ñ §ËÁ´

bk = 0

S = 4096

(1.1), áÅÐ

n(t)

´éÒ¹à·èÒ¡Ñº

N0 /2

¤×Í ºÔµà»ÅÕ Â¹Ê¶Ò¹Ð (bk

= ±1

ÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹Ð

ËÁÒÂ¶Ö§ äÁèÁÕ¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹Ð),

ºÔµ ËÃ×Í 1 à«¡àµÍÃì (sector),

g(t)

ak ∈ ±1

¤×Í ºÔµÍÔ¹¾Øµ·Õ ÁÕ¨Ó¹Ç¹

¤×Í ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð µÒÁÊÁ¡ÒÃ

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºººÇ¡·Õ ÁÕ¤ÇÒÁË¹Òá¹è¹Êà»¡µÃÑÁ¡ÓÅÑ§áººÊÍ§

ÊÑÒ³ read back

p(t)

¡ÒÃªÑ¡µÑÇÍÂèÒ§´éÇÂ¤ÇÒÁ¶Õ ¡ÒÃªÑ¡µÑÇÍÂèÒ§à·èÒ¡Ñº

1/T

â´ÂÊÁÁØµÔÇèÒ ¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃªÑ¡µÑÇÍÂèÒ§ÁÕ

¡ÒÃà¢éÒ¨Ñ§ËÇÐÃÐËÇèÒ§ÊÑÒ³ read back áÅÐÇ§¨ÃªÑ¡µÑÇÍÂèÒ§áººÊÁºÙÃ³ì (perfect synchroniza tion) ¨Ò¡¹Ñ ¹ ÅÓ´Ñº¢éÍÁÙÅàÍÒµì¾Øµ

{sk }¨Ð¶Ù¡» Í¹ä»ÂÑ§ÍÕ¤ÇÍäÅà«ÍÃì (equalizer) à¾× Í»ÃÑºÃÙ»ÃèÒ§¢Í§

ÊÑÒ³ãËéà» ¹ä»µÒÁ·ÒÃìà¡çµ·Õ µéÍ§¡ÒÃ áÅéÇ¡çÊè§ÅÓ´Ñº¢éÍÁÙÅàÍÒµì¾Øµ

{yk }

·Õ ä´é ä»·Ó¡ÒÃ¶Í´ÃËÑÊ

¢éÍÁÙÅ ´éÇÂÇ§¨ÃµÃÇ¨ËÒ (detector) à¾× Í ËÒ¤èÒ »ÃÐÁÒ³¢Í§ÅÓ´Ñº ¢éÍÁÙÅ ÍÔ¹¾Øµ

{ak }

·Õ à» ¹ ä»ä´é ÁÒ¡

·Õ ÊØ´ ã¹·Õ ¹Õ ¤èÒ SNR ·Õ ãªé¨Ð¹ÔÂÒÁâ´Â

µ SNR = 10 log10 àÁ× Í

Vp = 1

áÅÐ

σ2

Vp 2 σ2

¶ (dB)

¤×Í ¢¹Ò´ÊÙ§ÊØ´¢Í§ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È

N0 /(2T )

¤×Í ¡ÓÅÑ§¢Í§ÊÑÒ³Ãº¡Ç¹

n(t)

(6.26)

(isolated transition pulse)

¹Í¡¨Ò¡¹Õ áµèÅÐ¨Ø´¢Í§ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´

6.5.

¼Å¡ÒÃ·´ÅÍ§

131

−1

−2

BER

−3

−4

PRML: 22 states NPML (2−tap predictor): 24 states NPML (4−tap predictor): 26 states

−5

SNR (dB)

ÃÙ»·Õ 6.11: »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2

ºÔµ (BER) ¨Ð¶Ù¡ ¤Ó¹Ç³â´Âãªé ¢éÍÁÙÅ ËÅÒÂæ à«¡àµÍÃì ¨¹¡ÇèÒ ¨Ðä´é ¢éÍ¼Ô´¾ÅÒ´ºÔµ ÁÒ¡¡ÇèÒ ËÃ×Í à·èÒ ¡Ñº 1000 ºÔµ ÃÙ» ·Õ 6.11 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐ NPML ·Õ ND = 2 àÁ× Í ¡ÓË¹´ãËé·Ø¡ÃÐººãªé·ÒÃìà¡çµáºº PR4,

H(D) = 1 − D2

ã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML ¤×Í

22 = 4

·Õ ãªéã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ¤×Í áºº 2 á·ç») áÅÐ

22+4 = 64

22+2 = 16

Ê¶Ò¹Ð (ÊÓËÃÑºÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ

Ê¶Ò¹Ð (ÊÓËÃÑºÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 4 á·ç») ´Ñ§¹Ñ ¹¨ÐàËç¹ä´éÇèÒ

Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML áµè ¨Ò¡¼Å¡ÒÃ·´ÅÍ§µÒÁÃÙ» ·Õ 6.11 ¾ºÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML ÍÂèÒ§àËç¹ä´éªÑ´ ËÃ×Í ÍÒ¨¨Ð¡ÅèÒÇä´éè ÇèÒ ³ ÃÐ´Ñº BER =

10−4

Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾´Õ ¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ

PRML »ÃÐÁÒ³ 2 dB ¹Í¡¨Ò¡¹Õ ¨Ò¡¼Å¡ÒÃ·´ÅÍ§ÂÑ§¾ºÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ·Õ ãªéÇ§¨Ã¡ÃÍ§ ·Ó¹ÒÂ 2 á·ç» ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ã¡Åéà¤ÕÂ§¡ÑºÇ§¨Ã¡ÃÍ§·Ó¹ÒÂ 4 á·ç» ´Ñ§¹Ñ ¹ ÊÓËÃÑºÃÐºº·Õ ¾Ô¨ÒÃ³Ò¹Õ

132

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

0.078 0.076

Predictor MMSE

0.074 0.072 0.07 0.068 0.066 0.064 0.062

Number of predictor taps

ÃÙ»·Õ 6.12: »ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ·Õ ãªé¨Ó¹Ç¹á·ç»µèÒ§¡Ñ¹ ·Õ SNR = 17 dB

Ç§¨ÃµÃÇ¨ËÒ NPML ÊÒÁÒÃ¶ãªéÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» ¡çà¾ÕÂ§¾ÍµèÍ¡ÒÃãªé§Ò¹áÅéÇ à¹× Í§¨Ò¡ ãËé»ÃÐÊÔ·¸ÔÀÒ¾·Õ ã¡Åéà¤ÕÂ§¡Ñº¡ÒÃãªéÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 4 á·ç» áµè¤ÇÒÁ«Ñº«éÍ¹¨Ð¹éÍÂ¡ÇèÒÁÒ¡ ÃÙ»·Õ 6.12 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ·Õ ãªé¨Ó¹Ç¹á·ç»µèÒ§¡Ñ¹ ·Õ SNR = 17 dB ¨ÐàËç¹ä´éÇèÒ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ 2 á·ç» ¡çÁÕ»ÃÐÊÔ·¸ÔÀÒ¾à¾ÕÂ§¾ÍÊÓËÃÑº¡ÒÃãªé§Ò¹áÅéÇ à¹× Í§¨Ò¡ ¶Ö§áÁéÇèÒ¨Ðà¾Ô Á¨Ó¹Ç¹á·ç»ÁÒ¡¢Ö ¹ »ÃÐÊÔ·¸ÔÀÒ¾·Õ ä´é¡çà¾Ô Á¢Ö ¹¹éÍÂÁÒ¡ «Ö §äÁè¤ØéÁ¤èÒ¡Ñº¤ÇÒÁ«Ñº«éÍ¹·Õ ä´éÃÑº ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ÃÙ»·Õ 6.13 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐ NPM L ·Õ ND = 2.5 â´Âãªé·ÒÃìà¡çµáºº PR4 àËÁ×Í¹à´ÔÁ áµè¤ÃÒÇ¹Õ ¨Ð¾ºÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ãËé »ÃÐÊÔ·¸ÔÀÒ¾·Õ ´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML ¤èÍ¹¢éÒ§ÁÒ¡ àÁ× Íà·ÕÂº¡Ñº¡ÒÃ·Ó§Ò¹·Õ ND = 2 â´ÂÍÒ¨¨Ð ¡ÅèÒÇä´éèÇèÒ ³ ÃÐ´Ñº BER =

10−4

Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML

»ÃÐÁÒ³ 3 dB ·Ñ §¹Õ à» ¹à¾ÃÒÐÇèÒ ·Õ ¤ÇÒÁ¨Ø¢éÍÁÙÅ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§ (ËÃ×Í ND ÊÙ§) Í§¤ì»ÃÐ¡Íº ¢Í§ÊÑÒ³Ãº¡Ç¹·Õ á½§ÍÂÙè ã¹¢éÍÁÙÅ ·Õ ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐÁÕ ÅÑ¡É³Ð à» ç¹ ÊÑÒ³Ãº¡Ç¹áººÊÕ ÁÒ¡¢Ö ¹ ¨Ö§ ·ÓãËé¡ÒÃãªé §Ò¹Ç§¨ÃµÃÇ¨ËÒ NPML ä´é »ÃÐÊÔ·¸ÔÀÒ¾·Õ ´Õ ¡ÇèÒ

6.5.

¼Å¡ÒÃ·´ÅÍ§

133

−1

−2

BER

−3

−4

PRML: 22 states NPML (2−tap predictor): 24 states −5

SNR (dB)

ÃÙ»·Õ 6.13: »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2.5

¡ÒÃãªé§Ò¹Ç§¨ÃµÃÇ¨ËÒ PRML ÁÒ¡ à¾× ÍãËé ¡ÒÃà»ÃÕÂºà·ÕÂºà» ¹ ä»ÍÂèÒ§ÂØµÔ¸ÃÃÁã¹àÃ× Í§¢Í§¤ÇÒÁ«Ñº«éÍ¹¢Í§ÃÐºº ¨Ð·Ó¡ÒÃ·´ÅÍ§ à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº 3 ÃÐºº ·Õ ND = 2.5 ´Ñ§µèÍä»¹Õ

1) Ç§¨ÃµÃÇ¨ËÒ NPML ·Õ ãªé·ÒÃìà¡çµáºº PR4

H(D) = 1 − D2

áÅÐÇ§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2

á·ç»

2) Ç§¨ÃµÃÇ¨ËÒ PRML ·Õ ãªé·ÒÃìà¡çµáºº PR 2

3) Ç§¨ÃµÃÇ¨ËÒ GPRML

H(D) = 1 + 2D − 2D3 − D4

·Õ ãªé ·ÒÃìà¡çµ áºº GPR «Ö § ÍÍ¡áººâ´Âà§× Í¹ä¢ºÑ§¤Ñº áººâÁ¹Ô¡ (´Ù

ÃÒÂÅÐàÍÕÂ´ã¹ËÑÇ¢éÍ·Õ 3.2.1) â´Â·Õ ·ÒÃìà¡çµáºº GPR ¹Õ ¨Ð¶Ù¡ÍÍ¡áººÊÓËÃÑºáµèÅÐ SNR

µÒÁÃÙ» ·Õ 6.14 àÁ× Íá¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ãªé ã¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ´éÇÂÍÑÅ¡ÍÃÔ·ÖÁ ÇÕà·ÍÃìºÔ ¢Í§·Ø¡ ÃÐºº 2

Ç§¨ÃµÃÇ¨ËÒ GPRML ¤×Í Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ·Õ ãªé ·ÒÃìà¡çµ áºº GPR ã¹¢³Ð·Õ Ç§¨ÃµÃÇ¨ËÒ PRML ¤×Í Ç§¨Ã

µÃÇ¨ËÒÇÕà·ÍÃìºÔ·Õ ãªé·ÒÃìà¡çµáºº PR

134

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

−1

2+2

NPML: 2 = 16 states PRML: [1 2 0 −2 −1] GPRML: (5−tap GPR) −2

BER

−3

−4

−5

SNR (dB)

ÃÙ»·Õ 6.14: ¼Å¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐººµèÒ§æ ·Õ ND = 2.5

¨ÐÁÕ ¨Ó¹Ç¹Ê¶Ò¹Ðà·èÒ ¡Ñ¹ ¤×Í 16 Ê¶Ò¹Ð áÅÐÍÕ¤ÇÍäÅà«ÍÃì ·Õ ãªé ¢Í§áµèÅÐÃÐºº¨Ð¶Ù¡ ÍÍ¡áººãËé àËÁÒÐÊÁ¡Ñº·ÒÃìà¡çµ

H(D)

·Õ ¡ÓË¹´ ¨Ò¡ÃÙ»¨ÐàËç¹ä´éÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡

¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML ·Õ ãªé ·ÒÃìà¡çµ áºº PR áµè ÁÕ »ÃÐÊÔ·¸Ô ã¡Åéà¤ÕÂ§¡Ñº Ç§¨ÃµÃÇ¨ËÒ GPRML ·Ñ §¹Õ à» ¹ à¾ÃÒÐÇèÒ ·ÒÃìà¡çµ »ÃÐÊÔ·¸Ô¼Å

Heff (D) = H(D)[1 − P (D)]

·Õ ãªé ã¹¡ÒÃÊÃéÒ§á¼¹ÀÒ¾

à·ÃÅÅÔÊ¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡¾Ô¨ÒÃ³Òä´éÇèÒà» ¹·ÒÃìà¡çµáºº GPR áººË¹Ö §ä´é à¹× Í§¨Ò¡ ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Åà» ¹àÅ¢¨Ó¹Ç¹¨ÃÔ§

6.6

ÊÃØ»·éÒÂº·

àÁ× Í ÃÐºº·Ó§Ò¹·Õ ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÊÙ§ Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ¨ÐÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹áººÊÕ (colored noise) ÁÒ¡¢Ö ¹ ã¹¡Ã³Õ ¹Õ Ç§¨ÃµÃÇ¨ËÒ PRML äÁè ÊÒÁÒÃ¶·Ó§Ò¹ä´é ÍÂèÒ§ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ ´Ñ§¹Ñ ¹Ç§¨ÃµÃÇ¨ËÒ NPML ¨Ö§

6.7.

ààºº½ ¡ËÑ´·éÒÂº·

135

ä´é ¶Ù¡ ¹ÓÁÒãªé à¾× Í à¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº ·Ñ §¹Õ à¹× Í§ÁÒ¨Ò¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ NPML ¨ÐÁÕ ¡ÒÃãªé Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ (ã¹¡ÒÃ·Õ ¨Ð·ÓãËéÊÑÒ³Ãº¡Ç¹áººÊÕ¡ÅÒÂà» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇ) ÃèÇÁ¡Ñº Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔã¹¡ÒÃ¶Í´ÃËÑÊ ¢éÍÁÙÅ ¹Í¡¨Ò¡¹Õ ÂÑ§ ¾ºÇèÒ·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å·Õ ãªé ã¹¡ÒÃÊÃéÒ§ á¼¹ÀÒ¾à·ÃÅÅÔÊ ¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡ ¾Ô¨ÒÃ³Òä´é ÇèÒ à» ¹ ·ÒÃìà¡çµ áºº GPR ¨Ö§ à» ¹àËµØ¼Å¢éÍË¹Ö §ÇèÒ·ÓäÁÇ§¨ÃµÃÇ¨ËÒ NPML ¨Ö§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML à¾ÃÒÐÇèÒ ·ÒÃìà¡çµáºº GPR ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒ·ÒÃìà¡çµáºº PR µÒÁ·Õ Í¸ÔºÒÂã¹º··Õ 3 ¶Ö§áÁéÇèÒÇ§¨ÃµÃÇ¨ËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML áµèÇ§¨ÃµÃÇ¨ËÒ NPML ¨ÐÁÕ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡¡ÇèÒ à¾ÃÒÐ©Ð¹Ñ ¹ ã¹¡ÒÃµÑ´ÊÔ¹ã¨ÇèÒ¨Ð¹ÓÇ§¨ÃµÃÇ¨ËÒ NPML ÁÒãªé§Ò¹ËÃ×Í äÁè ãËé¾Ô¨ÒÃ³ÒÇèÒ »ÃÐÊÔ·¸ÔÀÒ¾·Õ ¨Ðä´éÃÑºà¾Ô Á¢Ö ¹¨Ð¤ØéÁ¤èÒ¡Ñº¤ÇÒÁ«Ñº«éÍ¹·Õ µÒÁÁÒËÃ×ÍäÁè

6.7

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§Í¸ÔºÒÂ·Õ ÁÒ¢Í§á¹Ç¤Ô´¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML

2. ¨§Í¸ÔºÒÂ¤ÇÒÁáµ¡µèÒ§¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐÇ§¨ÃµÃÇ¨ËÒ NPML

3. ¨Ò¡¡ÒÃÍÍ¡áºº·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì µÒÁáºº¨ÓÅÍ§ã¹ÃÙ»·Õ 3.2 ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § (perpendicular recording) ·Õ ND = 2.5 áÅÐ SNR = 20 dB â´Â¡ÓË¹´ ãËé ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ ¤×Í

H(D) = 1 + D

{1.56, 0.35, −0.66, −0.69, 0.81, 0.20} ·Ó¹ÒÂ

P (D),

·ÒÃìà¡çµ»ÃÐÊÔ·¸Ô¼Å

3.1) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 1 á·ç» 3.2) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» 3.3) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 3 á·ç» 3.4) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 4 á·ç»

â´Â ·Õ

Heff (D),

¢éÍÁÙÅ ¢Í§Ç§¨ÃµÃÇ¨ËÒ NPML ·Õ ãªé

»ÃÒ¡®ÇèÒ ÅÓ´Ñº ¢éÍ¼Ô´¾ÅÒ´

ak ∈ {−1, 1}

{wk }

·Õ ä´é ¤×Í

¨§ ¤Ó¹Ç³ ËÒ Ç§¨Ã ¡ÃÍ§

áÅÐáÊ´§á¼¹ÀÒ¾à·ÃÅÅÔÊ·Õ ãªéã¹¡ÒÃ¶Í´ÃËÑÊ

136

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

4. ·ÓàËÁ×Í¹ã¹¢éÍ 3 áµè ¡ÓË¹´ãËé ·ÒÃìà¡çµ ·Õ µéÍ§¡ÒÃ ¤×Í ¢éÍ¼Ô´¾ÅÒ´

H(D) = 1 + 2D + D2

áÅÐÅÓ´Ñº

{wk } = {−0.56, −1.65, −0.21, 0.49, −0.98, −0.09}

5. áºº¨ÓÅÍ§¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ áÅÐÍÕ¤ÇÍäÅà«ÍÃì ã¹ÃÙ» ·Õ 3.2 ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ áºº á¹ÇµÑ § ·Õ ND = 2.5 áÅÐ SNR = 20 dB ÊÒÁÒÃ¶·Õ ¨ÐÅ´ÃÙ»ä´éà» ¹áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ áººÊÁÁÙÅ µÒÁÃÙ»·Õ 6.6 àÁ× Í ·ÒÃìà¡çµ·Õ µéÍ§¡ÒÃ ¤×Í ÍÔ¹¾Øµ

H(D) = 1+D ¶éÒ¡ÓË¹´ãËé ÅÓ´Ñº¢éÍÁÙÅ

{ak } = {1, −1, −1, 1} áÅÐÊÑÒ³Ãº¡Ç¹ {wk } = {−0.41, −0.33, 0.41, −0.59,

−1.29}

¨§¶Í´ÃËÑÊ¢éÍÁÙÅ

´éÇÂÇ§¨ÃµÃÇ¨ËÒ NPML àÁ× Íãªé

5.1) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 1 á·ç» ¤×Í

P (D) = −0.2613D

5.2) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» ¤×Í

P (D) = −0.3929D − 0.5035D2

5.3) Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáºº 2 á·ç» ¤×Í

P (D) = −0.3443D − 0.4656D2 + 0.0964D3

6. ·ÓàËÁ×Í¹ã¹¢éÍ 5 áµè¡ÓË¹´ãËé·ÒÃìà¡çµ·Õ µéÍ§¡ÒÃ ¤×Í ÍÔ¹¾Øµ

{ak } = {−1, 1, 1, −1}

−1.12, −3.18}

áÅÐÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

H(D) = 1 + 2D + D2 ,

ÅÓ´Ñº¢éÍÁÙÅ

{wk } = {0.47, 0.25, −0.38, −0.09,

º··Õ 7

Ç§¨ÃµÃÇ¨ËÒ PDNP

ã¹º·¹Õ ¨Ð¡ÅèÒÇ¶Ö§·Õ ÁÒ, ËÅÑ¡¡ÒÃ·Ó§Ò¹, áÅÐ»ÃÐâÂª¹ì¢Í§ Ç§¨ÃµÃÇ¨ËÒ PDNP (pattern dependent noise predictive) [54] «Ö § à» ¹ Ç§¨ÃµÃÇ¨ËÒ·Õ ¶Ù¡ ÍÍ¡áººÁÒà¾× Í ¨Ñ´¡ÒÃ¡Ñº ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ (media jitter noise) «Ö § ¾ººèÍÂã¹ÃÐºº¡ÒÃºÑ¹·Ö¡ áÁèàËÅç¡ ·Õ ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ÊÙ§æ ´Ñ§·Õ ¨ÐÍ¸ÔºÒÂµèÍä»ã¹º·¹Õ ¾ÃéÍÁ·Ñ § áÊ´§¼Å¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾ÃÐËÇèÒ§Ç§¨ÃµÃÇ¨ËÒ PDNP áÅÐÇ§¨ÃµÃÇ¨ËÒ PRML

7.1

º·¹Ó

¨Ò¡·Õ ä´éÍ¸ÔºÒÂä»ã¹º··Õ 4 à·¤¹Ô¤ PRML ¤×Í à·¤¹Ô¤¡ÒÃãªé§Ò¹ÃèÇÁ¡Ñ¹ÃÐËÇèÒ§ÍÕ¤ÇÍäÅà«ÍÃìáºº PR (partial response equalizer) áÅÐÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ (Viterbi detector) «Ö §à» ¹·Õ ¹ÔÂÁãªé§Ò¹ ¡Ñ¹ ÁÒ¡ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì [27] à·¤¹Ô¤ PRML ¨Ð·Ó§Ò¹à» ¹ 2 ¢Ñ ¹µÍ¹ ¤×Í ¢Ñ ¹µÍ¹áÃ¡¨Ð·Ó¡ÒÃ»ÃÑº ÃÙ»ÃèÒ§¢Í§ÊÑÒ³·Õ ä´é ÃÑº ãËé à» ¹ ä»µÒÁÃÙ»ÃèÒ§¢Í§·ÒÃìà¡çµ (target) ·Õ µéÍ§¡ÒÃ áÅÐ¢Ñ ¹µÍ¹·Õ ÊÍ§¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅâ´ÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ·Õ ÊÃéÒ§¢Ö ¹¨Ò¡ ·ÒÃìà¡çµ·Õ ¡ÓË¹´äÇé Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¶×Í ÇèÒ à» ¹ Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº àËÁÒÐ·Õ ÊØ´ (optimal sequence detector) ¡çµèÍàÁ× Í Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ á½§ÍÂÙèã¹ÊÑÒ³·Õ ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅÁÕÅÑ¡É³Ð 137

138

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

à» ¹ ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ [15] ÍÂèÒ§äÃ¡çµÒÁã¹·Ò§»¯ÔºÑµÔ ¡ÒÃãªé §Ò¹ÍÕ¤ÇÍäÅà«ÍÃì áºº PR ¨ÐÊè§¼Å·ÓãËéÍ§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔÁÕ¤Ø³ ÅÑ¡É³Ðà» ¹ ÊÑÒ³Ãº¡Ç¹áººÊÕ (colored noise) â´Âà©¾ÒÐÍÂèÒ§ÂÔ § àÁ× Í ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÊÙ§ (ND ÊÙ§) «Ö § ã¹¡Ã³Õ ¹Õ Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨ÐäÁè ¶×Í ÇèÒ à» ¹ Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº àËÁÒÐ ·Õ ÊØ´ÍÕ¡µèÍä» ´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒ NPML (noise predictive maximum likelihood) [51, 52] ¨Ö§ ä´é¶Ù¡¹ÓÁÒãªéà¾× Íà¾Ô Á»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº â´Â·Õ Ç§¨ÃµÃÇ¨ËÒ NPML ¨ÐÁÕ¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó ãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ ¡èÍ¹·Õ ¨ÐÊè§¼ÅÅÑ¾¸ì·Õ ä´éä»·Ó¡ÒÃ¶Í´ÃËÑÊ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ã¹ º··Õ 6 áÊ´§ãËéàËç¹ÇèÒ Ç§¨ÃµÃÇ¨ËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRML â´Âà©¾ÒÐ ÍÂèÒ§ÂÔ §·Õ ¤ÇÒÁ¨Ø¢éÍÁÙÅ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§ ¹Í¡¨Ò¡¹Õ ·Õ ND ÊÙ§æ Í§¤ì»ÃÐ¡Íº¢Í§ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ÂÑ§¨ÐÁÕÅÑ¡É³Ð¢Ö ¹ÍÂÙè¡Ñº áºº¢éÍÁÙÅ (data pattern) µÑÇÍÂèÒ§àªè¹ ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× Í ºÑ¹·Ö¡ ¶×Íä´éÇèÒà» ¹ ÊÑÒ³Ãº¡Ç¹·Õ ¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ (pattern dependent noise) ¡ÅèÒÇ¤×Í ÃÐ´Ñº ¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ ¨Ð¢Ö ¹ ÍÂÙè ¡Ñº áºº¢éÍÁÙÅ ·Õ à¢ÕÂ¹Å§ä»ã¹ Ê× ÍºÑ¹·Ö¡ à·¤¹Ô¤µèÒ§æ ä´é¶Ù¡¹ÓàÊ¹Íà¾× Í·ÓãËéÊÑÒ³Ãº¡Ç¹»ÃÐàÀ·¹Õ [54, 55] ÁÕÅÑ¡É³Ð¡ÅÒÂ à» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇ (white noise) ¡èÍ¹·Õ ¨Ð·Õ ·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ã¹ÊèÇ¹µèÍä»¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP [54] áÅÐà·¤¹Ô¤ ¡ÒÃÅ´¤ÇÒÁ «Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP

7.2

¡ÒÃ¢Ö ¹ÍÂÙè¡Ñºààºº¢éÍÁÙÅ¢Í§ÊÑÒ³Ãº¡Ç¹

¾Ô¨ÒÃ³Òáºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ã¹ÃÙ»·Õ 7.1 ¡ÓË¹´ãËé ¢Í§ ªèÍ§ ÊÑÒ³ ã¹ â´àÁ¹ µÍºÊ¹Í§ÃÇÁã¹â´àÁ¹

D, H(D)

C(D) = (1 − D)G(D)

¤×Í ¼Å µÍºÊ¹Í§ ·ÒÃìà¡çµã¹ â´àÁ¹

¤×Í ¼ÅµÍºÊ¹Í§

D, Q(D)

¤×Í ¼Å

¢Í§Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó áÅÐÍÕ¤ÇÍäÅà«ÍÃì, áÅÐà¾× ÍãËé §èÒÂµèÍ ¡ÒÃÍ¸ÔºÒÂ

ÍÕ¤ÇÍäÅà«ÍÃìáºº zero forcing [2, 16] ¨Ð¶Ù¡¹ÓÁÒãªéã¹ÊèÇ¹¹Õ ¹Ñ ¹¤×Í

Q(D) = H(D)/C(D)

ã¹

·Ò§»¯ÔºÑµÔ ·ÒÃìà¡çµáÅÐÍÕ¤ÇÍäÅà«ÍÃì«Ö §¶Ù¡ÊÃéÒ§â´ÂÇ§¨Ã¡ÃÍ§àªÔ§àÊé¹áºº¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¨Ó¡Ñ´ (FIR: nite impulse response) ¨ÐÁÕ¿ §¡ìªÑ¹¶èÒÂâÍ¹·Õ áµ¡µèÒ§ä»¨Ò¡ ã¹·Ò§·ÄÉ®Õ à¾ÃÒÐ©Ð¹Ñ ¹ ¶éÒ ¡ÓË¹´ãËé

H 0 (D)

áÅÐ

H(D)

áÅÐ

Q0 (D) = H 0 (D)/C(D)

Q(D)

·Õ µéÍ§¡ÒÃ

¤×Í ¿ §¡ìªÑ¹ ¶èÒÂ

7.2.

¡ÒÃ¢Ö ¹ÍÂÙè¡Ñºààºº¢éÍÁÙÅ¢Í§ÊÑÒ³Ãº¡Ç¹

139

n(t)

ak {0,1}

1–D

g(t)

s(t)

p(t)

∆t k

LPF

tk = kT Q(D)

C(D)

equalizer

âk

detector

H(D) ÃÙ»·Õ 7.1: áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³

H 0 (D) 6= H(D)

áÅÐ

Q0 (D) 6= Q(D)

´Ñ§¹Ñ ¹ ¢éÍÁÙÅàÍÒµì¾Øµ¢Í§ÍÕ¤ÇÍäÅà«ÍÃìÊÒÁÒÃ¶à¢ÕÂ¹à» ¹ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìä´é ¤×Í

Y (D) = A(D)C(D)Q0 (D) + N (D)Q0 (D) = A(D)H 0 (D) + N (D)Q0 (D) = A(D)H 0 (D) + N (D)Q0 (D) + [A(D)H(D) − A(D)H(D)] = A(D)H(D) + A(D)[H 0 (D) − H(D)] + N (D)Q0 (D) | {z }

(7.1)

W (D) àÁ× Í

N (D)

¤×Í ÊÑÒ³Ãº¡Ç¹à¡ÒÊì ÊÕ ¢ÒÇáºººÇ¡ (AWGN) áÅÐ

W (D)

¤×Í ÊÑÒ³Ãº¡Ç¹

W (D)

ÃÇÁ·Õ ä´é ³ ´éÒ¹¢Òà¢éÒ¢Í§Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº µÒÁÊÁ¡ÒÃ (7.1) ¨ÐàËç¹ä´éÇèÒ ÊÑÒ³Ãº¡Ç¹ ÁÕÅÑ¡É³Ð¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ (data dependent) à¹× Í§¨Ò¡ ÁÕ¾¨¹ì

A(D)

ÍÂÙè

ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡ à» ¹¼ÅÁÒ¨Ò¡ ¡ÒÃàÅ× Í¹µÓáË¹è§¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð áººÊØèÁ (random transition shift) ÃÐËÇèÒ§¡ÃÐºÇ¹¡ÒÃ·ÓãËé Ê× Í ºÑ¹·Ö¡ ÁÕ ÊÀÒ¾¤ÇÒÁà» ¹ áÁèàËÅç¡ (magnetization) µÒÁ·Õ µéÍ§¡ÒÃ â´Â¨ÐÁÕ ¿ §¡ìªÑ¹ ¤ÇÒÁË¹Òá¹è¹ ¤ÇÒÁ¹èÒ¨Ðà» ¹ áººà¡ÒÊì à«ÕÂ¹·Õ ÁÕ ¤èÒ à©ÅÕ Â à·èÒ ¡Ñº ¤èÒ ÈÙ¹Âì áÅÐ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ ¡Ñº ¨Ó¡Ñ´ãËéÁÕ¤èÒäÁèà¡Ô¹ ¤èÒÊÑÁºÙÃ³ì¢Í§

T /2)

â´Â·Õ

σj

|bk |σj2

(¹Ñ ¹¤×Í

∆tk ∼ N (0, |bk |σj2 ))

¨Ð¶Ù¡¡ÓË¹´à» ¹¨Ó¹Ç¹à»ÍÃìà«ç¹µì¢Í§ºÔµà«ÅÅì

¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ ¨Ö§ ¢Ö ¹ ÍÂÙè ¡Ñº áºº¢éÍÁÙÅ ¢Í§

áÅÐ

áÅÐ¶Ù¡

|bk |

{ak }

¤×Í

´Ñ§¹Ñ ¹

ÃÙ» ·Õ 7.2

140

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

5 4.5

Noise power (dB)

4 3.5 3 2.5 2 1.5 1 001

100

010

110

001

101

011

111

Data pattern

ÃÙ»·Õ 7.2: ¡ÓÅÑ§ ÊÑÒ³Ãº¡Ç¹·Õ ¢Ö ¹ ¡Ñº áºº¢éÍÁÙÅ ³ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃì ·Õ ¶Ù¡ ÍÍ¡áºº ÊÓËÃÑº·ÒÃìà¡çµ EEPR2 [1 4 6 4 1] ¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ·Õ ND = 2.5, SNR = 30 dB, áÅÐ

σj /T = 10%

áÊ´§¡ÓÅÑ§ÊÑÒ³Ãº¡Ç¹ (noise power) ·Õ ¢Ö ¹¡Ñºáºº¢éÍÁÙÅ ³ ´éÒ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃìáºº 21 á·ç» (tap) ·Õ ¶Ù¡ÍÍ¡áººãËéÊÍ´¤ÅéÍ§¡Ñº·ÒÃìà¡çµ EEPR2,

H(D) = 1 + 4D + 6D2 + 4D3 +

D4 ,

¢Í§ÃÐºº¡ÒÃºÑ¹·Ö¡ áººá¹ÇµÑ § (perpendicular recording) ·Õ ND = 2.5, SNR = 30 dB,

áÅÐ

σj /T = 10%

¨ÐàËç¹ä´éªÑ´à¨¹ÇèÒ ¡ÓÅÑ§ÊÑÒ³Ãº¡Ç¹¨ÐÁÕ¤èÒÊÙ§ àÁ× ÍÅÓ´Ñº¢éÍÁÙÅÁÕ¡ÒÃà»ÅÕ Â¹

Ê¶Ò¹ÐËÅÒÂ¤ÃÑ § àªè¹ áºº¢éÍÁÙÅ 010 áÅÐ 101 à» ¹µé¹

7.3

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP

¾Ô¨ÒÃ³ÒÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ [15] â´Â·Õ àÁµÃÔ¡ÊÒ¢Ò (branch metric) ¤Ó¹Ç³ä´é¨Ò¡

λk (u, v) = |yk −

ν X i=0

hi ak−1 |2 {z

r̂k (u,v)

}

(7.2)

7.3.

àÁ× Í

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP

(u, v)

gram),

141

á·¹¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð

ä»ÂÑ§Ê¶Ò¹Ð

ã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ (trellis dia

¤×Í ¢éÍÁÙÅ·Õ ¨Ð·Ó¡ÒÃ¶Í´ÃËÑÊ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ,

ÊÑÒ³·Õ äÁè ÁÕ ÊÑÒ³Ãº¡Ç¹·Õ ÊÍ´¤ÅéÍ§¡Ñº

(u, v)

r̂k (u, v)

¤×Í ¢éÍÁÙÅàÍÒµì¾ØµªèÍ§

(¹Ñ ¹¤×Í ¤èÒ ·Õ áÊ´§ÍÂÙè ã¹áµèÅÐàÊé¹ ÊÒ¢Ò¢Í§

á¼¹ÀÒ¾à·ÃÅÅÔÊ àªè¹ µÒÁ·Õ áÊ´§ã¹ÃÙ»·Õ 4.6) «Ö §ËÒä´é¨Ò¡

rk = ak ∗ hk =

ν X

ak−i hi

(7.3)

i=0 àÁ× Í

∗

¤×Í µÑÇ´Óà¹Ô¹¡ÒÃ¤Í¹âÇÅÙªÑ¹ (convolution operator),

µéÍ§¡ÒÃ,

¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô µÑÇ·Õ

¢Í§·ÒÃìà¡çµ, áÅÐ

H(D)

Pν

k=0 hk D

k ¤×Í ·ÒÃìà¡çµ·Õ

¤×Í Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§·ÒÃìà¡çµ

«Ö §ËÒä´é¨Ò¡ (´Ùáºº¨ÓÅÍ§¡ÒÃ

ÍÍ¡áºº·ÒÃìà¡çµã¹ÃÙ»·Õ 3.2)

wk = yk − rk D

â´Â¼Å¡ÒÃá»Å§

¢éÍÁÙÅ ¶éÒ Êè§ ¢éÍÁÙÅ

¤×Í

W (D)

(7.4)

µÒÁÊÁ¡ÒÃ (7.1) ¨ÐÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹·Õ ¢Ö ¹ÍÂÙè¡Ñºáºº

à¢éÒ ä»·Ó¡ÒÃ¶Í´ÃËÑÊ ´éÇÂÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ »ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» ¢Í§ÍÑµÃÒ

¢éÍ¼Ô´¾ÅÒ´ºÔµ (BER) ·Õ ä´é ÃÑº ¨ÐäÁè ´Õ à¾ÃÒÐ©Ð¹Ñ ¹ ã¹¡ÒÃ·Õ ¨Ðà¾Ô Á »ÃÐÊÔ·¸ÔÀÒ¾ÃÇÁ¢Í§ÃÐºº ¨Ð µéÍ§ÁÕ ¡ÒÃ¹Ó¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËé ÊÑÒ³Ãº¡Ç¹à» ¹ ÊÕ ¢ÒÇ ·ÓãËé¢éÍÁÙÅ

(noise whitening process) à¾× Í

ÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇ ¡èÍ¹·Õ ¨ÐÊè§¼ÅÅÑ¾¸ì·Õ ä´éä»·Ó¡ÒÃ¶Í´ÃËÑÊ´éÇÂ

Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ´Ñ§¹Ñ ¹ ã¹¡ÒÃãªé à·¤¹Ô¤ ¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ (noise prediction) ÃèÇÁ ¡ÑºÇ§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ð·ÓãËéàÁµÃÔ¡ÊÒ¢Òã¹ÊÁ¡ÒÃ (7.2) µéÍ§¶Ù¡´Ñ´á»Å§à» ¹

λk (u, v) = |yk − r̂k (u, v) − ŵk |2 àÁ× Í

ŵk

(7.5)

¤×Í ÊÑÒ³Ãº¡Ç¹·Õ ¶Ù¡·Ó¹ÒÂ «Ö §ËÒä´é¨Ò¡

ŵk =

L X

pi wk−i

(7.6)

i=1 â´Â·Õ á·ç»,

P (D) = pi

i=1 pi D

i ¤×Í Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ (prediction lter) ÊÑÒ³Ãº¡Ç¹áºº

¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô µÑÇ·Õ

142

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ÒÃ·Ó¹ÒÂ

¤×Í

ek = wk − ŵk ËÃ×Í

wk =

L X

(7.7)

pi wk−i + ek

(7.8)

i=1 â´ÂÇ§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹

P (D)

·Õ ´Õ¨ÐµéÍ§·ÓãËé¢éÍ¼Ô´¾ÅÒ´·Õ à¡Ô´¨Ò¡¡ÒÃ·Ó¹ÒÂ

ÁÕ

ÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇãËéÁÒ¡·Õ ÊØ´ àÁ× ÍÃÐºº·Ó§Ò¹·Õ ¤ÇÒÁ¨Ø¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§æ ¨Ð·ÓãËéÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹ ¨Ð¢Ö ¹ ÍÂÙè ¡Ñº áºº¢éÍÁÙÅ ´Ñ§¹Ñ ¹ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹·Õ àËÁÒÐÊØ´ ÍÂÙè ¡Ñº áºº¢éÍÁÙÅ ´éÇÂàªè¹¡Ñ¹ à¾ÃÒÐ©Ð¹Ñ ¹ ã¹¡ÒÃËÒ¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§

P (D)

¡ç ¤ÇÃ·Õ ¨Ð¢Ö ¹

¨ÐµéÍ§¨Ñ´ ÃÙ» ÊÁ¡ÒÃ

(7.8) ãËÁè ´Ñ§¹Õ

wk (a) =

L X

pi (a)wk−i (a) + ek (a)

(7.9)

i=1 àÁ× Í

ãªéá·¹áºº¢éÍÁÙÅµèÒ§æ ·Õ à» ¹ä»ä´é ÊÁ¡ÒÃ (7.9) ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§àÁ·ÃÔ¡«ìä´é ¤×Í

wk (a) = p(a)T w(a) + ek (a) â´Â·Õ

p(a)

·Ó¹ÒÂ, áÅÐ

[p1 (a), p2 (a), . . . , pL (a)]T

w(a)

¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§ àÇ¡àµÍÃì

w(a)T

(7.10)

¤×Í àÇ¡àµÍÃì á¹ÇµÑ § ¢Í§¤èÒ ÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§

[wk−1 (a), wk−2 (a), . . . , wk−L (a)]T P (D)

ÊÒÁÒÃ¶¤Ó¹Ç³ËÒä´é â´Â¡ÒÃ¤Ù³ ·Ñ § ÊÍ§¢éÒ§¢Í§ÊÁ¡ÒÃ (7.10) ´éÇÂ

áÅéÇãÊèµÑÇ´Óà¹Ô¹¡ÒÃ¤èÒ¤Ò´ËÁÒÂ (expectation operator) «Ö §¨Ðä´é¼ÅÅÑ¾¸ìà» ¹

£ ¤ £ ¤ E wk (a)w(a)T = p(a)T E w(a)w(a)T = p(a)T R(a) àÁ× Í

£ ¤ E w(a)w(a)T ¤×Í àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì (auto correlation matrix) ¢Í§ÊÑÒ³ £ ¤ wk (a), áÅÐ E ek (a)w(a)T = 0 µÒÁËÅÑ¡¡ÒÃàªÔ§µÑ §©Ò¡ (orthogonality principle)

R(a)

Ãº¡Ç¹

(7.11)

[25] á¡éÊÁ¡ÒÃ (7.11) ¨Ðä´é¼ÅÅÑ¾¸ìà» ¹

p(a)T = E[wk (a)w(a)T ] R−1 (a)

(7.12)

7.3.

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP

143

áÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ (predictor error variance) ¤×Í [54]

£ ¤ £ ¤ £ ¤T σp2 (a) = E wk (a)2 − E wk (a)w(a)T R−1 (a)E wk (a)w(a)T

(7.13)

ÊÁ¡ÒÃ (7.12) áÅÐ (7.13) áÊ´§ãËéàËç¹ÇèÒ ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂáÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹ ¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ¨Ð¢Ö ¹ÍÂÙè¡ÑºªèÇ§àÇÅÒ

·Õ ¾Ô¨ÒÃ³Ò (³ ªèÇ§àÇÅÒ

Ë¹Ö §æ ¡çÍÒ¨¨ÐÁÕáºº¢éÍÁÙÅ

·Õ µèÒ§¡Ñ¹ ä´é) ÍÂèÒ§äÃ¡çµÒÁ ¤èÒ ·Ñ § 2 ¤èÒ ¹Õ ÊÒÁÒÃ¶·Õ ¨Ð·ÓãËé äÁè ¢Ö ¹ ¡Ñº ªèÇ§àÇÅÒ

¡çä´é ¶éÒ ÊÁÁØµÔ ãËé

ÃÐººà» ¹áººÊàµªÑ¹à¹ÃÕ (stationary) [10, 26] ËÃ×Í¶éÒà» ¹ÃÐºº·Õ äÁèà» ¹áººÊàµªÑ¹à¹ÃÕ ÍÑÅ¡ÍÃÔ·ÖÁ áºº»ÃÑºµÑÇ (adaptive algorithm) [4, 10, 16] ÊÒÁÒÃ¶·Õ ¨Ð¶Ù¡¹ÓÁÒãªéã¹¡ÒÃ»ÃÑº¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ áÅÐ¤èÒ¤ÇÒÁá»Ã»ÃÇ¹¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂä´é à¹× Í§¨Ò¡ ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ («Ö § à» ¹ ¼ÅÁÒ¨Ò¡¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËé ÊÑÒ³Ãº¡Ç¹à» ¹ ÊÕ ¢ÒÇ) ¢Ö ¹ ÍÂÙè ¡Ñº áºº¢éÍÁÙÅ µÒÁ·Õ áÊ´§ã¹ÊÁ¡ÒÃ (7.13) ¤èÒ àÁµÃÔ¡ ÊÒ¢Ò¢Í§ Ç§¨ÃµÃÇ¨ËÒ PDNP ¨ÐµéÍ§¤Ó¹Ö§¶Ö§¡ÒÃ¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ´éÇÂ à¾ÃÒÐ©Ð¹Ñ ¹ àÁµÃÔ¡ÊÒ¢Ò¢Í§Ç§¨Ã µÃÇ¨ËÒ PDNP ÊÒÁÒÃ¶à¢ÕÂ¹ä´éà» ¹

λk (u, v) = log (σp (u, v)) + àÁ× Í

σp2 (u, v)

à¡Õ ÂÇ¢éÍ§¡Ñº

|yk − r̂k (u, v) − ŵk (u, v)|2 2σp2 (u, v)

(u, v),

¢éÍÁÙÅ·Õ à¡Õ ÂÇ¢éÍ§¡Ñº

áÅÐ

ŵk (u, v)

(u, v)

(7.14)

(u, v)

¤×Í ÊÑÒ³Ãº¡Ç¹·Õ ¶Ù¡·Ó¹ÒÂ·Õ ÊÍ´¤ÅéÍ§¡Ñº

áÅÐáºº¢éÍÁÙÅ·Õ

(u, v)

áÅÐáºº

«Ö §ËÒä´é¨Ò¡

ŵk (u, v) =

L X

pi (u, v){yk−i − r̂k−i (u, v)}

(7.15)

i=1 ¨Ò¡ÊÁ¡ÒÃ (7.12) áÅÐ (7.13) ¨Ð¾ºÇèÒ Ç§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³ á»Ã»ÃÇ¹¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ

P (D)

áÅÐ

σp2

P (D) =

PL i

pi D i

áÅÐ¤èÒ¤ÇÒÁ

¨Ð¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅã¹áµèÅÐàÊé¹ÊÒ¢Ò ´Ñ§¹Ñ ¹ ¤èÒ¾ÒÃÒÁÔàµÍÃì

µÒÁáºº¢éÍÁÙÅ·Õ ÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

(u, v)

¹Ñ ¹æ

ã¹·Ò§»¯ÔºÑµÔáÅéÇ ¤èÒÊÑÁ»ÃÐÊÔ·¸Ô ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹

p(a)

¨Ð¢Ö ¹ÍÂÙè¡Ñº¢éÍÁÙÅ

ºÔµÀÒÂã¹Ë¹éÒµèÒ§àÅ× Í¹áºº¨Ó¡Ñ´ ( nite sliding window) [56] «Ö §à¢ÕÂ¹á·¹´éÇÂÊÑÅÑ¡É³ì

aW k−M

144

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊÓËÃÑº¤èÒ¨Ó¹Ç¹àµçÁºÇ¡ Ê¶Ò¹Ðà·èÒ¡Ñº

áÅÐ

2max(ν+L, M )+W

´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒ PDNP ¨Ðãªéá¼¹ÀÒ¾à·ÃÅÅÔÊ·Õ ÁÕ¨Ó¹Ç¹

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP ã¹ÊèÇ¹¹Õ ¨Ð¾Ô¨ÒÃ³Òà©¾ÒÐ¡Ã³Õ·Õ

W =0

Ê¶Ò¹Ð·Ñ §ËÁ´·Õ ãªéã¹á¼¹ÀÒ¾à·ÃÅÅÔÊÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

7.4

áÅÐ

M < ν +L

à¾ÃÒÐ©Ð¹Ñ ¹ ¨Ó¹Ç¹

2ν+L

ÍÑÅ¡ÍÃÔ·ÖÁ PS PDNP

ÍÑÅ¡ÍÃÔ·ÖÁ PDNP ·Õ Í¸ÔºÒÂä»ã¹ËÑÇ¢éÍ ·Õ 7.3 µéÍ§¡ÒÃá¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ÁÕ ¨Ó¹Ç¹Ê¶Ò¹Ð·Ñ §ËÁ´

2ν+L

ÍÂèÒ§äÃ¡çµÒÁ ¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP ÊÒÁÒÃ¶·ÓãËéÅ´Å§ä´éâ´Âãªéá¹Ç¤Ô´ ¡ÒÃ

» Í¹¡ÅÑº¤èÒµÑ´ÊÔ¹ã¨ (decision feedback) [53] áÅÐà¾× ÍãËéÃÐººÁÕ»ÃÐÊÔ·¸ÔÀÒ¾·Õ ÂÍÁÃÑºä´é á¹Ç¤Ô´ ¹Õ µéÍ§¡ÒÃ¤ÇÒÁÅÖ¡ (depth) ¡ÒÃ» Í¹¡ÅÑº ¤èÒ µÑ´ÊÔ¹ã¨·Õ ¤èÍ¹¢éÒ§¹éÍÂ àÁ× Í à·ÕÂº¡Ñº ¤ÇÒÁÂÒÇ (ËÃ×Í ¨Ó¹Ç¹á·ç») ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ «Ö §ËÁÒÂ¤ÇÒÁÇèÒ á¼¹ÀÒ¾à·ÃÅÅÔÊ·Õ ãªéÂÑ§¨Óà» ¹ µéÍ§¶Ù¡ ¢ÂÒÂãËé ãËè ¢Ö ¹ (trellis expansion) ¹Ñ ¹¤×Í ÁÕÕ¨Ó¹Ç¹Ê¶Ò¹ÐÁÒ¡¢Ö ¹ ¡ÇèÒ ÃÐºº·Õ äÁè ãªé Ç§¨Ã ¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ ã¹ÊèÇ¹¹Õ ¨ÐÍ¸ÔºÒÂ ÇÔ¸Õ¡ÒÃ·Õ àÊ¹Íã¹ [53]

«Ö §¤ÅéÒÂ¡Ñºá¹Ç¤Ô´

¡ÒÃ»ÃÐÁÇÅ¼Åáººà¾Íà«ÍÃì

äÇàÇÍÃì (PSP: per survivor processing) [57] ÊÓËÃÑºÅ´¤ÇÒÁ«Ñº«éÍ¹¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ PDNP â´Â ÍÑÅ¡ÍÃÔ·ÖÁãËÁè·Õ ä´é ã¹Ë¹Ñ§Ê×Í¹Õ ¨ÐàÃÕÂ¡ÇèÒ ÍÑÅ¡ÍÃÔ·ÖÁ PS PDNP (per survivor PDNP algorith m) Ç§¨ÃµÃÇ¨ËÒ PS PDNP ¨Ð·Ó§Ò¹µÒÁÍÑÅ¡ÍÃÔ·ÖÁ PDNP º¹¾× ¹°Ò¹¢Í§á¹Ç¤Ô´ PSP «Ö § ¨Ð ·ÓãËé á¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ãªé ã¹Ç§¨ÃµÃÇ¨ËÒ PS PDNP ÁÕ ¨Ó¹Ç¹Ê¶Ò¹Ðà·èÒ à´ÔÁ (ËÃ×Í à·èÒ ¡Ñº ÃÐºº·Õ äÁèãªèÇ§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹) ¡ÅèÒÇ¤×Í á·¹·Õ ¨Ð·Ó¡ÒÃ¢ÂÒÂá¼¹ÀÒ¾à·ÃÅÅÔÊãËéãËè¢Ö ¹ Ç§¨ÃµÃÇ¨ËÒ PS PDNP ¨Ð·Ó¡ÒÃÁÍ§ÂéÍ¹¡ÅÑº ä»µÒÁàÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè µÒÁá¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ÁÒ¶Ö§ ³ ¨Ø´µèÍ (node) ·Õ ¡ÓÅÑ§ ¾Ô¨ÒÃ³Ò áÅéÇ ãªé ¢éÍÁÙÅ µèÒ§æ ·Õ ÊÍ´¤ÅéÍ§¡Ñº àÊé¹·Ò§·Õ ÂÑ§ ÁÕ ªÕÇÔµ ÍÂÙè ¹Ñ ¹ ã¹¡ÒÃ¤Ó¹Ç³ËÒ¤èÒÊÑÒ³Ãº¡Ç¹·Õ ¶Ù¡·Ó¹ÒÂ ËÃ×ÍÍÒ¨¨Ð¡ÅèÒÇä´éÇèÒ Ç§¨ÃµÃÇ¨ËÒ PS PDNP ÂÑ§¤§ãªéÊÁ¡ÒÃ (7.14) ã¹¡ÒÃ¤Ó¹Ç³ËÒ¤èÒàÁµÃÔ¡ÊÒ¢Ò Â¡àÇé¹áµè ÊÑÒ³Ãº¡Ç¹·Õ ¶Ù¡·Ó¹ÒÂ¨Ð¶Ù¡ ¤Ó¹Ç³¨Ò¡

ŵk (u, v) =

L X i=1

pi (u, v)ẑk−i (u, v)

(7.16)

7.4.

ÍÑÅ¡ÍÃÔ·ÖÁ PS PDNP

time k (0) -1 -1

145

zˆk −2 ( A )

k+1

zˆk −1 ( A ) time k

zˆk ( 0,1)

k+1

A (1) 1 -1

(1)

zˆk −2 ( B )

2 -2

(2) -1 1

0 -2

ak = 1

ak = -1

(3) 1 1

zˆk ( 2,1) zˆk −1 ( B )

yk −1 = 1

yk − 2 = 0.5

(a) Trellis diagram: PR4

yk = 0.15

(b) Decoding procedure

ÃÙ»·Õ 7.3: (a) á¼¹ÀÒ¾à·ÃÅÅÔÊÊÓËÃÑº·ÒÃìà¡çµáºº PR4 áÅÐ (b) ¢Ñ ¹µÍ¹¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂ á¼¹ÀÒ¾à·ÃÅÅÔÊ

àÁ× Í

ẑk−i (u, v)

¤×Í ÊÑÒ³Ãº¡Ç¹·Õ á½§ÍÂÙè ã¹¢éÍÁÙÅ

·Õ à» ¹ ¼Å·ÓãËé à¡Ô´ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

(u, v)

«Ö §¹ÔÂÒÁâ´Â

ẑk (u, v) = yk (u, v) − r̂k (u, v)

(7.17)

{ẑk−1 , ẑk−2 , . . . , ẑk−L }

2ν

Ê¶Ò¹Ð

ÊÓËÃÑº·Ø¡àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµ

ÍÂÙè

µÑÇÍÂèÒ§·Õ 7.1

ÃÙ»·Õ 7.3 áÊ´§µÑÇÍÂèÒ§¡ÒÃËÒ¤èÒÊÑÒ³Ãº¡Ç¹·Õ á½§ÍÂÙèã¹¢éÍÁÙÅ

ãËé à¡Ô´ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐÊÍ´¤ÅéÍ§¡Ñº

H(D) = 1 − D2 , ÁÕ¨Ó¹Ç¹

L=2

(u, v)

·Õ à» ¹¼Å·Ó

µÒÁÊÁ¡ÒÃ (7.17) ¢Í§ÃÐºº·Õ ãªé ·ÒÃìà¡çµ áºº PR4,

«Ö §ÁÕá¼¹ÀÒ¾à·ÃÅÅÔÊµÒÁÃÙ»·Õ 7.3(a) àÁ× ÍÇ§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹·Õ ãªé

á·ç»

146

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÇÔ¸Õ·Ó

ãËé¾Ô¨ÒÃ³ÒÊ¶Ò¹Ð (1) ³ àÇÅÒ

k+1

µÒÁ·Õ áÊ´§ã¹ÃÙ»·Õ 7.3(b) ¨ÐàËç¹ä´éÇèÒÁÕàÊé¹·Ò§·Õ ÇÔ §

à¢éÒÁÒËÒÊ¶Ò¹Ð (1) à» ¹¨Ó¹Ç¹ 2 àÊé¹·Ò§ ¤×Í àÊé¹·Ò§ A áÅÐ B à¾ÃÒÐ©Ð¹Ñ ¹ ¤èÒ ÊÁ¡ÒÃ (7.16) ÊÓËÃÑº

ẑk−i (u, v)

ã¹

= 1 áÅÐ 2 ËÒä´é´Ñ§µèÍä»¹Õ ÊÓËÃÑºàÊé¹·Ò§ A ¨Ðä´éÇèÒ

ẑk (0, 1) = yk − r̂k (0, 1) = 0.15 − 2 = −1.85 ẑk−1 (A) = ẑk−1 (0, 1) = yk−1 − r̂k−1 (0, 0) = 1 − 0 = 1 ẑk−2 (A) = ẑk−2 (0, 1) = yk−2 − r̂k−2 (0, 0) = 0.5 − 0 = 0.5 áÅÐÊÓËÃÑºàÊé¹·Ò§ B ¨Ðä´éÇèÒ

ẑk (2, 1) = yk − r̂k (2, 1) = 0.15 − 0 = 0.15 ẑk−1 (B) = ẑk−1 (2, 1) = yk−1 − r̂k−1 (3, 2) = 1 − (−2) = 3 ẑk−2 (B) = ẑk−2 (2, 1) = yk−2 − r̂k−2 (1, 3) = 0.5 − 2 = −1.5

7.5

¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP

ã¹¡ÒÃà»ÃÕÂºà·ÕÂº¤ÇÒÁ«Ñº«éÍ¹ (complexity) ¢Í§Ç§¨ÃµÃÇ¨ËÒ ¨Ð¾Ô¨ÒÃ³Ò¨Ò¡¨Ó¹Ç¹µÑÇ´Óà¹Ô¹¡ÒÃ (operator) ÊÓËÃÑº¡ÒÃºÇ¡ (addition) áÅÐ¡ÒÃ¤Ù³ (multiplication) ·Õ µéÍ§ãªéã¹¡ÒÃ·Ó§Ò¹¢Í§áµèÅÐ Ç§¨ÃµÃÇ¨ËÒ µÒÃÒ§·Õ 7.1 à»ÃÕÂºà·ÕÂº¤ÇÒÁ«Ñº«éÍ¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP áÅÐ PS PDNP àÁ× Í

¤×Í ¨Ó¹Ç¹áºº¢éÍÁÙÅ·Õ ãªéã¹Ç§¨ÃµÃÇ¨ËÒ PDNP áÅÐ PS PDNP ¨Ò¡µÒÃÒ§¨ÐàËç¹ä´éÇèÒ Ç§¨Ã

µÃÇ¨ËÒ PS PDNP ÁÕ¤ÇÒÁ«Ñº«éÍ¹áÅÐµéÍ§¡ÒÃãªéË¹èÇÂ¤ÇÒÁ¨Ó (memory requirement) ¹éÍÂ¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PDNP ÁÒ¡

7.6

¼Å¡ÒÃ·´ÅÍ§

ã¹ÊèÇ¹¹Õ ¨Ð·Ó¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML áÅÐ PDNP â´Âãªéáºº¨ÓÅÍ§ ªèÍ§ÊÑÒ³ µÒÁÃÙ»·Õ 7.1 àÁ× ÍÊÑÒ³ read back ÊÒÁÒÃ¶à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÁ¡ÒÃ¤³ÔµÈÒÊµÃì

7.6.

¼Å¡ÒÃ·´ÅÍ§

147

µÒÃÒ§·Õ 7.1: ¨Ó¹Ç¹¢Í§µÑÇ´Óà¹Ô¹¡ÒÃ·Õ ãªéµèÍ¢éÍÁÙÅ 1 ºÔµ ¢Í§Ç§¨ÃµÃÇ¨ËÒ PDNP áÅÐ PS PDNP

Ç§¨ÃµÃÇ¨ËÒ

¨Ó¹Ç¹¢Í§µÑÇ´Óà¹Ô¹¡ÒÃ·Õ ãªéµèÍ¢éÍÁÙÅ 1 ºÔµ

(detector) Ç§¨ÃµÃÇ¨ËÒ PDNP

Ë¹èÇÂ¤ÇÒÁ¨Ó·Õ µéÍ§¡ÒÃ

¡ÒÃºÇ¡

¡ÒÃ¤Ù³

(memory requirement)

(4L + 7)2ν+L

(2L + 8)2ν+L

(2L + 4)2ν+L + Np L + 2

(2L + 8)2ν

(2L + 8)2ν + Np L

Ç§¨ÃµÃÇ¨ËÒ PS PDNP

ä´é¤×Í

p(t) =

S−1 X

bk g(t − kT + ∆tk ) + n(t)

(7.18)

k=0

ak ∈ {0, 1}

àÁ× Í

¤×Í ¢éÍÁÙÅ ºÔµ ÍÔ¹¾Øµ ·Õ ÁÕ ¨Ó¹Ç¹·Ñ §ËÁ´

ºÔµà»ÅÕ Â¹Ê¶Ò¹Ð (bk

= ±1

ÁÕ¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹Ð),

S = 4096

ºÔµ,

bk = (ak − ak−1 )

ÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹á»Å§Ê¶Ò¹ÐºÇ¡ËÃ×ÍÅº áÅÐ

g(t)

bk = 0

n(t)

¤×Í ÊÑÒ³

Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºººÇ¡ (AWGN) ·Õ ÁÕ¤ÇÒÁË¹Òá¹è¹Êà»¡µÃÑÁ¡ÓÅÑ§áººÊÍ§´éÒ¹à·èÒ¡Ñº

∆tk

¤×ÍäÁè

¤×Í ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹ÐµÒÁÊÁ¡ÒÃ (1.1) ÊÓËÃÑºÃÐºº¡ÒÃ

ºÑ¹·Ö¡áººá¹Ç¹Í¹ áÅÐµÒÁÊÁ¡ÒÃ (1.2) ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §,

áÅÐ

¤×Í

N0 /2,

¤×Í ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡ (media jitter noise) ·Õ ÁÕ¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹

¤ÇÒÁ¹èÒ¨Ðà» ¹ áººà¡ÒÊì à«ÕÂ¹ (Gaussian probability density function) â´ÂÁÕ ¤èÒà©ÅÕ Â à·èÒ ¡Ñº ¤èÒ ÈÙ¹Âì áÅÐ¤èÒ ¤ÇÒÁá»Ã»ÃÇ¹à·èÒ ¡Ñº à¡Ô¹

T /2)

àÁ× Í

σj

|bk |σj2

(¹Ñ ¹¤×Í

∆tk ∼ N (0, |bk |σj2 ))

¨Ð¶Ù¡ ¡ÓË¹´à» ¹ ¨Ó¹Ç¹à»ÍÃìà«ç¹µì ¢Í§ºÔµ à«ÅÅì

(absolute value) ¢Í§

áÅÐ¶Ù¡ ¨Ó¡Ñ´ ãËé ÁÕ ¤èÒ äÁè

áÅÐ

|bk |

¤×Í ¤èÒÊÑÁºÙÃ³ì

ÊÑÒ³ read back

p(t)

¨Ð¶Ù¡Êè§¼èÒ¹ä»ÂÑ§Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó (LPF: low pass lter) ºÑµà·ÍÃì

àÇÔÃìµÍÑ¹´Ñº·Õ 7 áÅÐ¶Ù¡·Ó¡ÒÃªÑ¡µÑÇÍÂèÒ§´éÇÂ¤ÇÒÁ¶Õ ¡ÒÃªÑ¡µÑÇÍÂèÒ§à·èÒ¡Ñº

1/T

â´ÂÊÁÁØµÔÇèÒ¡ÃÐºÇ¹

¡ÒÃã¹¡ÒÃªÑ¡ µÑÇÍÂèÒ§ÁÕ ¡ÒÃà¢éÒ ¨Ñ§ËÇÐÃÐËÇèÒ§ÊÑÒ³ read back áÅÐÇ§¨ÃªÑ¡ µÑÇÍÂèÒ§áººÊÁºÙÃ³ì (perfect synchronization) ¨Ò¡¹Ñ ¹ ÅÓ´Ñº¢éÍÁÙÅàÍÒµì¾Øµ

{sk } ¨Ð¶Ù¡» Í¹ä»ÂÑ§ÍÕ¤ÇÍäÅà«ÍÃì à¾× Í»ÃÑº

¤Ø³ÅÑ¡É³Ð¢Í§ÊÑÒ³ãËéà» ¹ä»µÒÁ·ÒÃìà¡çµ·Õ µéÍ§¡ÒÃ áÅéÇ¡çÊè§ÅÓ´Ñº¢éÍÁÙÅàÍÒµì¾Øµ

{yk }

·Ó¡ÒÃ¶Í´ÃËÑÊ¢éÍÁÙÅ´éÇÂÇ§¨ÃµÃÇ¨ËÒ (detector) à¾× ÍËÒ¤èÒ»ÃÐÁÒ³¢Í§ÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ

·Õ ä´éä»

{ak }

·Õ

148

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

à» ¹ä»ä´éÁÒ¡·Õ ÊØ´ ã¹º·¹Õ ¤èÒ SNR ¨Ð¹ÔÂÒÁâ´Â

µ SNR = 10 log10 àÁ× Í

Ei N0

¶ (7.19)

¤×Í ¾ÅÑ§§Ò¹¢Í§¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¢Í§ªèÍ§ÊÑÒ³

¹Í¡¨Ò¡¹Õ áµèÅÐ¨Ø´ ¢Í§ BER

¨Ð¶Ù¡ ¤Ó¹Ç³â´Âãªé ¢éÍÁÙÅ ËÅÒÂæ à«¡àµÍÃì (sector) ¨¹¡ÇèÒ ¨Ðä´é ¢éÍ¼Ô´¾ÅÒ´ºÔµ ÁÒ¡¡ÇèÒ ËÃ×Í à·èÒ ¡Ñº 1000 ºÔµ Ç§¨ÃµÃÇ¨ËÒ 3 áºº ¤×Í Ç§¨ÃµÃÇ¨ËÒ PRML, Ç§¨ÃµÃÇ¨ËÒ PDNP, áÅÐÇ§¨ÃµÃÇ¨ËÒ PS PDNP ¨Ð¶Ù¡·Ó¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾ ÊÓËÃÑºÃÐºº·Õ ãªé·ÒÃìà¡çµáºº GPR3 (·ÒÃìà¡çµáºº 3 á·ç» ·Õ ¶Ù¡ÍÍ¡áººµÒÁà§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡ [19]) áÅÐÍÕ¤ÇÍäÅà«ÍÃìáºº 21 á·ç» â´Â·Õ ·ÒÃìà¡çµ áºº GPR3 ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ ¤×Í ÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § ¤×Í

H(D) = 1 + 0.05D − 0.65D2

H(D) = 1+1.25D +0.62D2

áÅÐÊÓËÃÑº

ÃÙ»·Õ 7.4 à»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾

N D = 2.5

áÅÐÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡

σj /T = 10%

¨Ò¡ÃÙ»·Õ 7.4(a) ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ Ç§¨ÃµÃÇ¨ËÒ PS PDNP ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ã¡Åéà¤ÕÂ§¡ÑºÇ§¨ÃµÃÇ¨ËÒ PDNP áµèÇ§¨ÃµÃÇ¨ËÒ·Ñ §ÊÍ§¹Õ ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PRM L â´Âà©¾ÒÐÍÂèÒ§ÂÔ § ·Õ SNR ÊÙ§ (¹Ñ ¹¤×Í àÁ× Í ÊÑÒ³Ãº¡Ç¹ËÅÑ¡ ã¹ÃÐºº ¤×Í ÊÑÒ³Ãº¡Ç¹ ¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡) ã¹¢³Ð·Õ ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ § (´ÙÃÙ»·Õ 7.4(b)) Ç§¨ÃµÃÇ¨ËÒ PRML ´ÙàËÁ×Í¹¨ÐÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒÇ§¨ÃµÃÇ¨ËÒ PS PDNP áÅÐÇ§¨ÃµÃÇ¨ËÒ PDNP àÅç¡¹éÍÂ ·Õ SNR µ Ó ·Ñ §¹Õ ÍÒ¨¨Ðà» ¹à¾ÃÒÐÇèÒ ·Õ SNR µ Ó ÊÑÒ³Ãº¡Ç¹ËÅÑ¡ã¹ÃÐººäÁèãªèÊÑÒ³Ãº¡Ç¹ ¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡ ´Ñ§¹Ñ ¹ Ç§¨ÃµÃÇ¨ËÒ PS PDNP áÅÐÇ§¨ÃµÃÇ¨ËÒ PDNP «Ö §¶Ù¡ÍÍ¡áººÁÒãËé ¨Ñ´¡ÒÃ¡Ñº ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ ¨Ö§ äÁè ÊÒÁÒÃ¶·Ó§Ò¹ä´é ÍÂèÒ§ÁÕ »ÃÐÊÔ·¸ÔÀÒ¾ ÍÂèÒ§äÃ ¡çµÒÁ ·Õ SNR ÊÙ§ Ç§¨ÃµÃÇ¨ËÒ PS PDNP áÅÐÇ§¨ÃµÃÇ¨ËÒ PDNP ¨ÐÁÕ »ÃÐÊÔ·¸ÔÀÒ¾´Õ ¡ÇèÒ Ç§¨Ã µÃÇ¨ËÒ PRML ÁÒ¡ ¨Ò¡¡ÒÃ¼Å·´ÅÍ§áÊ´§ãËéàËç¹ä´éÇèÒ Ç§¨ÃµÃÇ¨ËÒ PS PDNP ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ã¡Åéà¤ÕÂ§¡Ñº Ç§¨ÃµÃÇ¨ËÒ PDNP à¾ÃÒÐ©Ð¹Ñ ¹ ã¹·Ò§»¯ÔºÑµÔ Ç§¨ÃµÃÇ¨ËÒ PS PDNP ÍÒ¨¨Ð¶Ù¡ ¹ÓÁÒãªéá·¹Ç§¨ÃµÃÇ¨ËÒ PDNP à¹× Í§¨Ò¡ ÁÕ¤ÇÒÁ«Ñº«éÍ¹¹éÍÂ¡ÇèÒÁÒ¡ 1

¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹ áÅÐÁÕ¤èÒà·èÒ¡Ñº

g (t)/2

ÊÓËÃÑºÃÐºº¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §

g 0 (t)

ÊÓËÃÑºÃÐºº

7.7.

ÊÃØ»·éÒÂº·

149

−1

PRML (4 states) PS − PDNP (4 states) PDNP (32 states) −2

BER

−3

−4

−5

(a) SNR (dB) 0

PRML (4 states) PS − PDNP (4 states) PDNP (32 states) −1

BER

−2

−3

−4

(b) SNR (dB)

ÃÙ»·Õ 7.4:

»ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ» ¢Í§ BER ¢Í§Ç§¨ÃµÃÇ¨ËÒµèÒ§æ ÊÓËÃÑº ÃÐºº¡ÒÃºÑ¹·Ö¡ (a) áºº

á¹Ç¹Í¹ áÅÐ (b) áººá¹ÇµÑ § ·Õ ND = 2.5 áÅÐ

7.7

σj /T = 10%

ÊÃØ»·éÒÂº·

àÁ× Í ¤ÇÒÁ¨Ø ¢éÍÁÙÅ ¢Í§ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ÊÙ§ ¢Ö ¹ ÊÑÒ³Ãº¡Ç¹·Õ ´éÒ¹¢Òà¢éÒ ¢Í§Ç§¨ÃµÃÇ¨ËÒÊÑÅÑ¡É³ì ¹Í¡¨Ò¡¨ÐÁÕÅÑ¡É³Ðà» ¹ÊÑÒ³Ãº¡Ç¹áººÊÕ (colored noise) áÅéÇ ÂÑ§¨ÐÁÕÅÑ¡É³Ð¢Ö ¹ÍÂÙè¡Ñºáºº

150

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¢éÍÁÙÅ (data pattern) ´éÇÂ àªè¹ ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì ¢Í§Ê× Í ºÑ¹·Ö¡ (media jitter noise) â´Â ·Õ ÃÐ´Ñº¤ÇÒÁÃØ¹áÃ§¢Í§ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡¨Ð¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ·Õ à¢ÕÂ¹Å§ä»ã¹ Ê× Í ºÑ¹·Ö¡ Ç§¨ÃµÃÇ¨ËÒ PDNP ¨Ö§ ä´é ¶Ù¡ ÍÍ¡áºº¢Ö ¹ ÁÒ à¾× Í ¨Ñ´¡ÒÃ¡Ñº ÊÑÒ³Ãº¡Ç¹àËÅèÒ¹Õ â´Â ¨Ðà» ¹¡ÒÃ·Ó§Ò¹ÃèÇÁ¡Ñ¹ÃÐËÇèÒ§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹¡ÑºÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ ¶Ö§áÁéÇèÒ Ç§¨ÃµÃÇ¨ËÒ PDNP ¨ÐãËé »ÃÐÊÔ·¸ÔÀÒ¾·Õ ´Õ ¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML ÁÒ¡ áµè Ç§¨Ã µÃÇ¨ËÒ PDNP ÁÕ ¤ÇÒÁ«Ñº«éÍ¹ÁÒ¡¡ÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML à¾ÃÒÐÇèÒ á¼¹ÀÒ¾à·ÃÅÅÔÊ ·Õ ãªé ã¹ Ç§¨ÃµÃÇ¨ËÒ PDNP ¨ÐÁÕ ¨Ó¹Ç¹Ê¶Ò¹Ðà¾Ô Á ÁÒ¡¢Ö ¹ à¹× Í§ÁÒ¨Ò¡¨Ó¹Ç¹á·ç» ¢Í§Ç§¨Ã¡ÃÍ§·Ó¹ÒÂ ÊÑÒ³Ãº¡Ç¹ » ËÒ¹Õ ÊÒÁÒÃ¶·Õ ¨Ðá¡éä¢ä´é â´Â ¡ÒÃ»ÃÐÂØ¡µì ãªé ÍÑÅ¡ÍÃÔ·ÖÁ PDNP µÒÁá¹Ç¤Ô´ ¢Í§ PSP «Ö §¨Ðä´é¼ÅÅÑ¾¸ìà» ¹ Ç§¨ÃµÃÇ¨ËÒ PS PDNP «Ö §ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ã¡Åéà¤ÕÂ§¡ÑºÇ§¨ÃµÃÇ¨ËÒ PDNP áµèÁÕ¤ÇÒÁ«Ñº«éÍ¹¹éÍÂ¡ÇèÒÁÒ¡

7.8

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§Í¸ÔºÒÂ·Õ ÁÒ¢Í§á¹Ç¤Ô´¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ PDNP

2. ¨§¾ÔÊÙ¨¹ì¤èÒ¤ÇÒÁá»Ã»ÃÇ¹¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ µÒÁÊÁ¡ÒÃ (7.13)

3. ¨§¾ÔÊÙ¨¹ì¤èÒàÁµÃÔ¡ÊÒ¢Ò·Õ ãªéã¹Ç§¨ÃµÃÇ¨ËÒ PDNP µÒÁÊÁ¡ÒÃ (7.14)

4. ¨§Í¸ÔºÒÂ¤ÇÒÁáµ¡µèÒ§¢Í§Ç§¨ÃµÃÇ¨ËÒ PRML, Ç§¨ÃµÃÇ¨ËÒ NPML, áÅÐÇ§¨ÃµÃÇ¨ËÒ PDNP

5. ¨§Í¸ÔºÒÂËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§Ç§¨ÃµÃÇ¨ËÒ PS PDNP

6. ¨§¾ÔÊÙ¨¹ì¨Ó¹Ç¹¢Í§µÑÇ´Óà¹Ô¹¡ÒÃ (¡ÒÃºÇ¡áÅÐ¡ÒÃ¤Ù³) ·Õ ãªéµèÍ¢éÍÁÙÅ 1 ºÔµ µÒÁ·Õ áÊ´§ã¹ µÒÃÒ§·Õ 7.1

7. ¨§¾ÔÊÙ¨¹ì¨Ó¹Ç¹Ë¹èÇÂ¤ÇÒÁ¨Ó·Õ µéÍ§¡ÒÃ µÒÁ·Õ áÊ´§ã¹µÒÃÒ§·Õ 7.1

º··Õ 8

¡ÒÃÍÍ¡ààººÃËÑÊ RLL

ã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§Ë¹éÒ·Õ áÅÐËÅÑ¡¡ÒÃ·Ó§Ò¹¢Í§ÃËÑÊ RLL (run length limited) [9] «Ö §à» ¹·Õ ¹ÔÂÁ ãªé§Ò¹ÁÒ¡ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ¾ÃéÍÁ·Ñ §áÊ´§¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áºº ÃËÑÊ RLL ÍÂèÒ§§èÒÂ à¾× Íãªéã¹¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ¢éÍÁÙÅ

8.1

º·¹Ó

ÃËÑÊ RLL ¤×Í ÃËÑÊÁÍ´ÙàÅªÑ¹ (modulation code) »ÃÐàÀ·Ë¹Ö §·Õ ¹ÔÂÁãªéÁÒ¡ã¹ÍØ»¡Ã³ìÎÒÃì´´ÔÊ¡ì ä´Ã¿ì â´Â¨Ð·ÓË¹éÒ·Õ ã¹¡ÒÃ¡ÓË¹´¨Ó¹Ç¹¢Í§ºÔµ 0 áÅÐºÔµ 1 (µÒÁÃÙ»áºº¢Í§ NRZI) ·Õ àÃÕÂ§ µÔ´ ¡Ñ¹ ã¹ÅÓ´Ñº ¢éÍÁÙÅ ·Õ µéÍ§¡ÒÃ¨Ðà¢ÕÂ¹Å§ä»ã¹Ê× Í ºÑ¹·Ö¡ â´Â·Ñ Çä» ÃËÑÊ RLL ¨Ð¶Ù¡ ¡ÓË¹´´éÇÂ ¾ÒÃÒÁÔàµÍÃì 4 µÑÇ ¤×Í

m, n, d,

áÅÐ

â´Â¨ÐÍÂÙèã¹ÃÙ»¢Í§ÃËÑÊ

m/n (d, k)

àÁ× Í

¤×Í ¨Ó¹Ç¹¢éÍÁÙÅºÔµÍÔ¹¾Øµ (µèÍ¡ÒÃà¢éÒÃËÑÊË¹Ö §¤ÃÑ §) ·Õ ¨Ð·Ó¡ÒÃà¢éÒÃËÑÊ RLL

¤×Í ¨Ó¹Ç¹¢éÍÁÙÅºÔµàÍÒµì¾Øµ (µèÍ¡ÒÃà¢éÒÃËÑÊË¹Ö §¤ÃÑ §) ·Õ ä´é¨Ò¡¡ÒÃà¢éÒÃËÑÊ RLL â´Â·Ñ Çä»

n≥m

àÊÁÍ

¤×Í àÅ¢¨Ó¹Ç¹àµçÁ·Õ ¡ÓË¹´¨Ó¹Ç¹·Õ¹ éÍÂ·Õ ÊØ´¢Í§ºÔµ 0 ·Õ ÍÂÙèÃÐËÇèÒ§ºÔµ 1

¤×Í àÅ¢¨Ó¹Ç¹àµçÁ·Õ ¡ÓË¹´¨Ó¹Ç¹·ÕÁ Ò¡·Õ ÊØ´¢Í§ºÔµ 0 ·Õ ÍÂÙèÃÐËÇèÒ§ºÔµ 1 151

152

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

# input bits

RLL code

(m bits)

# output bits (n bits)

ÃÙ»·Õ 8.1: áºº¨ÓÅÍ§¡ÒÃà¢éÒÃËÑÊ RLL

àÁ× Í ¢éÍÁÙÅºÔµ 1 ¨ÐÊÍ´¤ÅéÍ§¡Ñº¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð (transition) ¢Í§¡ÃÐáÊä¿¿ Òà¢ÕÂ¹ (write cur rent) ·Õ ¨Ð» Í¹à¢éÒä»ã¹ËÑÇà¢ÕÂ¹ (write head) à¾× Í·ÓãËéÊ× ÍºÑ¹·Ö¡ ³ ºÃÔàÇ³·Õ µéÍ§¡ÒÃ¨Ðà¢ÕÂ¹¢éÍÁÙÅ Å§ä»ÁÕÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ (magnetization) µÒÁ·Õ µéÍ§¡ÒÃ ÊèÇ¹¢éÍÁÙÅºÔµ 0 ËÁÒÂ¶Ö§ äÁèÁÕ¡ÒÃ à»ÅÕ Â¹Ê¶Ò¹Ð¢Í§¡ÃÐáÊä¿¿ Òà¢ÕÂ¹ à¾ÃÒÐ©Ð¹Ñ ¹ ¾ÒÃÒÁÔàµÍÃì

¨ÐªèÇÂ·ÓãËé ºÔµ 1 ÊÍ§ºÔµ ÍÂÙèËèÒ§

¡Ñ¹ «Ö § ¨ÐªèÇÂÅ´¼Å¡ÃÐ·º¢Í§¡ÒÃá·Ã¡ÊÍ´ÃÐËÇèÒ§ÊÑÅÑ¡É³ì (ISI: intersymbol interference) ÊèÇ¹¾ÒÃÒÁÔàµÍÃì

à¡Ô´¢Ö ¹ÊÁ ÓàÊÁÍà¾ÕÂ§¾Í à¾× Í·Õ ¨Ð·ÓãËéÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÐÃÕ (timing recovery) ÊÒÁÒÃ¶·Ó§Ò¹ä´é ÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ µÑÇÍÂèÒ§àªè¹ ¶éÒÅÓ´Ñº¢éÍÁÙÅ·Õ ¨Ðà¢ÕÂ¹Å§ä»ã¹Ê× ÍºÑ¹·Ö¡ ¤×Í

···11111 ··· 11111··· ÅÓ´Ñº ¢éÍÁÙÅ ¹Õ ¶×Í ÇèÒ à» ¹ ÅÓ´Ñº ¢éÍÁÙÅ ·Õ äÁè ´Õ à¹× Í§¨Ò¡ ¨Ð·ÓãËé à¡Ô´ » ËÒ ISI ÍÂèÒ§ÃØ¹áÃ§ ã¹·Ò§ µÃ§¡Ñ¹¢éÒÁ ¶éÒÅÓ´Ñº¢éÍÁÙÅ·Õ ¨Ðà¢ÕÂ¹Å§ä»ã¹Ê× ÍºÑ¹·Ö¡ ¤×Í

···00000 ··· 00000··· ¡ç ¨Ð¶×Í ÇèÒ à» ¹ ÅÓ´Ñº ¢éÍÁÙÅ ·Õ äÁè ´Õ àªè¹¡Ñ¹ à¹× Í§¨Ò¡ ¨Ð·ÓãËé à¡Ô´ » ËÒàÃ× Í§¡ÒÃà¢éÒ ¨Ñ§ËÇÐ (synchro nization) ¢Í§ÃÐººä·ÁÁÔ § ÃÔ ¤Ñ¿àÇÍÐÃÕ à¾ÃÒÐ©Ð¹Ñ ¹ à¾× Í ËÅÕ¡àÅÕ Â§ÅÓ´Ñº ¢éÍÁÙÅ ·Ñ § 2 áºº¹Õ ¨Ö§ ÁÕ ¤ÇÒÁ¨Óà» ¹ ·Õ ¨ÐµéÍ§à¢éÒ ÃËÑÊ ÅÓ´Ñº ¢éÍÁÙÅ ´éÇÂÃËÑÊ RLL «Ö § ã¹·Ò§»¯ÔºÑµÔ áÅéÇ ¡ÒÃà¢éÒ áÅÐ¶Í´ÃËÑÊ ´éÇÂÃËÑÊ RLL ÊÒÁÒÃ¶·Óä´é§èÒÂâ´Â¡ÒÃãªé µÒÃÒ§¤é¹ËÒ (look up table) ã¹¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ ¢éÍÁÙÅ ÃÙ»·Õ 8.1 áÊ´§áºº¨ÓÅÍ§¡ÒÃà¢éÒÃËÑÊ RLL â´Â·Õ ÍÑµÃÒÃËÑÊ (code rate) ¨Ð¹ÔÂÒÁâ´Â ¨Ó¹Ç¹ ºÔµÍÔ¹¾Øµ

ËÒÃ´éÇÂ¨Ó¹Ç¹ºÔµàÍÒµì¾Øµ

¹Ñ ¹¤×Í

m ≤1 n

(8.1)

8.2.

à¹× Í§¨Ò¡ ¨Ó¹Ç¹ºÔµàÍÒµì¾Øµ

(D, K)

153

àÊÁÍ ´Ñ§¹Ñ ¹ ¢éÍàÊÕÂ¢Í§¡ÒÃà¢éÒÃËÑÊ RLL ·Õ àËç¹ä´éªÑ´à¨¹¡ç¤×Í ¨Ð·ÓãËéà¡Ô´ ºÔµÊèÇ¹à¡Ô¹ (redun

dant bit) «Ö § ¨Ð·ÓãËé ÊÙàÊÕÂ à¹× Í·Õ ¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ ·Õ µéÍ§¡ÒÃã¹ÎÒÃì´ ´ÔÊ¡ì ä´Ã¿ì ä»ºÒ§ÊèÇ¹ ´Ñ§¹Ñ ¹ ã¹¡ÒÃàÅ×Í¡ÃËÑÊ RLL ã´ÁÒãªé §Ò¹ ¡ç ¤ÇÃ·Õ ¨ÐàÅ×Í¡ãªé ÃËÑÊ RLL ·Õ ÁÕ ÍÑµÃÒÃËÑÊ

à¢éèÒã¡Åé ¤èÒ 1

ãËé ÁÒ¡·Õ ÊØ´ à¾× Í Å´¡ÒÃÊÙàÊÕÂ à¹× Í·Õ ¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ ·Õ µéÍ§¡ÒÃ ÊÓËÃÑº à¹× ÍËÒã¹º·¹Õ ¨ÐÍ¸ÔºÒÂ¶Ö§ ¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áººÃËÑÊ RLL ÍÂèÒ§§èÒÂ àÁ× Í¡ÓË¹´¾ÒÃÒÁÔàµÍÃì

8.2

m, n, d,

áÅÐ

¡ÓË¹´ãËé ÅÓ´Ñº ¢éÍÁÙÅ ÁÕ ¤ÇÒÁÂÒÇ·Ñ §ÊÔ ¹ ºÑ§¤Ñº (constraint)

(d, k)

ÁÒãËé

(d, k)

ºÔµ ¨Ó¹Ç¹ÅÓ´Ñº ¢éÍÁÙÅ ·Ñ §ËÁ´ ·Õ ÊÍ´¤ÅéÍ§¡Ñº à§× Í¹ä¢

ÊÒÁÒÃ¶ËÒä´é¨Ò¡ÊÁ¡ÒÃµèÍä»¹Õ [9]

N (L) = L + 1, 1 ≤ L ≤ d + 1

(8.2)

N (L) = N (L − 1) + N (L − d − 1), d + 1 ≤ L ≤ k

(8.3)

N (L) = d + k + 1 − L +

k X

N (L − i − 1), k < L ≤ d + k

(8.4)

i=d

N (L) =

k X

N (L − i − 1), L > d + k

(8.5)

i=d

àÁ× Í

N (L) = 0

ÊÓËÃÑº

L<0

ã¹¡Ã³Õ ·Õ ¾ÒÃÒÁÔàµÍÃì

áÅÐ

k =∞

N (0) = 1

¨Ó¹Ç¹ÅÓ´Ñº ¢éÍÁÙÅ ·Ñ §ËÁ´·Õ ÊÍ´¤ÅéÍ§¡Ñº à§× Í¹ä¢ºÑ§¤Ñº

(d, ∞)

¨ÐÊÒÁÒÃ¶ËÒä´é¨Ò¡ÊÁ¡ÒÃµèÍä»¹Õ

àÁ× Í

Nd (L) = 0

·Ñ §ËÁ´

Nd (L)

Nd (L) = L + 1, 1 ≤ L ≤ d + 1

(8.6)

Nd (L) = Nd (L − 1) + Nd (L − d − 1), L > d + 1

(8.7)

ÊÓËÃÑº

L<0

·Õ ÁÕ¤ÇÒÁÂÒÇ

áÅÐ

Nd (0) = 1

µÒÃÒ§·Õ 8.1 áÊ´§µÑÇÍÂèÒ§¨Ó¹Ç¹ÅÓ´Ñº ¢éÍÁÙÅ

·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº

(d, ∞)

154

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

µÒÃÒ§·Õ 8.1: ºÑ§¤Ñº

µÑÇÍÂèÒ§¨Ó¹Ç¹ÅÓ´Ñº ¢éÍÁÙÅ ·Ñ §ËÁ´

Nd (L)

·Õ ÁÕ ¤ÇÒÁÂÒÇ

·Õ ÊÍ´¤ÅéÍ§¡Ñº à§× Í¹ä¢

(d, ∞) d

L=4

L=5

L=6

L=7

L=8

L=9

L = 10

144

àÁ× Í·ÃÒº¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Ñ §ËÁ´

·Ñ §ËÁ´

N (L)

·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº

(d, k)

·Õ ÊÒÁÒÃ¶¹ÓÁÒãªéá·¹ÅÓ´Ñº¢éÍÁÙÅáµèÅÐÅÓ´Ñº¨ÐÁÕ¤èÒà·èÒ¡Ñº

K = d log2 {N (L)} e (bits) àÁ× Í

dxe

áÅéÇ ¨Ó¹Ç¹ºÔµ

(8.8)

á·¹¨Ó¹Ç¹àµçÁ ºÇ¡·Õ ¹éÍÂ·Õ ÊØ´ ·Õ ÁÕ ¤èÒ ÁÒ¡¡ÇèÒ ËÃ×Í à·èÒ ¡Ñº ¤èÒ

ÊÒÁÒÃ¶ãªé¢éÍÁÙÅºÔµ¨Ó¹Ç¹ 3 ºÔµ

{000,

àªè¹ ¶éÒ

N4 (6) = 8

¡ç

001, 010, 011, 100, 101, 110, 111} ã¹¡ÒÃá·¹ÅÓ´Ñº

¢éÍÁÙÅáµèÅÐáºº

8.3

¤ÇÒÁ¨Ø¢Í§ÃËÑÊ RLL ààºº

(d, k)

ã¹·ÄÉ¯Õ¢Í§ÃÐººÊ× ÍÊÒÃ ¤ÇÒÁ¨Ø (capacity) ËÁÒÂ¶Ö§ ¤èÒÊÙ§ÊØ´¢Í§ÍÑµÃÒÃËÑÊ

·Õ ÊÒÁÒÃ¶·ÓãËé

ÊÑÁÄ·¸Ô¼Åä´é «Ö §¨Ð¹ÔÂÒÁâ´Â [9]

1 log2 {N (L)} L→∞ n

C(d, k) = lim àÁ× Í

N (L)

C(d, k)

¤×Í ¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Ñ §ËÁ´·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº

(8.9)

(d, k)

¹Í¡¨Ò¡¹Õ ¤èÒ¤ÇÒÁ¨Ø

ÂÑ§ à» ¹ ¾ÒÃÒÁÔàµÍÃì ·Õ ºè§ºÍ¡¶Ö§ ¤ÇÒÁÊÒÁÒÃ¶ã¹¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ ¢èÒÇÊÒÃ¢Í§¼Ùéãªé ·Õ µéÍ§¡ÒÃ

¨Ðà¢ÕÂ¹Å§ä»ã¹Ê× Í ºÑ¹·Ö¡ (äÁè ¹Ñº ºÔµ ÊèÇ¹à¡Ô¹) ¹Ñ ¹¤×Í ¶éÒ ¤èÒ ÊÒÁÒÃ¶¨Ñ´à¡çº¢éÍÁÙÅ¢èÒÇÊÒÃ¢Í§¼Ùéãªéä´éÁÒ¡àªè¹¡Ñ¹

C(d, k)

ÂÔ § ÁÒ¡ ¡ç áÊ´§ÇèÒ ÃÐºº

8.3.

¤ÇÒÁ¨Ø¢Í§ÃËÑÊ RLL ààºº

(D, K)

155

¹Í¡¨Ò¡¹Õ ã¹¡ÒÃà»ÃÕÂºà·ÕÂº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃËÑÊ RLL áººµèÒ§æ ÊÒÁÒÃ¶·Óä´éâ´Â¡ÒÃ¾Ô¨ÒÃ³Ò ·Õ ¤èÒ »ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ (code e ciency) «Ö §¹ÔÂÒÁâ´Â

η=

R C(d, k)

(8.10)

¡ÅèÒÇ¤×Í ÃËÑÊ RLL ·Õ ÁÕ¤èÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊÁÒ¡ ¡çáÊ´§ÇèÒÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ã¹¡ÒÃãªé§Ò¹ÊÙ§

8.3.1

(d, k)

ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº¢Í§ÃËÑÊ RLL ààºº

à¹× Í§¨Ò¡ ¡ÒÃ¤Ó¹Ç³ËÒ¤èÒ ¤ÇÒÁ¨Ø

C(d, k)

´Ñ§¹Ñ ¹ â´Â·Ñ Çä» ¨Ö§¹ÔÂÁ¤Ó¹Ç³ËÒ¤èÒ

L → ∞

ã¹ÊÁ¡ÒÃ (8.9) àÁ× Í

C(d, k)

·Óä´é ¤èÍ¹¢éÒ§ÅÓºÒ¡

¨Ò¡ ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº (asymptotic infor

mation rate) «Ö §¹ÔÂÒÁâ´Â [58]

C(d, k) = log2 {λmax } àÁ× Í

λmax

¤×Í ÃÒ¡¨Ó¹Ç¹¨ÃÔ§ (real root) ·Õ ÁÕ¤èÒÁÒ¡ÊØ´ ¢Í§ÊÁ¡ÒÃ

xk+2 − xk+1 − xk−d+1 + 1 = 0,

k<∞

(8.12)

xd+1 − xd − 1 = 0,

k=∞

(8.13)

µÒÃÒ§·Õ 8.2 áÊ´§ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§ àÊé¹ ¡Ó¡Ñº

C(d, k)

¡ÒÃá¡éÊÁ¡ÒÃ (8.11) (8.13) áÅÐàÁ× Í¾Ô¨ÒÃ³Ò¤èÒ ãªé·Ñ Çä»¨ÐÁÕ¤èÒ¾ÒÃÒÁÔàµÍÃì

8.3.2

(8.11)

d≤2

¢Í§ÃËÑÊ RLL áºº

C(d, k)

(d, k)

µèÒ§æ ·Õ ä´é ¨Ò¡

ã¹µÒÃÒ§·Õ 8.2 ¨Ð¾ºÇèÒ ÃËÑÊ RLL ·Õ

àÊÁÍ à¾× Í·Õ ¨ÐÃÑº»ÃÐ¡Ñ¹ä´éÇèÒÍÑµÃÒÃËÑÊ

R ≥ 1/2

ÍÑµÃÒ¤ÇÒÁË¹Òàà¹è¹

ÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR (density ratio) ËÃ×Í ¤ÇÒÁË¹Òá¹è¹ ¡ÒÃºÃÃ¨Ø

(packing density) à» ¹

¾ÒÃÒÁÔàµÍÃì ·Õ ºè§ºÍ¡¶Ö§ ÃÐÂÐ·Ò§·Ò§¡ÒÂÀÒ¾ (physical distance) ÃÐËÇèÒ§µÓáË¹è§ ¢Í§¡ÒÃà»ÅÕ Â¹ Ê¶Ò¹Ð·Õ µÔ´¡Ñ¹ 2 µÓáË¹è§ ¢Í§ÅÓ´Ñº¢éÍÁÙÅ·Õ à¢éÒÃËÑÊ RLL «Ö §¹ÔÂÒÁâ´Â

DR = (1 + d)R

(8.14)

156

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

µÒÃÒ§·Õ 8.2: ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº¢Í§ÃËÑÊ RLL áºº

â´Â·Õ

d=1

d=2

d=3

d=4

(d, k)

d=0

0.6942

0.8792

0.4057

0.9468

0.5515

0.2878

0.9752

0.6174

0.4057

0.2232

0.9881

0.6509

0.4650

0.3218

0.1823

0.9997

0.6909

0.5418

0.4460

0.3746

0.3158

0.9999

0.6939

0.5501

0.4615

0.3991

0.3513

∞

1.0000

0.6942

0.5515

0.4650

0.4057

0.3620

µèÒ§æ

d=5

¤×Í ÍÑµÃÒÃËÑÊ

µÒÃÒ§·Õ 8.3 áÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¤ÇÒÁ¨Ø àÁ× Í¤ÇÒÁ¨Ø

C(d, k)

C(d, k) áÅÐÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR ¨ÐàËç¹ä´éÇèÒ

Å´Å§ ¤èÒÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR ¡ç¨Ðà¾Ô Á¢Ö ¹ ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¹Õ ÊÒÁÒÃ¶Í¸ÔºÒÂä´é

´Ñ§µèÍä»¹Õ ¨Ò¡ÊÁ¡ÒÃ (8.14) àÁ× Í¾ÒÃÒÁÔàµÍÃì

à¾Ô Á¢Ö ¹ ¤èÒ DR ¡ç¨Ðà¾Ô Á¢Ö ¹ áµè¾ÒÃÒÁÔàµÍÃì

¢Ö ¹ ¹Õ ÁÕ ¤ÇÒÁËÁÒÂÇèÒ ¢éÍÁÙÅ ·Õ ¶Ù¡ à¢éÒ ÃËÑÊ ¨ÐÁÕ ºÔµ ÊèÇ¹à¡Ô¹ à¾Ô Á ÁÒ¡¢Ö ¹ (à¾ÃÒÐÇèÒ ¾ÒÃÒÁÔàµÍÃì

·Õ à¾Ô Á

¤×Í

¨Ó¹Ç¹ºÔµ 0 ¹éÍÂÊØ´ ·Õ ÍÂÙè ÃÐËÇèÒ§ºÔµ 1) ¶éÒ ¾Ô¨ÒÃ³ÒÇèÒ Ê× Í ºÑ¹·Ö¡ ÁÕ à¹× Í·Õ ã¹¡ÒÃ¨Ñ´ à¡çº ¢éÍÁÙÅ ·Õ ¨Ó¡Ñ´ ´Ñ§¹Ñ ¹ ÃÐººÊÒÁÒÃ¶·Õ ¨Ð¨Ñ´à¡çº¢éÍÁÙÅ¢èÒÇÊÒÃ¢Í§¼Ùéãªéä´é¹éÍÂÅ§ à¹× Í§¨Ò¡ µéÍ§àËÅ×Íà¹× Í·Õ ºÒ§ÊèÇ¹äÇé ÊÓËÃÑº¨Ñ´à¡çººÔµÊèÇ¹à¡Ô¹ à¾ÃÒÐ©Ð¹Ñ ¹ ¨Ö§Êè§¼Å·ÓãËé¤èÒ¤ÇÒÁ¨Ø

8.4

C(d, k)

·Õ ¤Ó¹Ç³ä´éÁÕ¤èÒ¹éÍÂÅ§

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ (FSM: nite state machine) ¢Í§ÃËÑÊ RLL ¨ÐáÊ´§ãËéàËç¹¶Ö§ ¡ÒÃà»ÅÕ Â¹á»Å§ ¢Í§Ê¶Ò¹Ðã¹ÃËÑÊ RLL µÒÁà§× Í¹ä¢ºÑ§¤Ñº ¢Í§¾ÒÃÒÁÔàµÍÃì

(d, k)

¨ÐÁÕà¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´µÒÁÃÙ»·Õ 8.2 àÁ× Í

(d, k)

¤×Í Ê¶Ò¹Ð

µÑÇÍÂèÒ§àªè¹ ÃËÑÊ RLL áºº

áÅÐµÑÇàÅ¢·Õ áÊ´§ÍÂÙèµÒÁàÊé¹ÅÙ¡ÈÃ

¤×Í ¢éÍÁÙÅºÔµàÍÒµì¾Øµ·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì

(d, k) ¨Ò¡ÃÙ»·Õ 8.2 Ê¶Ò¹ÐàÃÔ Áµé¹

8.4.

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL

157

µÒÃÒ§·Õ 8.3: ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¤ÇÒÁ¨Ø

C(d, k)

C(d, ∞)

0.6942

1.3884

0.5515

1.6545

0.4650

1.8600

0.4057

2.0285

0.3620

2.1720

DR =

áÅÐÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR

(1 + d)C(d, ∞)

S d +1

ÃÙ»·Õ 8.2: à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

¨ÐÍÂÙè·Õ Ê¶Ò¹Ð

S k +1

(d, k)

¨ÐµéÍ§à» ¹ºÔµ 0 à» ¹¨Ó¹Ç¹ÍÂèÒ§¹éÍÂ ä»ÂÑ§ Ê¶Ò¹Ð

Sd+1 )

µÑÇµÔ´µèÍ¡Ñ¹ (¹Ñ ¹¤×Í Ê¶Ò¹Ð

¾ÍÅÓ´Ñº ¢éÍÁÙÅ ÁÕ ºÔµ 0 ¤Ãº

¡ç¨Ðà´Ô¹·Ò§à» ¹àÊé¹µÃ§

µÑÇ áÅéÇ ¨Ò¡à§× Í¹ä¢ºÑ§¤Ñº

(d, k)

áÊ´§ÇèÒ ºÔµ

µÑÇ¶Ñ´ä»ÊÒÁÒÃ¶à» ¹ä´é·Ñ §ºÔµ 0 ËÃ×ÍºÔµ 1 «Ö §¶éÒà» ¹ºÔµ 1 àÁ× Íã´ ÃÐºº¡ç¨ÐµéÍ§ÇÔ §¡ÅÑºä»àÃÔ Áµé¹·Õ Ê¶Ò¹Ð

ãËÁè áµè¶éÒà» ¹ºÔµ 0 ¡ç¨ÐÁÕºÔµ 0 ä´éÍÕ¡äÁèà¡Ô¹

k−d

µÑÇ áÅÐàÁ× ÍÁÕºÔµ 0 µÔ´µèÍ¡Ñ¹¤Ãº

µÑÇáÅéÇ ºÔµµÑÇ¶Ñ´ä»¨ÐµéÍ§à» ¹ºÔµ 1 à·èÒ¹Ñ ¹ ¹Ñ ¹¤×Í ÃÐºº¨Ð¶Ù¡ºÑ§¤ÑºãËé¡ÅÑºä»àÃÔ Áµé¹·Õ Ê¶Ò¹Ð

ãËÁèâ´ÂÍÑµâ¹ÁÑµÔ

µÑÇÍÂèÒ§·Õ 8.1

(d, k) = (1, 3) ÇÔ¸Õ·Ó

¾ÒÃÒÁÔàµÍÃì

(1, 3)

ËÁÒÂ¶Ö§ ÅÓ´Ñº¢éÍÁÙÅ¨ÐÁÕºÔµ 0 ÍÂèÒ§¹éÍÂË¹Ö §µÑÇ ËÃ×ÍÍÂèÒ§ÁÒ¡ÊÒÁµÑÇ

158

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÃÙ»·Õ 8.3: à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(1, 3)

µÔ´µèÍ¡Ñ¹ ·Õ ÍÂÙèÃÐËÇèÒ§ºÔµ 1 «Ö §ÊÒÁÒÃ¶à¢ÕÂ¹à» ¹à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ä´é µÒÁÃÙ»·Õ 8.3

8.5

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ ¢Í§ÃËÑÊ RLL áºº

(d, k)

ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè ã¹ÃÙ» ¢Í§ àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹

Ê¶Ò¹Ð (state transition matrix) ä´é «Ö §¹ÔÂÒÁâ´Â àÁ·ÃÔ¡«ì á¹ÇµÑ § â´Â·Õ ÊÁÒªÔ¡¢Í§àÁ·ÃÔ¡«ì

D(i, j)

¹Ñ ¹¤×Í á¶Ç·Õ

·Õ ÁÕ¢¹Ò´

áÅÐá¹ÇµÑ §·Õ

(k + 1) j

á¶Ç áÅÐ

¨Ð¶Ù¡¡ÓË¹´â´Â

D(i, 1) = 1, i ≥ d + 1   1, j = i + 1 D(i, j) =  0, else µÑÇÍÂèÒ§àªè¹ à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ðä´é´Ñ§¹Õ

(1, 3)



(k + 1)

(8.15)

µÒÁÃÙ»·Õ 8.3 ÊÒÁÒÃ¶à¢ÕÂ¹à» ¹àÁ·ÃÔ¡«ì

 0 1 0 0

     1 0 1 0   D=    1 0 0 1    1 0 0 0 àÁ·ÃÔ¡«ì

(8.16)

ã¹ÊÁ¡ÒÃ (8.16) ÊÒÁÒÃ¶ÊÃéÒ§ä´é ´Ñ§µèÍä»¹Õ ¶éÒ ¡ÓË¹´ãËé áµèÅÐá¶Çá·¹Ê¶Ò¹Ð

áµèÅÐ Ê¶Ò¹Ð ¡ÅèÒÇ¤×Í á¶Ç ·Õ Ë¹Ö § ãªé á·¹ Ê¶Ò¹Ð

áÅÐ á¶Ç ·Õ ÊÍ§ ãªé á·¹ Ê¶Ò¹Ð

à» ¹µé¹

áÅÐ

8.5.

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

159

à» ¹µé¹ ´Ñ§¹Ñ ¹ ã¹¡ÒÃÊÃéÒ§àÁ·ÃÔ¡«ì ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¨Ò¡à¤Ã× Í§

á¹ÇµÑ § ·Õ ÊÍ§ãªé á·¹Ê¶Ò¹Ð

Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº (Ê¶Ò¹Ð

S1 )

(1, 3)

µÒÁÃÙ»·Õ 8.3 ãËé¾Ô¨ÒÃ³Ò·ÕÅÐá¹ÇµÑ § àªè¹ ã¹á¹ÇµÑ §·Õ Ë¹Ö §

ãËé ´Ù ÇèÒ ÁÕ àÊé¹ ÅÙ¡ÈÃ¨Ò¡Ê¶Ò¹Ð

ÇèÒ ÁÕàÊé¹ÅÙ¡ÈÃ¨Ò¡Ê¶Ò¹Ð

S2 , S3 ,

áÅÐ

ã´ºéÒ§·Õ ÇÔ § à¢éÒ ÁÒ·Õ Ê¶Ò¹Ð

¨Ò¡ÃÙ» ·Õ 8.3 ¨Ð¾º

´Ñ§¹Ñ ¹ ã¹á¹ÇµÑ §·Õ Ë¹Ö §¹Õ ¤èÒ 1 ¨Ð¶Ù¡ãÊèà¢éÒä»ã¹á¶Ç·Õ

ÊÍ§, á¶Ç·Õ ÊÒÁ, áÅÐá¶Ç·Õ ÊÕ ÊèÇ¹á¶Ç·Õ Ë¹Ö §¨ÐãËéà» ¹¤èÒ 0 ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ¶éÒ¾Ô¨ÒÃ³Ò·Õ á¹ÇµÑ § ·Õ ÊÍ§ (Ê¶Ò¹Ð

S2 )

ãËé´ÙÇèÒÁÕàÊé¹ÅÙ¡ÈÃ¨Ò¡Ê¶Ò¹Ð

¾ºÇèÒ ÁÕàÊé¹ÅÙ¡ÈÃ¨Ò¡Ê¶Ò¹Ð

ã´ºéÒ§·Õ ÇÔ §à¢éÒÁÒ·Õ Ê¶Ò¹Ð

àÊé¹à´ÕÂÇ·Õ ÇÔ §ÁÒ·Õ Ê¶Ò¹Ð

¨Ò¡ÃÙ»·Õ 8.3 ¨Ð

´Ñ§¹Ñ ¹ ¤èÒ 1 ¨Ð¶Ù¡ãÊèà¢éÒä»ã¹á¶Ç·Õ

Ë¹Ö § ÊèÇ¹á¶ÇÍ× ¹æ ¨ÐÁÕ¤èÒà» ¹¤èÒ 0 à» ¹µé¹ ÊÓËÃÑºã¹¡Ã³Õ·Õ ¾ÒÃÒÁÔàµÍÃì

k=∞

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

à¢ÕÂ¹ãËéÍÂÙèã¹ÃÙ»¢Í§àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð ·Õ ÊÁÒªÔ¡¢Í§àÁ·ÃÔ¡«ì

D(i, j)

·Õ ÁÕ¢¹Ò´

(d + 1)

á¶Ç áÅÐ

(d, ∞)

(d + 1)

ÊÒÁÒÃ¶

á¹ÇµÑ § â´Â

¨Ð¶Ù¡¡ÓË¹´â´Â

D(i, j) = 1, j = i + 1 D(d + 1, 1) = D(d + 1, d + 1) = 1 D(i, j) = 0, else

µÑÇÍÂèÒ§·Õ 8.2

µÒÁà§× Í¹ä¢ºÑ§¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì

ÇÔ¸Õ ·Ó

(8.17)

¾ÒÃÒÁÔàµÍÃì

(0, 3)

(d, k) = (0, 3)

ËÁÒÂ¶Ö§ ÅÓ´Ñº ¢éÍÁÙÅ ¨ÐÁÕ ºÔµ 0 ÍÂèÒ§¹éÍÂË¹Ö § µÑÇ ËÃ×Í ÍÂèÒ§ÁÒ¡ÊÒÁ

µÑÇ µÔ´µèÍ ¡Ñ¹ ·Õ ÍÂÙè ÃÐËÇèÒ§ ºÔµ 1 «Ö § ÊÒÁÒÃ¶ à¢ÕÂ¹ à» ¹ à¤Ã× Í§ Ê¶Ò¹Ð ¨Ó¡Ñ´ ä´é µÒÁ ÃÙ» ·Õ 8.4 â´Â ·Õ àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ÊÍ´¤ÅéÍ§¡Ñºà¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¹Õ ¤×Í



 1 1 0 0

     1 0 1 0   D=    1 0 0 1    1 0 0 0

160

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÃÙ»·Õ 8.4: à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

8.5.1

(0, 3)

¡ÒÃËÒÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

C(d, k)

¨Ò¡ÊÙµÃã¹ÊÁ¡ÒÃ (8.11) ¹Ñ ¹¤×Í

D λmax

Ê¶Ò¹Ð

(8.18)

«Ö §ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ

det(D − λI) = 0 àÁ× Í det(·) ¤×Í ¡ÒÃËÒ¤èÒ´Õà·ÍÃìÁÔá¹¹µì (determinant), ·Õ ÁÕ¢¹Ò´à·èÒ¡ÑºàÁ·ÃÔ¡«ì

8.5.2

áÅÐ

¤×Í àÁ·ÃÔ¡«ìàÍ¡ÅÑ¡É³ì (identity matrix)

¨Ò¡à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(d, k)

¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Õ à» ¹ä»ä´é·Ñ §ËÁ´·Õ ÁÕ¤ÇÒÁÂÒÇ

(8.19)

¨ÐÁÕ¤èÒà·èÒ¡Ñº ¤èÒ¢Í§ÊÁÒªÔ¡á¶Ç·Õ

µÑÇÍÂèÒ§·Õ 8.3

·Õ áÊ´§ã¹ÃÙ»·Õ 8.2 àÁ× Í

L ºÔµ ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð Si

áÅÐá¹ÇµÑ §·Õ

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

¢éÍÁÙÅ·Õ à» ¹ä»ä´é·Ñ §ËÁ´·Õ ÁÕ¤ÇÒÁÂÒÇ

¢Í§àÁ·ÃÔ¡«ì

(0, 2)

ºÔµ ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

(d, k)

¤×Í Ê¶Ò¹Ð

´Ñ§¹Ñ ¹

áÅéÇä»ÊÔ ¹ÊØ´·Õ Ê¶Ò¹Ð

¹Ñ ¹¤×Í

DL (i, j)

áÊ´§ã¹ÃÙ»·Õ 8.5 ¨§ËÒ¨Ó¹Ç¹ÅÓ´Ñº

áÅéÇä»ÊÔ ¹ÊØ´·Õ Ê¶Ò¹Ð

ÊÓËÃÑº

8.5.

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

161

1 S1

ÃÙ»·Õ 8.5: à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(0, 2)

0 ≤ i, j ≤ 3 ÇÔ¸Õ ·Ó

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ ¢Í§ÃËÑÊ RLL áºº

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

(0, 2)

ã¹ÃÙ» ·Õ 8.5 ÊÒÁÒÃ¶à¢ÕÂ¹ãËé ÍÂÙè ã¹ÃÙ» ¢Í§

ä´é ¤×Í



 1 1 0

  D= 1 0 1  1 0 0

   

2 ºÔµ   2 1 1     D2 =  2 1 0    1 1 0

´Ñ§¹Ñ ¹ ¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Õ à» ¹ä»ä´é·Ñ §ËÁ´·Õ ÁÕ¤ÇÒÁÂÒÇ

(8.20)

ËÒä´é¨Ò¡

«Ö §ÁÕ¤èÒà·èÒ¡Ñº

(8.21)

ÊÁ¡ÒÃ (8.21) ºÍ¡ãËé·ÃÒºÇèÒ

ÅÓ´Ñº¢éÍÁÙÅ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

S1 → S1

ÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

D(1, 1) = 2

µÑÇ ¤×Í

{01,

11}

ÅÓ´Ñº¢éÍÁÙÅ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

S2 → S1

ÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

D(2, 1) = 2

µÑÇ ¤×Í

{01,

11}

ÅÓ´Ñº¢éÍÁÙÅ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

S3 → S1

ÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

D(3, 1) = 1

µÑÇ ¤×Í

{11}

ÅÓ´Ñº¢éÍÁÙÅ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

S1 → S2

ÁÕ¨Ó¹Ç¹à·èÒ¡Ñº

D(1, 2) = 2

µÑÇ ¤×Í

{10}

162

8.6

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¢Ñ ¹µÍ¹¡ÒÃÍÍ¡ààººÃËÑÊ RLL

ã¹ÊèÇ¹¹Õ ¨ÐáÊ´§¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áººµÒÃÒ§¤é¹ËÒ à¾× Íãªéã¹¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ RLL â´ÂãªéµÑÇÍÂèÒ§ ´Ñ§µèÍä»¹Õ

µÑÇÍÂèÒ§·Õ 8.4

¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ RLL áºº

¤ÃÑ §·Õ ¼èÒ¹¡ÒÃà¢éÒÃËÑÊáÅéÇ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº

ÇÔ¸Õ·Ó

n=3

(0, 2)

â´Â·Õ ¢éÍÁÙÅáµèÅÐ

¾ÃéÍÁ·Ñ §ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

¡ÒÃÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ RLL ÊÒÁÒÃ¶áºè§ÍÍ¡à» ¹ 4 ¢Ñ ¹µÍ¹ ´Ñ§¹Õ

¢Ñ ¹µÍ¹·Õ 1:

ãËé¾Ô¨ÒÃ³Ò´ÙÇèÒ ¢éÍÁÙÅ 3 ºÔµÁÕ·Ñ §ËÁ´¡Õ áºº «Ö §¨Ðä´éÇèÒ ÁÕ·Ñ §ËÁ´ 8 áºº ¤×Í

{000, 001, 010, 011, 100, 101, 110, 111} ¢Ñ ¹µÍ¹·Õ 2:

ÇèÒ ÁÕ¢éÍÁÙÅ·Ñ §ËÁ´ 7 áºº·Õ ¼èÒ¹à§× Í¹ä¢ºÑ§¤Ñº

(0, 2)

«Ö §¨Ð¾º

¹Ñ ¹¤×Í

{001, 010, 011, 100, 101, 110, 111} ¢Ñ ¹µÍ¹·Õ 3:

ãËéÅÍ§¹Ó¢éÍÁÙÅ·Õ ä´é¨Ò¡¢Ñ ¹µÍ¹·Õ 2 áµèÅÐµÑÇ ÁÒ·Ó¡ÒÃµèÍ¡Ñ¹·Ñ §·Ò§«éÒÂáÅÐ·Ò§¢ÇÒ

áÅéÇ´ÙÇèÒ ÁÕ¢éÍÁÙÅµÑÇäË¹ºéÒ§·Õ àÁ× Í¹ÓÁÒµèÍ¡Ñ¹áÅéÇ ¨ÐäÁèÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº ¾ºÇèÒ ¢éÍÁÙÅ 001 áÅÐ 100 àÁ× Í¹Óä»µèÍ¡Ñº¢éÍÁÙÅµÑÇÍ× ¹¨Ð·ÓãËéà§× Í¹ä¢ºÑ§¤Ñº

(0, 2)

ã¹·Õ ¹Õ ¨Ð

¼Ô´ä» ´Ñ§¹Ñ ¹

¢éÍÁÙÅ 001 áÅÐ 100 ¨ÐµéÍ§¶Ù¡ µÑ´ ·Ô § ä» ·ÓãËé ¢éÍÁÙÅ ·Õ ËÅ§àËÅ×Í ÍÂÙè ÁÕ à¾ÕÂ§ 5 áºº ·Õ ¼èÒ¹à§× Í¹ä¢ ºÑ§¤Ñº

(0, 2)

¹Ñ ¹¤×Í

{010, 011, 101, 110, 111} «Ö §¢éÍÁÙÅàËÅèÒ¹Õ ¡ç¤×Í ¢éÍÁÙÅ·Õ ÊÒÁÒÃ¶¹ÓÁÒãªéà» ¹¢éÍÁÙÅ·Õ ¼èÒ¹¡ÒÃà¢éÒÃËÑÊ RLL áÅéÇ ¢Ñ ¹µÍ¹·Õ 4:

¨Ò¡¢éÍÁÙÅ·Ñ § 5 áºº·Õ ä´éã¹¢Ñ ¹µÍ¹·Õ 3 ãËéàÅ×Í¡ÁÒ 4 áºº (áººã´¡çä´é) à¾× Íãªéã¹

¡ÒÃÊÃéÒ§µÒÃÒ§¤é¹ËÒ ÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ¢éÍÁÙÅÍÔ¹¾Øµ·ÕÅÐ 2 ºÔµ ¹Ñ ¹¤×Í 11} «Ö §¨Ðä´é µÒÁµÒÃÒ§·Õ 8.4 áÅÐ¨Ðä´éÇèÒ ÍÑµÃÒÃËÑÊ ¤×Í

{00,

01,

10,

8.6.

¢Ñ ¹µÍ¹¡ÒÃÍÍ¡ààººÃËÑÊ RLL

163

µÒÃÒ§·Õ 8.4: µÒÃÒ§¤é¹ËÒÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ RLL áºº ¢éÍÁÙÅÍÔ¹¾Øµ

¢éÍÁÙÅàÍÒµì¾Øµ

010

011

101

110

(0, 2)

2 3

ã¹·Ó¹Í§à´ÕÂÇ¡Ñ¹ ¡ÒÃËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ RLL ÊÒÁÒÃ¶ËÒä´é µÒÁ¢Ñ ¹µÍ¹µèÍä»¹Õ àÃÔ Áµé¹ ãËéÊÃéÒ§à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÑÊ RLL áºº

(0, 2)

«Ö §¨Ðä´éµÒÁÃÙ»·Õ 8.5 ¨Ò¡¹Ñ ¹ãËéÊÃéÒ§àÁ·ÃÔ¡«ì

¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð·Õ ÊÍ´¤ÅéÍ§¡Ñº à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ ã¹ÃÙ» ·Õ 8.5 «Ö § ¨Ðä´é ¼ÅÅÑ¾¸ì µÒÁÊÁ¡ÒÃ (8.20) ¹Ñ ¹¤×Í



 1 1 0

   

«Ö § ÊÒÁÒÃ¶ËÒä´é ¨Ò¡á¡é ÊÁ¡ÒÃ (8.19)

¹Ñ ¹¤×Í



 1 1 0



 1 0 0

        det  1 0 1  − λ  0 1 0  = 0     1 0 0 0 0 1   1−λ 1 0     det  1 −λ 1  = 0   1 0 −λ −λ3 + λ2 + λ + 1 = 0

(8.22)

164

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

â´Â¡ÒÃá¡éÊÁ¡ÒÃ (8.22) àÃÒ¨Ðä´éÇèÒ

λ = 1.8393, −0.4196 + 0.6063i, −0.4196 − 0.6063i ´Ñ§¹Ñ ¹

λD max = 1.8393

¨Ð¶Ù¡¹ÓÁÒãªéã¹¡ÒÃ¤Ó¹Ç³ËÒ¤ÇÒÁ¨Ø

C(d, k)

µÒÁÊÁ¡ÒÃ (8.18) ¹Ñ ¹¤×Í

C(d, k) = log2 {λmax } = log2 {1.8393} = 0.87916 áÅÐ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

ËÒä´é¨Ò¡ÊÁ¡ÒÃ (8.10) «Ö §¨Ðä´éÇèÒ

η=

8.7

R 2/3 = = 0.7583 C(d, k) 0.87916

µÑÇÍÂèÒ§ÃËÑÊ RLL ààººµèÒ§æ

ÃËÑÊ RLL ÁÕËÅÒÂáºº¢Ö ¹ÍÂÙè¡Ñº¾ÒÃÒÁÔàµÍÃì

(d, k)

áÅÐÍÑµÃÒÃËÑÊ

·Õ ãªé ã¹ÂØ¤àÃÔ Áµé¹¢Í§ÍØ»¡Ã³ì

ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ÃËÑÊ RLL ·Õ ãªé¨ÐÁÕª× ÍÇèÒ ÃËÑÊ FM (frequency modulation) â´ÂÁÕµÒÃÒ§¤é¹ËÒ ÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ µÒÁÃÙ»·Õ 8.6(a) â´ÂÃËÑÊ FM ¹Õ ¨Ðãªé§Ò¹ÃèÇÁ¡ÑºÇ§¨ÃµÃÇ¨ËÒ¨Ø´ÊÙ§ÊØ´ (peak detector) áÅÐÁÕÍÑµÃÒÃËÑÊ

R = 1/2 «Ö §¨Ð·ÓãËéµéÍ§ÊÙàÊÕÂ¾× ¹·Õ ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ìä»»ÃÐÁÒ³

50% à¾× Íà¡çº¢éÍÁÙÅºÔµÊèÇ¹à¡Ô¹ µÑÇÍÂèÒ§¡ÒÃà¢éÒÃËÑÊàªè¹ ¶éÒÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ ¤×Í ¢éÍÁÙÅ·Õ ä´é¨Ò¡¡ÒÃà¢éÒÃËÑÊ FM ¤×Í

{110000}

ÅÓ´Ñº

{11 11 01 01 01 01}

ÊÑ§à¡µ¨Ð¾ºÇèÒ ÃËÑÊ FM ÂÍÁãËéÅÓ´Ñº¢éÍÁÙÅ·Õ à¢éÒÃËÑÊáÅéÇÁÕºÔµ 1 µÔ´¡Ñ¹ä´é «Ö §¨Ð¡èÍãËéà¡Ô´» ËÒ àÃ× Í§ ISI ´Ñ§¹Ñ ¹ ¨Ö§ÁÕ¡ÒÃ¾Ñ²¹ÒÃËÑÊãËÁè·Õ àÃÕÂ¡ÇèÒ ÃËÑÊ MFM (modi ed frequency modulation) ËÃ×ÍºÒ§¤ÃÑ §àÃÕÂ¡ÇèÒ ÃËÑÊÁÔÅàÅÍÃì (Miller code) «Ö §ÁÕµÒÃÒ§¤é¹ËÒÊÓËÃÑº¡ÒÃà¢éÒáÅÐ¶Í´ÃËÑÊ µÒÁ ÃÙ» ·Õ 8.6(b) â´Â·Õ

x = 0

¶×Í ÇèÒ à» ¹ ÃËÑÊ RLL áºº

0.5/0.5515 = 0.9066

¶éÒ ºÔµ ¡èÍ¹Ë¹éÒ ºÔµ

(1, 3)

ÁÕ ¤èÒ à» ¹ ºÔµ 1 ¹Í¡¹Ñ ¹

áÅÐÁÕ ÍÑµÃÒÃËÑÊ

R = 1/2

{01 01 00 10 10 01 01}

ÃËÑÊ MFM ¹Õ

â´Â¨ÐÁÕ »ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

µÑÇÍÂèÒ§¡ÒÃà¢éÒÃËÑÊ àªè¹ ¶éÒÅÓ´Ñº¢éÍÁÙÅÍÔ¹¾Øµ ¤×Í

·Õ ä´é¨Ò¡¡ÒÃà¢éÒÃËÑÊ MFM ¤×Í

x = 1

{1100011}

η =

ÅÓ´Ñº¢éÍÁÙÅ

à» ¹µé¹ ¹Í¡¨Ò¡¹Õ ÃÙ»·Õ 8.6(c) áÅÐ 8.6(d)

áÊ´§µÑÇÍÂèÒ§ÃËÑÊ RLL áººµèÒ§æ ·Õ ãªéã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ¨Ò¡ÇÔÇÑ²¹Ò¡ÒÃ¢Í§¡ÒÃ¾Ñ²¹ÒÃËÑÊ RLL

8.7.

µÑÇÍÂèÒ§ÃËÑÊ RLL ààººµèÒ§æ

165

user bits

coded bits

user bits

coded bits

0 1

01 11

0 1

x0 01

(a) FM code

(b) MFM code

user bits

coded bits

user bits

coded bits

00 01 10 11 0000 0001 1000 1001

101 100 001 010 101000 100000 001000 010000

10 11 000 010 011 0010 0011

0100 1000 000100 100100 001000 00100100 00001000

(d) 1/2 (1,7) RLL code

ÃÙ»·Õ 8.6: µÑÇÍÂèÒ§ÃËÑÊ RLL áººµèÒ§æ ·Õ ãªéã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

¨Ð¾ºÇèÒ ¾ÒÃÒÁÔàµÍÃì

·Õ ãªéã¹ÃËÑÊ RLL ¨Ð¤èÍÂæ Å´Å§ à¾× ÍÅ´¨Ó¹Ç¹ºÔµÊèÇ¹à¡Ô¹ ·ÓãËéÊÒÁÒÃ¶

¨Ñ´à¡çº¢éÍÁÙÅ·Õ µéÍ§¡ÒÃã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ìä´éÁÒ¡¢Ö ¹ ã¹¡ÒÃµÑ´ÊÔ¹ã¨ÇèÒ¨ÐàÍÒÃËÑÊ RLL ã´ÁÒãªé§Ò¹ã¹ÃÐºº¨Ð¢Ö ¹ÍÂÙè¡Ñº» ¨¨ÑÂËÅÒÂæ ÍÂèÒ§ ´Ñ§¹Õ 1) ¾ÒÃÒÁÔàµÍÃì

2) ÍÑµÃÒÃËÑÊ

3) ¤ÇÒÁ¨Ø

(d, k)

R = m/n

C(d, k)

4) »ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

5) ÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR

166

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

«Ö §â´Â·Ñ Çä»áÅéÇ ¨Óà» ¹µéÍ§»ÃÐ¹Õ»ÃÐ¹ÍÁ» ¨¨ÑÂ·Ñ §ËÁ´ãËéàËÁÒÐÊÁ¡ÑºÊÀÒ¾áÇ´ÅéÍÁã¹¡ÒÃ·Ó§Ò¹ ¢Í§ÃÐºº ÃËÑÊ RLL ·Õ à¤Âãªéã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì àªè¹ ÃËÑÊ RLL áºº

4/5 (0, 2),

áÅÐÃËÑÊ RLL áºº

8/9 (0, 3)

1/2 (2, 7),

ÃËÑÊ RLL áºº

à» ¹µé¹ ÊÑ§à¡µ¨Ð¾ºÇèÒ ÃËÑÊ RLL ·Õ ãªé¨ÐÁÕÍÑµÃÒÃËÑÊà¢éÒ

ã¡Åé¤èÒ 1 àÃ× ÍÂæ à¾× ÍÅ´¨Ó¹Ç¹ºÔµÊèÇ¹à¡Ô¹ áÅÐ¾ÒÃÒÁÔàµÍÃì

·Õ ãªé¡ç¨ÐÁÕ¤èÒà» ¹¤èÒ 0 ¹Ñ ¹¤×Í ÂÍÁãËé

ÁÕºÔµ 1 µÔ´¡Ñ¹ä´é «Ö §¶Ö§áÁéÇèÒ¨Ð¡èÍãËéà¡Ô´» ËÒàÃ× Í§ ISI áµèÃÐºº¡çÊÒÁÒÃ¶¨Ñ´¡ÒÃ¡Ñº ISI ¹Õ ä´é´éÇÂ à·¤¹Ô¤ PRML µÒÁ·Õ Í¸ÔºÒÂã¹º··Õ 4

8.8

ÃËÑÊ

(0, G/I)

ÊÓËÃÑºªèÍ§ÊÑÒ³ PRML

ÊÓËÃÑºªèÍ§ÊÑÒ³ PRML ·Õ ãªé·ÒÃìà¡çµáºº PR4, (·Õ äÁèÁÕÊÑÒ³Ãº¡Ç¹) ³ àÇÅÒ

H(D) = 1 − D2 ,

¢éÍÁÙÅàÍÒµì¾ØµªèÍ§ÊÑÒ³

ÁÕ¤èÒà·èÒ¡Ñº¼ÅµèÒ§ÃÐËÇèÒ§¢éÍÁÙÅÍÔ¹¾Øµ 2 µÑÇ ³ àÇÅÒ

áÅÐ

k−2

´Ñ§¹Ñ ¹ ªèÍ§ÊÑÒ³¹Õ ¨ÐÁÕ ¤Ø³ÊÁºÑµÔ ¾ÔàÈÉ·Õ ÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ ÂèÍÂàÅ¢¤Õ (odd subsequence) ¨Ðà» ¹ ÍÔÊÃÐ¨Ò¡ÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè (even subsequence) ´Ñ§¹Ñ ¹ à¾× Í·Õ ¨ÐÅ´Ë¹èÇÂ¤ÇÒÁ¨ÓàÊé¹·Ò§ (path memory) ¢Í§Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ ¨Ó¹Ç¹¢Í§ºÔµ 0 ·Õ àÃÕÂ§µÔ´µèÍ ¡Ñ¹ ¢Í§áµèÅÐÅÓ´Ñº ¢éÍÁÙÅ ÂèÍÂ¨Ð µéÍ§ÁÕä´éäèÁèà¡Ô¹

µÑÇ áÅÐà¾× ÍªèÇÂ·ÓãËéÃÐººä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÐÃÕÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾

áÅÐ¨Ó¹Ç¹¢Í§ºÔµ 0 ·Õ àÃÕÂ§µÔ´µèÍ¡Ñ¹ã¹ÅÓ´Ñº¢éÍÁÙÅÃÇÁ (ÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Õ ÁÒÃÇÁ¡ÑºÅÓ´Ñº¢éÍÁÙÅ ÂèÍÂàÅ¢¤Ùè) ¨ÐµéÍ§ÁÕä´éäèÁèà¡Ô¹ 0 ã¹ÃËÑÊ

(0, G/I)

µÑÇ àËÁ×Í¹¡Ñº¾ÒÃÒÁÔàµÍÃì

ã¹ÃËÑÊ RLL áºº

(d, k)

ÊÓËÃÑº¤èÒ

¹Ñ ¹¨ÐËÁÒÂ¶Ö§ ÃÐººÍ¹ØÒµãËéÅÓ´Ñº¢éÍÁÙÅÃÇÁÊÒÁÒÃ¶ÁÕºÔµ 1 àÃÕÂ§µÔ´µèÍ¡Ñ¹

ä´é àËÁ×Í¹¡Ñº¾ÒÃÒÁÔàµÍÃì

ã¹ÃËÑÊ RLL áºº

(d, k)

[9, 59, 60] à¾ÃÒÐÇèÒ Ç§¨ÃµÃÇ¨ËÒ PRML

ÁÕ¤ÇÒÁÊÒÁÒÃ¶ã¹¨Ñ´¡ÒÃ¡Ñº ISI ·Õ à¡Ô´¢Ö ¹ä´é ¶éÒ¡ÓË¹´ãËé

ÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Õ

γo

áÅÐÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè

γe

¨Ð¹ÔÂÒÁâ´Â [60]

γ o = {γ1 , γ3 , γ5 , . . . , γ2dn/2e−1 } γ e = {γ2 , γ4 , γ6 , . . . , γ2bn/2c } àÁ× Í

bxc

ÂèÍÂàÅ¢¤Õ

á·¹¨Ó¹Ç¹àµçÁºÇ¡·Õ ÁÒ¡·Õ ÊØ´ ·Õ ÁÕ¤èÒ¹éÍÂ¡ÇèÒËÃ×Íà·èÒ¡Ñº¤èÒ

γo

áÅÐÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè

γe

¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº

dn/2e

´Ñ§¹Ñ ¹ ¨Ðä´éÇèÒ ÅÓ´Ñº¢éÍÁÙÅ

áÅÐ

bn/2c

µÒÁÅÓ´Ñº ÅÓ´Ñº

8.9.

ÊÃØ»·éÒÂº·

¢éÍÁÙÅ

ÃÇÁ

ÁÕºÔµ 0 àÃÕÂ§µÔ´µèÍ¡Ñ¹ä´éäÁèà¡Ô¹

¡Ñ¹ä´éäÁèà¡Ô¹

µÑÇÍÂèÒ§·Õ 8.5 RLL áºº

ÇÔ¸Õ·Ó

167

µÑÇ àÁ× Í

áÅÐ

¡ÓË¹´ãËé

(0, G/I)

γ = {110100101000110011} G

áÅÐ

·Õ ¡ÓË¹´ãËéÁÒ ¨Ðä´éÇèÒ

¢Í§

G=3

áÅÐ

γe

ÁÕºÔµ 0 àÃÕÂ§µÔ´µèÍ

I=4

¤×Í ÅÓ´Ñº ¢éÍÁÙÅ ·Õ ¶Ù¡ à¢éÒ ÃËÑÊ ´éÇÂÃËÑÊ

γ o = {100110101}

γo

¡çµèÍàÁ× Í ÅÓ´Ñº¢éÍÁÙÅ

à» ¹àÅ¢¨Ó¹Ç¹àµçÁºÇ¡

¨§ËÒ¤èÒ¾ÒÃÒÁÔàµÍÃì

¨Ò¡ÅÓ´Ñº¢éÍÁÙÅ

µÑÇ áÅÐÅÓ´Ñº¢éÍÁÙÅÂèÍÂ

(0, G/I)

γ, γo,

¹Ñ ¹¤×Í ÅÓ´Ñº¢éÍÁÙÅ

áÅÐ

γe

áÅÐ

γ e = {110000101}

¤×Í 3, 2, áÅÐ 4 µÒÁÅÓ´Ñº

¶Ù¡à¢éÒÃËÑÊ´éÇÂÃËÑÊ RLL áºº

¨Ò¡µÑÇÍÂèÒ§·Õ 8.5 ¨ÐÊÑ§à¡µàËç¹ä´éÇèÒ ÅÓ´Ñº ¢éÍÁÙÅ ·Õ ¶Ù¡ à¢éÒ ÃËÑÊ ´éÇÂÃËÑÊ RLL áºº ·Õ ¶Ù¡µéÍ§¹Ñ ¹ ¤èÒ ¾ÒÃÒÁÔàµÍÃì

G ≤ 2I

ÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ì àªè¹ ÃËÑÊ

8.9

àÊÁÍ µÑÇÍÂèÒ§ÃËÑÊ

8/9 (0, 4/4)

(0, G/I)

áÅÐÃËÑÊ

(0, 3/4)

(0, G/I)

·Õ ãªé ã¹ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼Å

16/17 (0, 6/6)

à» ¹µé¹

ÊÃØ»·éÒÂº·

â´Â·Ñ Çä» ÃËÑÊ RLL ÁÕ ËÅÒÂÃÙ»áºº ã¹º·¹Õ ä´é Í¸ÔºÒÂ¶Ö§ ËÅÑ¡¡ÒÃ·Ó§Ò¹áÅÐ¢Ñ ¹µÍ¹¡ÒÃÍÍ¡áºº ÃËÑÊ RLL (run length limited) µÒÁà§× Í¹ä¢ºÑ§¤Ñº

(d, k)

â´Â·Õ ¾ÒÃÒÁÔàµÍÃì

¨Ðà» ¹ µÑÇ¡ÓË¹´

¨Ó¹Ç¹·Õ ¹éÍÂ·Õ ÊØ´ ¢Í§ºÔµ 0 ·Õ ÍÂÙè ÃÐËÇèÒ§ºÔµ 1 (µÒÁÃÙ»áºº NRZI) áÅÐ¾ÒÃÒÁÔàµÍÃì

¨Ðà» ¹

µÑÇ¡ÓË¹´ÁÒ¡·Õ ÊØ´¢Í§ºÔµ 0 ·Õ ÍÂÙèÃÐËÇèÒ§ºÔµ 1 à¹× Í§¨Ò¡ ºÔµ 1 á·¹¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð¢Í§¡ÃÐáÊ ä¿¿ Ò à¢ÕÂ¹ ´Ñ§¹Ñ ¹ ¾ÒÃÒÁÔàµÍÃì

¨Ö§ ªèÇÂÅ´¼Å¡ÃÐ·º·Õ à¡Ô´ ¨Ò¡ ISI ã¹¢³Ð·Õ ¾ÒÃÒÁÔàµÍÃì

¨Ð

ÃÑº»ÃÐ¡Ñ¹ÇèÒ ÅÓ´Ñº¢éÍÁÙÅ·Õ à¢ÕÂ¹Å§ã¹Ê× ÍºÑ¹·Ö¡¨ÐÁÕ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ðà» ¹ÃÐÂÐæ à¾× ÍªèÇÂ·ÓãËéÃÐºº ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÐÃÕÊÒÁÒÃ¶·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ÍÂèÒ§äÃ¡çµÒÁ ã¹» ¨¨ØºÑ¹¹Õ ÃËÑÊ RLL ·Õ ¹ÔÂÁ ãªéÁÑ¡¨ÐÍÂÙèã¹ÃÙ»¢Í§ÃËÑÊ ´ÔÊ¡ìä´Ã¿ì

(0, G/I)

«Ö §à» ¹ÃËÑÊ·Õ ¶Ù¡ÍÍ¡áººÁÒãËéãªé§Ò¹¡ÑºÃÐºº PRML ¢Í§ÎÒÃì´

168

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ã¹¡ÒÃàÅ×Í¡ÃËÑÊ RLL ÁÒãªé§Ò¹¨ÐµéÍ§¤Ó¹Ö§¶Ö§» ¨¨ÑÂµèÒ§æ ä´éá¡è ¾ÒÃÒÁÔàµÍÃì

¤ÇÒÁ¨Ø

C(d, k),

»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

η,

(d, k),

ÍÑµÃÒÃËÑÊ

áÅÐ ÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹ DR à» ¹µé¹ à¾× ÍãËéä´éÃËÑÊ

RLL ·Õ ´ÕÊØ´ÊÓËÃÑº§Ò¹»ÃÐÂØ¡µì¹Ñ ¹æ ¢éÍÊÑ§à¡µ·Õ ¾º¢Í§ÃËÑÊ RLL ·Õ ¹ÓÁÒãªé§Ò¹ã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì ã¹» ¨¨ØºÑ¹ ¤×Í ¾ÒÃÒÁÔàµÍÃì

¨Ð¤èÍÂæ Å´Å§ÁÒà» ¹¤èÒ 0 áÅÐÍÑµÃÒÃËÑÊ

¢Í§ÃËÑÊ RLL ·Õ ãªé ¡çÁÕ

¤èÒà¢éÒã¡Åé¤èÒ 1 ÁÒ¡¢Ö ¹àÃ× ÍÂæ ·Ñ §¹Õ à¾× Íà» ¹¡ÒÃÅ´¨Ó¹Ç¹ºÔµÊèÇ¹à¡Ô¹·Õ à¡Ô´¢Ö ¹ã¹ÃÐºº ·ÓãËéÊÒÁÒÃ¶ ¨Ñ´à¡çº¢éÍÁÙÅ¢èÒÇÊÒÃ¢Í§¼Ùéãªéä´éÁÒ¡¢Ö ¹

8.10

ààºº½ ¡ËÑ´·éÒÂº·

1. ¨§¤Ó¹Ç³ËÒ¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ·Ñ §ËÁ´·Õ ÁÕ¤ÇÒÁÂÒÇ·Ñ §ÊÔ ¹

(d, k)

L ºÔµ ·Õ ÊÍ´¤ÅéÍ§¡Ñºà§× Í¹ä¢ºÑ§¤Ñº

àÁ× Í

1.1)

d = 0, k = 2,

áÅÐ

L=5

1.2)

d = 1, k = 3,

áÅÐ

L=6

1.3)

d = 1, k = 7,

áÅÐ

L = 10

1.4)

d = 2, k = 7,

áÅÐ

L = 10

1.5)

d = 2, k = ∞,

áÅÐ

L = 10

2. ¨§áÊ´§á¼¹ÀÒ¾à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´ áÅÐ¤Ó¹Ç³ËÒàÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð ¢Í§ÃËÑÊ RLL µÒÁà§× Í¹ä¢ºÑ§¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì

2.1)

d=1

áÅÐ

k=5

2.2)

d=1

áÅÐ

k=7

2.3)

d=2

áÅÐ

k=5

2.4)

d=2

áÅÐ

k=7

(d, k)

3. ¨Ò¡â¨·Âìã¹¢éÍ·Õ 2 ¨§¤Ó¹Ç³ËÒ¤ÇÒÁ¨Ø ¼ÅÅÑ¾¸ì·Õ äè´é¡Ñº

C(d, k)

àÁ× Í

C(d, k)

â´ÂãªéÊÁ¡ÒÃ (8.12) ¾ÃéÍÁ·Ñ §à»ÃÕÂºà·ÕÂº

·Õ ¤Ó¹Ç³ä´é¨Ò¡ÊÁ¡ÒÃ (8.18)

8.10.

ààºº½ ¡ËÑ´·éÒÂº·

169

4. ¨§ËÒ¨Ó¹Ç¹ÅÓ´Ñº ¢éÍÁÙÅ ·Õ à» ¹ ä»ä´é ·Ñ §ËÁ´·Õ ÁÕ ¤ÇÒÁÂÒÇ ÊÔ ¹ÊØ´·Õ Ê¶Ò¹Ð

d = 0, k = 2,

áÅÐ

L=5

4.2)

d = 1, k = 3,

áÅÐ

L=5

4.3)

d = 1, k = 7,

áÅÐ

L = 10

4.4)

d = 2, k = 7,

áÅÐ

L = 10

5. ¡ÓË¹´ãËéÅÓ´Ñº¢éÍÁÙÅ·Õ ¶Ù¡à¢éÒÃËÑÊ´éÇÂÃËÑÊ RLL áºº ¢Í§

ºÔµ ·Õ ÍÍ¡¨Ò¡Ê¶Ò¹Ð

¢Í§ÃËÑÊ RLL µÒÁà§× Í¹ä¢ºÑ§¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì

4.1)

(0, G/I)

(d, k)

áÅéÇ ä»

àÁ× Í

¨§ËÒ¤èÒ¾ÒÃÒÁÔàµÍÃì

áÅÐ

´Ñ§µèÍä»¹Õ

5.1)

γ = {10101000101001100101}

5.2)

γ = {10010100001101001100111101}

5.3)

γ = {11100011001010001001100101}

6. ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃÑº ¡ÒÃà¢éÒ áÅÐ¶Í´ÃËÑÊ RLL áºº ¼èÒ¹¡ÒÃà¢éÒÃËÑÊáÅéÇ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº

L=2

L=3

L=4

(1, 2)

â´Â·Õ ¢éÍÁÙÅ áµèÅÐ¤ÃÑ § ·Õ

¾ÃéÍÁ·Ñ §ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

8. ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃÑº ¡ÒÃà¢éÒ áÅÐ¶Í´ÃËÑÊ RLL áºº ¼èÒ¹¡ÒÃà¢éÒÃËÑÊáÅéÇ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº

â´Â·Õ ¢éÍÁÙÅ áµèÅÐ¤ÃÑ § ·Õ

¾ÃéÍÁ·Ñ §ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

7. ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃÑº ¡ÒÃà¢éÒ áÅÐ¶Í´ÃËÑÊ RLL áºº ¼èÒ¹¡ÒÃà¢éÒÃËÑÊáÅéÇ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡Ñº

(0, 1)

(1, 3)

â´Â·Õ ¢éÍÁÙÅ áµèÅÐ¤ÃÑ § ·Õ

¾ÃéÍÁ·Ñ §ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

170

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÀÒ¤¼¹Ç¡ ¡

µÒÃÒ§¿ §¡ìªÑ¹

¿ §¡ìªÑ¹

Q(x)

à» ¹¿ §¡ìªÑ¹·Õ ÊÒÁÒÃ¶¨Ñ´ãËéÍÂÙèã¹ÃÙ»¢Í§¿ §¡ìªÑ¹¡ÒÃá¨¡á¨§ÊÐÊÁ¢Í§µÑÇá»ÃÊØèÁáºº

à¡ÒÊìà«ÕÂ¹ä´é«Ö §à» ¹·Õ ¹ÔÂÁãªé§Ò¹·Ò§´éÒ¹Ê¶ÔµÔÈÒÊµÃìáÅÐ´éÒ¹ÇÔÈÇ¡ÃÃÁÈÒÊµÃì â´Â¿ §¡ìªÑ¹ ¹ÔÂÒÁ´Ñ§¹Õ

1 Q(x) = √ 2π

∞

Q(x)

½ 2¾ y dy exp − 2

(¡.1)

«Ö §à» ¹¡ÒÃËÒ¤èÒ»ÃÔ¾Ñ¹¸ìÊèÇ¹ËÒ§¢Í§¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹áººà¡ÒÊìà«ÕÂ¹àÁ× Í ¤×Í ¿ §¡ìªÑ¹àÅ¢ªÕ ¡ÓÅÑ§ (exponential function) â´Â·Ñ Çä» ¤èÒ¢Í§¿ §¡ìªÑ¹ ÊÒÁÒÃ¶ËÒä´é¨Ò¡µÒÃÒ§¤é¹ËÒ (look up table) áµèã¹¡Ã³Õ·Õ ¤èÒä´é´Ñ§¹Õ

xÀ3

½ 2¾ 1 x Q(x) ≈ √ exp − 2 x 2π

µÒÃÒ§µèÍä»¹Õ ¨ÐáÊ´§¤èÒ¢Í§¿ §¡ìªÑ¹

Q(x)

ÊÓËÃÑº

0 ≤ x ≤ 3.59

171

¨Ð

Q(x)

¿ §¡ìªÑ¹

ÊÓËÃÑº¤èÒ

Q(x)

exp{·}

µèÒ§æ

ÊÒÁÒÃ¶»ÃÐÁÒ³

(¡.2)

172

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

Q(x)

0.50000

0.36

Q(x) 0.35942

0.72

Q(x) 0.23576

1.08

Q(x) 0.14007

1.44

Q(x) 0.0749340

0.01

0.49601

0.37

0.35569

0.73

0.23270

1.09

0.13786

1.45

0.0735290

0.02

0.49202

0.38

0.35197

0.74

0.22965

1.10

0.13567

1.46

0.0721450

0.03

0.48803

0.39

0.34827

0.75

0.22663

1.11

0.133500

1.47

0.070781

0.04

0.48405

0.40

0.34458

0.76

0.22363

1.12

0.131360

1.48

0.069437

0.05

0.48006

0.41

0.34090

0.77

0.22065

1.13

0.129240

1.49

0.068112

0.06

0.47608

0.42

0.33724

0.78

0.21770

1.14

0.127140

1.50

0.066807

0.07

0.47210

0.43

0.33360

0.79

0.21476

1.15

0.125070

1.51

0.065522

0.08

0.46812

0.44

0.32997

0.80

0.21186

1.16

0.123020

1.52

0.064255

0.09

0.46414

0.45

0.32636

0.81

0.20897

1.17

0.121000

1.53

0.063008

0.10

0.46017

0.46

0.32276

0.82

0.20611

1.18

0.119000

1.54

0.061780

0.11

0.45620

0.47

0.31918

0.83

0.20327

1.19

0.117020

1.55

0.060571

0.12

0.45224

0.48

0.31561

0.84

0.20045

1.20

0.115070

1.56

0.059380

0.13

0.44828

0.49

0.31207

0.85

0.19766

1.21

0.113140

1.57

0.058208

0.14

0.44433

0.50

0.30854

0.86

0.19489

1.22

0.111230

1.58

0.057053

0.15

0.44038

0.51

0.30503

0.87

0.19215

1.23

0.109350

1.59

0.055917

0.16

0.43644

0.52

0.30153

0.88

0.18943

1.24

0.107490

1.60

0.054799

0.17

0.43251

0.53

0.29806

0.89

0.18673

1.25

0.105650

1.61

0.053699

0.18

0.42858

0.54

0.29460

0.90

0.18406

1.26

0.103830

1.62

0.052616

0.19

0.42465

0.55

0.29116

0.91

0.18141

1.27

0.102040

1.63

0.051551

0.20

0.42074

0.56

0.28774

0.92

0.17879

1.28

0.100270

1.64

0.050503

0.21

0.41683

0.57

0.28434

0.93

0.17619

1.29

0.098525

1.65

0.049471

0.22

0.41294

0.58

0.28096

0.94

0.17361

1.30

0.096800

1.66

0.048457

0.23

0.40905

0.59

0.27760

0.95

0.17106

1.31

0.095098

1.67

0.047460

0.24

0.40517

0.60

0.27425

0.96

0.16853

1.32

0.093418

1.68

0.046479

0.25

0.40129

0.61

0.27093

0.97

0.16602

1.33

0.091759

1.69

0.045514

0.26

0.39743

0.62

0.26763

0.98

0.16354

1.34

0.090123

1.70

0.044565

0.27

0.39358

0.63

0.26435

0.99

0.16109

1.35

0.088508

1.71

0.043633

0.28

0.38974

0.64

0.26109

1.00

0.15866

1.36

0.086915

1.72

0.042716

0.29

0.38591

0.65

0.25785

1.01

0.15625

1.37

0.085343

1.73

0.041815

0.30

0.38209

0.66

0.25463

1.02

0.15386

1.38

0.083793

1.74

0.040930

0.31

0.37828

0.67

0.25143

1.03

0.15151

1.39

0.082264

1.75

0.040059

0.32

0.37448

0.68

0.24825

1.04

0.14917

1.40

0.080757

1.76

0.039204

0.33

0.37070

0.69

0.24510

1.05

0.14686

1.41

0.079270

1.77

0.038364

0.34

0.36693

0.70

0.24196

1.06

0.14457

1.42

0.077804

1.78

0.037538

0.35

0.36317

0.71

0.23885

1.07

0.14231

1.43

0.076359

1.79

0.036727

173

Q(x)

1.80

0.035930

2.16

0.0153860

2.52

0.0058677

2.88

0.00198840

3.24

0.00059765

1.81

0.035148

2.17

0.0150030

2.53

0.0057031

2.89

0.00192620

3.25

0.00057703

1.82

0.034380

2.18

0.0146290

2.54

0.0055426

2.90

0.00186580

3.26

0.00055706

1.83

0.033625

2.19

0.0142620

2.55

0.0053861

2.91

0.00180710

3.27

0.00053774

1.84

0.032884

2.20

0.0139030

2.56

0.0052336

2.92

0.00175020

3.28

0.00051904

1.85

0.032157

2.21

0.0135530

2.57

0.0050849

2.93

0.00169480

3.29

0.00050094

1.86

0.031443

2.22

0.0132090

2.58

0.0049400

2.94

0.00164110

3.30

0.00048342

1.87

0.030742

2.23

0.0128740

2.59

0.0047988

2.95

0.00158890

3.31

0.00046648

1.88

0.030054

2.24

0.0125450

2.60

0.0046612

2.96

0.00153820

3.32

0.00045009

1.89

0.029379

2.25

0.0122240

2.61

0.0045271

2.97

0.00148900

3.33

0.00043423

1.90

0.028717

2.26

0.0119110

2.62

0.0043965

2.98

0.00144120

3.34

0.00041889

1.91

0.028067

2.27

0.0116040

2.63

0.0042692

2.99

0.00139490

3.35

0.00040406

1.92

0.027429

2.28

0.0113040

2.64

0.0041453

3.00

0.00134990

3.36

0.00038971

1.93

0.026803

2.29

0.0110110

2.65

0.0040246

3.01

0.00130620

3.37

0.00037584

1.94

0.026190

2.30

0.0107240

2.66

0.0039070

3.02

0.00126390

3.38

0.00036243

1.95

0.025588

2.31

0.0104440

2.67

0.0037926

3.03

0.00122280

3.39

0.00034946

1.96

0.024998

2.32

0.0101700

2.68

0.0036811

3.04

0.00118290

3.40

0.00033693

1.97

0.024419

2.33

0.0099031

2.69

0.0035726

3.05

0.00114420

3.41

0.00032481

1.98

0.023852

2.34

0.0096419

2.70

0.0034670

3.06

0.00110670

3.42

0.00031311

1.99

0.023295

2.35

0.0093867

2.71

0.0033642

3.07

0.00107030

3.43

0.00030179

2.00

0.022750

2.36

0.0091375

2.72

0.0032641

3.08

0.00103500

3.44

0.00029086

2.01

0.022216

2.37

0.0088940

2.73

0.0031667

3.09

0.00100080

3.45

0.00028029

2.02

0.021692

2.38

0.0086563

2.74

0.0030720

3.10

0.00096760

3.46

0.00027009

2.03

0.021178

2.39

0.0084242

2.75

0.0029798

3.11

0.00093544

3.47

0.00026023

2.04

0.020675

2.40

0.0081975

2.76

0.0028901

3.12

0.00090426

3.48

0.00025071

2.05

0.020182

2.41

0.0079763

2.77

0.0028028

3.13

0.00087403

3.49

0.00024151

2.06

0.019699

2.42

0.0077603

2.78

0.0027179

3.14

0.00084474

3.50

0.00023263

2.07

0.019226

2.43

0.0075494

2.79

0.0026354

3.15

0.00081635

3.51

0.00022405

2.08

0.018763

2.44

0.0073436

2.80

0.0025551

3.16

0.00078885

3.52

0.00021577

2.09

0.018309

2.45

0.0071428

2.81

0.0024771

3.17

0.00076219

3.53

0.00020778

2.10

0.017864

2.46

0.0069469

2.82

0.0024012

3.18

0.00073638

3.54

0.00020006

2.11

0.017429

2.47

0.0067557

2.83

0.0023274

3.19

0.00071136

3.55

0.00019262

2.12

0.017003

2.48

0.0065691

2.84

0.0022557

3.20

0.00068714

3.56

0.00018543

2.13

0.016586

2.49

0.0063872

2.85

0.0021860

3.21

0.00066367

3.57

0.00017849

2.14

0.016177

2.50

0.0062097

2.86

0.0021182

3.22

0.00064095

3.58

0.00017180

2.15

0.015778

2.51

0.0060366

2.87

0.0020524

3.23

0.00061895

3.59

0.00016534

174

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ÀÒ¤¼¹Ç¡ ¢

ÊÙµÃ¤³ÔµÈÒÊµÃì·Õ ÊÓ¤Ñ

ÀÒ¤¼¹Ç¡¹Õ ¨ÐáÊ´§ÊÙµÃ¤³ÔµÈÒÊµÃì ·Õ ãªéºèÍÂÊÓËÃÑº ¡ÒÃÇÔà¤ÃÒÐËì ÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ ÎÒÃì´´ÔÊ¡ìä´Ã¿ì¢Í§Ë¹Ñ§Ê×ÍàÅèÁ¹Õ

¢.1

µÃÕâ¡³ÁÔµÔ (Trigonometric)

sin(−α) = − sin(α) cos(−α) = cos(α) sin(α) = cos(α − π/2) sin2 (α) + cos2 (α) = 1 sin(α ± β) = sin(α) cos(β) ± cos(α) sin(β) cos(α ± β) = cos(α) cos(β) ∓ sin(α) sin(β) sin(α) sin(β) =

1 2

cos(α − β) − 12 cos(α + β)

sin(α) cos(β) =

1 2

sin(α + β) + 12 sin(α − β)

cos(α) cos(β) =

1 2

cos(α − β) + 21 cos(α + β)

cos(α) sin(β) =

1 2

sin(α + β) − 12 sin(α − β) 175

176

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

sin(2α) = 2 sin(α) cos(α) cos(2α) = cos2 (α) − sin2 (α) = 1 − 2 sin2 (α) = 2 cos2 (α) − 1 sin2 (α) = 21 {1 − cos(2α)} cos2 (α) = 21 {1 + cos(2α)} ejα = cos(α) + j sin(α) sin(α) = (ejα − e−jα )/(2j) cos(α) = (ejα + e−jα )/2

¢.2

R R R R R R R R R R R R R

»ÃÔ¾Ñ¹¸ìäÁè¨Ó¡Ñ´à¢µ (Inde nite Integral)

u dv = uv −

v du

àÁ× Í

xn dx = xn+1 /(n + 1)

áÅÐ

àÁ× Í

à» ¹¿ §¡ìªÑ¹¢Í§

n 6= −1

x−1 dx = ln(x) eax dx = eax /a ln(x) dx = x ln(x) − x xeax dx = eax (ax − 1)/a2 x2 eax dx = eax (a2 x2 − 2ax + 2)/a3 sin(ax) dx = −(1/a) cos(ax) cos(ax) dx = (1/a) sin(ax) sin2 (ax) dx = x/2 − sin(2ax)/4a x sin(ax) dx = (1/a2 ){sin(ax) − ax cos(ax)} cos2 (ax) dx = x/2 + sin(2ax)/4a x cos(ax) dx = (1/a2 ){cos(ax) + ax sin(ax)}

ÀÒ¤¼¹Ç¡ ¤

¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì¢Í§àÇ¡àµÍÃìààÅÐàÁ·ÃÔ¡«ì

ÀÒ¤¼¹Ç¡¹Õ ¨ÐÊÃØ»ÊÙµÃ¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì (di erentiation) ¢Í§àÇ¡àµÍÃìáÅÐàÁ·ÃÔ¡«ì«Ö §¨Ðà» ¹»ÃÐâÂª¹ì µèÍ¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìã¹Ë¹Ñ§Ê×ÍàÅèÁ¹Õ ¡ÓË¹´ãËé

áÅÐ

à» ¹àÇ¡àµÍÃìá¹ÇµÑ § (column vector) ¢¹Ò´

á¶Ç áÅÐ 1 á¹ÇµÑ §) áÅÐãËé

k×1

à» ¹àÁ·ÃÔ¡«ì¨ÑµØÃÑÊ (square matrix) ¢¹Ò´

(¹Ñ ¹¤×ÍÁÕ¨Ó¹Ç¹

k×k

´Ñ§¹Ñ ¹

¨Ò¡¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì¢Í§àÇ¡àµÍÃìààÅÐàÁ·ÃÔ¡«ì¨Ðä´é¤ÇÒÁÊÑÁ¾Ñ¹¸ì´Ñ§¹Õ

xT u = uT x ¡ ¢ ∂ xT u =x ∂u ∂ (Au) = AT ∂u ∂ (Au) =A ∂uT áÅÐ

¶éÒàÁ·ÃÔ¡«ì

(¤.1)

(¤.2)

(¤.3)

(¤.4)

¡ ¢ ¡ ¢ ∂ uT Au = A + AT u ∂u A

à» ¹àÁ·ÃÔ¡«ì·Õ ÊÁÁÒµÃ (symmetric) ¹Ñ ¹¤×Í

A = AT

¡ ¢ ∂ uT Au = 2Au ∂u 177

(¤.5) ¨Ðä´éÇèÒ

(¤.6)

178

áÅÐ

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ ¢ ∂ 2 uT Au = 2A ∂u ∂uT

(¤.7)

ÀÒ¤¼¹Ç¡ §

¤ÓÈÑ¾·ìà·¤¹Ô¤

¡ÃÐºÇ¹¡ÒÃà¢ÕÂ¹

write process minimization process

¡ÃÐºÇ¹¡ÒÃ·ÓãËéÁÕ¤èÒ¹éÍÂÊØ´

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹

noise prediction process

¡ÃÐºÇ¹¡ÒÃã¹¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ ¡ÃÐºÇ¹¡ÒÃÍèÒ¹

read process write current

¡ÃÐáÊä¿¿ Òà¢ÕÂ¹ ¡ÅØèÁ¢éÍÁÙÅ

data packet

¡ÒÃ¡Å ÓÃËÑÊ¾ÑÅÊì

PCM (pulse code modulation) modulation

¡ÒÃ¡Å ÓÊÑÒ³ (¡ÒÃÁÍ´ÙàÅµ) ¡ÒÃ¢ÂÒÂÊÑÒ³Ãº¡Ç¹

noise enhancement

synchronization

¡ÒÃà¢éÒ¨Ñ§ËÇÐ

perfect synchronization

¡ÒÃà¢éÒ¨Ñ§ËÇÐÍÂèÒ§ÊÁºÙÃ³ì ¡ÒÃ¤Ò´ËÁÒÂ, ¤èÒ¤Ò´ËÁÒÂ ¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ

sampling

¡ÒÃà´Ô¹áººÊØèÁ

random walk

acquisition

¡ÒÃµÃÇ¨ËÒÅÓ´Ñº ¡ÒÃµÔ´µÒÁ

digital data storage

projection

¡ÒÃªÑ¡µÑÇÍÂèÒ§

¡ÒÃä´éÁÒ

expectation

data storage

noise whitening process

sequence detection

tracking

179

180

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¡ÒÃ·Ó¹ÒÂÊÑÒ³Ãº¡Ç¹ ¡ÒÃá·Ã¡ÊÍ´

noise prediction

interference

¡ÒÃá·Ã¡ÊÍ´ÃÐËÇèÒ§ÊÑÅÑ¡É³ì

ISI (intersymbol interference)

¡ÒÃºÇ¡ ¡ÒÃà»ÃÕÂºà·ÕÂº ¡ÒÃàÅ×Í¡ ¡ÒÃºÑ¹·Ö¡

ACS (add compare select)

recording

¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §

perpendicular recording

¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹

longitudinal recording binary recording

¡ÒÃºÑ¹·Ö¡áººäº¹ÒÃÕ ¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡

magnetic recording

¡ÒÃ»ÃÐÁÇÅ¼Åáººà¾Íà«ÍÃìäÇàÇÍÃì

¡ÒÃ»ÃÑº¤èÒ·Ò§àÇÅÒ ¡ÒÃ» Í¹¡ÅÑº

timing adjustment

feedback

¡ÒÃ» Í¹¡ÅÑº¤èÒµÑ´ÊÔ¹ã¨ ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

decision feedback

transition

¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È

¡ÒÃá»Å§«Õ

isolated transition

transform

¡ÒÃá»Å§¿ÙàÃÕÂÃì

Fourier transform

¡ÒÃá»Å§¿ÙàÃÕÂÃì·Õ µèÍà¹× Í§·Ò§àÇÅÒ ¡ÒÃá¾Ãè¡ÃÐ¨ÒÂ¢Í§¢éÍ¼Ô´¾ÅÒ´ ¡ÒÃÃº¡Ç¹

PSP (per survivor processing)

digital signal processing

¡ÒÃ»ÃÐÁÇÅ¼ÅÊÑÒ³´Ô¨Ô·ÑÅ

continuous time Fourier transform error propagation

disturbance

¡ÒÃÅºÅéÒ§ÊÀÒ¾áÁèàËÅç¡

demagnetization

¡ÒÃàÅ× Í¹µÓáË¹è§¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð

transition shift

¡ÒÃàÅ× Í¹µÓáË¹è§¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐáººÊØèÁ ¡ÒÃË¹èÇ§àÇÅÒ¡ÒÃµÑ´ÊÔ¹ã¨ ¡ÒÃËÒÍ¹Ø¾Ñ¹¸ì ¡ÓÅÑ§

decision delay

di erentiation

power

à¡ÒÊìà«ÕÂ¹ ¢¹Ò´

random transition shift

Gaussian magnitude

¢éÍ¼Ô´¾ÅÒ´

error prediction error

MSE (mean squared error)

MMSE (minimum mean squared error)

frequency error phase error

181

¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ

timing error

¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ·Õ ËÅ§àËÅ×ÍÍÂÙè ¢éÍÁÙÅäº¹ÒÃÕ

binary data

¢éÍÁÙÅÇÔÂØµ (á«Áà» Å) ¤ÇÃ¨Ðà» ¹ÁÒ¡ÊØ´ ¤ÇÒÁ¨Ø

residual timing error

discrete data ML (maximum likelihood)

capacity

¤ÇÒÁ¨ØªèÍ§ÊÑÒ³

channel capacity

complexity

¤ÇÒÁ«Ñº«éÍ¹

¤ÇÒÁ¶Õ ¡ÒÃªÑ¡µÑÇÍÂèÒ§ ¤ÇÒÁ¶Õ µÑ´

sampling rate

cut o frequency normalized frequency

¤ÇÒÁ¶Õ áºº¹ÍÃìÁÍÅäÅ«ì ¤ÇÒÁ¶Õ ä¹¤ÇÔµÊì

Nyquist frequency

¤ÇÒÁ¹èÒ¨Ðà» ¹

probability

¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´

probability of error

¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´ÅÓ´Ñº ¤ÇÒÁá»Ã»ÃÇ¹

probability of sequence error

variance

¤ÇÒÁäÁèà» ¹àªÔ§àÊé¹

nonlinearity

¤ÇÒÁË¹Òá¹è¹¡ÒÃºÃÃ¨Ø

packing density

¤ÇÒÁË¹Òá¹è¹¢Í§¡ÒÃºÑ¹·Ö¡áºº¹ÍÃìÁÍÅäÅ«ì ¤ÇÒÁË¹Òá¹è¹àªÔ§¾× ¹·Õ

areal density

¤ÇÒÁË¹Òá¹è¹Êà»¡µÃÑÁ¡ÓÅÑ§ ¤Í¹âÇÅÙªÑ¹

power spectral density

convolution

ND (normalized recording density)

mean square

mean

¤èÒµÑ´ÊÔ¹ã¨

decision

¤èÒµÑ´ÊÔ¹ã¨¢³ÐË¹Ö §áººá¢ç§ ¤Òº (àÇÅÒ)

instantaneous hard decision

period

¤Òº¡ÒÃªÑ¡µÑÇÍÂèÒ§ ¤ÒºàÇÅÒ¢Í§ºÔµ ¤èÒàÁµÃÔ¡ÊÒ¢Ò

sampling period bit period branch metric

¤èÒàÁµÃÔ¡àÊé¹·Ò§

path metric

¤èÒÅÑ¡É³Ðà©¾ÒÐ

eigenvalue

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´

FSM ( nite state machine)

à¤Ã× Í§ËÁÒÂà¢éÒ¨Ñ§ËÇÐ §Ò¹»ÃÐÂØ¡µì (áÍ¾ÅÔà¤ªÑ¹)

sync mark application

182

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

à§× Í¹ä¢ºÑ§¤Ñº

constraint

à§× Í¹ä¢ºÑ§¤ÑºáººâÁ¹Ô¡ ¨Ò¹ (¨Ò¹ºÑ¹·Ö¡)

disk

¨Ò¹ºÑ¹·Ö¡áÁèàËÅç¡ ¨ÔµàµÍÃì

monic constraint

magnetic disk

jitter

¨ÔµàµÍÃì·Ò§àÇÅÒ

timing jitter

node

¨Ø´µèÍ ¨Ø´ÊÁ´ØÅ

equilibrium point

¨Ø´àÊ¶ÕÂÃÀÒ¾

stable point

ªèÍ§ÊÑÒ³

channel

ªèÍ§ÊÑÒ³ÇÔÂØµ

discrete channel

ªèÍ§ÊÑÒ³Ê× ÍÊÒÃ

communication channel

ªèÍ§ÊÑÒ³ÍèÒ¹

read channel

ªÔ»ªèÍ§ÊÑÒ³ÍèÒ¹ àªÔ§àÊé¹

read channel chip

linear

«éÍ¹àËÅ× ÍÁ

overlap superparamagnetic

«Ùà»ÍÃì¾ÒÃÒáÁ¡à¹µÔ¡ à«¡àµÍÃì

sector

á«Áà» Å, µÑÇÍÂèÒ§ ä«à¤ÔÅÊÅÔ» ´Ô¨Ô·ÑÅ

sample

cycle slip digital

´Õà·ÍÃìÁÔá¹¹µì à´«ÔàºÅ

determinant

dB (decibel)

â´àÁ¹

domain

â´àÁ¹

â´àÁ¹¤ÇÒÁ¶Õ

domain frequency domain

â´àÁ¹àÇÅÒ

time domain

µÑÇ¤Ù³ÅÒ¡ÃÒ¹¨ì µÑÇªÕ ºÍ¡

domain

Lagrange multiplier

indicator

convolution operator expectation operator delay operator

predecessor look up table

183

·ÒÃìà¡çµ

target

·ÒÃìà¡çµ·Õ àËÁÒÐ·Õ ÊØ´

optimal target

·ÒÃìà¡çµáºº GPR

generalized partial response (GPR) target

·ÒÃìà¡çµáºº PR

partial response (PR) target

·ÓãËéà» ¹ºÃÃ·Ñ´°Ò¹

normalize

à·¤¹Ô¤¡ÒÃ»ÃÐÁÒ³¤èÒã¹ªèÇ§ à·ÃÐäºµì á·ç»

interpolation technique

TB (terabyte) tap

ä·ÁÁÔ §¿ §¡ìªÑ¹

timing function

ä·ÁÁÔ §¿ §¡ìªÑ¹áºº¹ÍÃìÁÍÅäÅ«ì

normalized timing function

timing recovery

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Õ ãªé¡Ñ¹·Ñ Çä» ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº¹ÔÃ¹ÑÂ

conventional timing recovery

deductive timing recovery

ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº»ÃÐÁÒ³¤èÒã¹ªèÇ§ ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáººÍØ»¹ÑÂ ä·ÁÁÔ §ÅÙ» ºÔµ

interpolated timing recovery

inductive timing recovery

timing loop

bit

ºÔµ¢èÒÇÊÒÃ

message bit

bit cell

transition bit

redundant bit bandwidth

áº¹´ìÇÔ´·ìà¡Ô¹à» ¹ÈÙ¹Âì áº¹´ìÇÔ´·ì¢Í§ÅÙ»

zero excess bandwidth

loop bandwidth

áºº¢éÍÁÙÅ

data pattern

áºº¨ÓÅÍ§

model

áºº¨ÓÅÍ§¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ãà¿ÊÅçÍ¡ÅÙ»áººàªÔ§àÊé¹ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³àÊÁ×Í¹¨ÃÔ§ áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³ÍØ´Á¤µÔ

äº¹ÒÃÕ (°Ò¹ÊÍ§)

ideal channel model

binary

»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÑÊ

equivalent discrete time channel model

realistic channel model

byte

äºµì (1 äºµì = 8 ºÔµ)

linearized phase locked loop (PLL) model

code e ciency

»ÃÑº¤èÒ (ãËéà» ¹» ¨¨ØºÑ¹)

update

»ÃÔÁÒ³Ë¹èÇ§àÇÅÒã¹ÅÙ»

loop delay

184

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

¼ÅµÍºÊ¹Í§

response

¼ÅµÍºÊ¹Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð ¼ÅµÍºÊ¹Í§¢Í§ÃÐºº

system response

¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ ¼ÅµÍºÊ¹Í§ä´ºÔµ

transition response

frequency response dibit response

¼ÅµÍºÊ¹Í§·ÒÃìà¡çµ

target response

¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹

PR (partial response) PRML (partial response maximum likelihood)

impulse response FIR ( nite impulse response)

IIR (in nite impulse response)

CD (compact disc)

á¼è¹´ÕÇÕ´Õ

DVD (digital versatile disc)

á¼è¹ºÑ¹·Ö¡áÁèàËÅç¡ á¼¹ÀÒ¾

magnetic oppy disk

diagram

á¼¹ÀÒ¾à·ÃÅÅÔÊ ¾ÅÑ§§Ò¹

GPR (generalized partial response)

trellis diagram

energy

¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ

unit energy

¾ËØ¹ÒÁ (â¾ÅÔâ¹àÁÕÂÅ)

polynomial

à¾Íà«ÍÃìäÇàÇÍÃìä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ

per survivor timing recovery

à¾Íà«ÍÃìäÇàÇÍÃìä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕáºº·Ó§Ò¹« Ó â¾Å ¿ÅÑ¡«ì ¿ §¡ìªÑ¹

per survivor iterative timing recovery

pole ux function

¿ §¡ìªÑ¹¢Ñ ¹ºÑ¹ä´

step function

¿ §¡ìªÑ¹¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹

probability density function

Kronecker delta function

Dirac delta function

¿ §¡ìªÑ¹¶èÒÂâÍ¹

transfer function

¿ §¡ìªÑ¹ÍÔÁ¾ÑÅÊì

impulse function

ä¿¿ Ò¡ÃÐáÊµÃ§ ÀÒÇÐ

d.c. (direct current)

mode

ÀÒÇÐ¡ÒÃä´éÁÒ

Gaussian probability density function

acquisition mode

185

ÀÒÇÐ¡ÒÃä´éÁÒáººÊÁºÙÃ³ì ÀÒÇÐ¡ÒÃµÔ´µÒÁ

perfect acquisition

tracking mode

ÀÒÇÐ¡ÒÃ½ ¡ÍºÃÁ

training mode

àÁµÃÔ¡ (µÑÇÇÑ´)

metric

àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð àÁ·ÃÔ¡«ìÊËÊÑÁ¾Ñ¹¸ì¢éÒÁ

cross correlation matrix

àÁ·ÃÔ¡«ìÍÑµÊËÊÑÁ¾Ñ¹¸ì

auto correlation matrix identity matrix

àÁ·ÃÔ¡«ìàÍ¡ÅÑ¡É³ì äÁèà¢éÒ¨Ñ§ËÇÐ

state transition matrix

asynchronous

äÁèÁÕÊËÊÑÁ¾Ñ¹¸ì¡Ñ¹

uncorrelated ECC (error correction code)

ÃËÑÊá¡éä¢¢éÍ¼Ô´¾ÅÒ´ ÃËÑÊ¤Í¹âÇÅÙªÑ¹ ÃËÑÊÁÍ´ÙàÅªÑ¹

convolutional code modulation code

ÃÐ´Ñº¢Õ´àÃÔ Áà»ÅÕ Â¹

threshold level

ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ

data storage system

ÃÐºº¡ÒÃºÑ¹·Ö¡áÁèàËÅç¡ ÃÐºº·Õ ¶Ù¡à¢éÒÃËÑÊ

magnetic recording system

coded system

ÃÐºº·Õ ÁÕá¶º¤ÇÒÁ¶Õ ¨Ó¡Ñ´ ÃÐºº·Õ äÁèä´é¶Ù¡à¢éÒÃËÑÊ ÃÐººÊ× ÍÊÒÃ´Ô¨Ô·ÑÅ ÃÐÂÐ

band limited system uncoded system

digital communication system

stage

MSD (mean squared distance)

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å

e ective distance

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§ ÃÐÂÐ·Ò§ÂØ¤ÅÔ´

Euclidean distance

squared e ective distance

squared Euclidean distance

RMS (root mean square)

waveform

àÃ¨ÔÊàµÍÃìáººàÅ× Í¹

shift register

ÅÍ¡ÒÃÔ·ÖÁ¸ÃÃÁªÒµÔ

natural logarithm

ÅÍ§¼Ô´ÅÍ§¶Ù¡ ÅÓ´Ñº

trial and error

sequence

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´

error sequence

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ

input error sequence

ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§

valid input error sequence

186

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÅÓ´Ñº¢éÍÁÙÅ

data sequence

ÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Õ

odd subsequence

ÅÓ´Ñº¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè

even subsequence

Ç§¨Ã VCO Ç§¨Ã¡ÃÍ§

VCO (voltage controlled oscillator) lter interpolation lter

prediction error lter

predictor lter

linear lter LPF (low pass lter)

Ç§¨Ã¡ÃÍ§¼èÒ¹µ Ó

Ç§¨Ã¡ÃÍ§¼èÒ¹µ ÓÍØ´Á¤µÔ

ideal low pass lter

loop lter

Ç§¨Ã¡ÃÍ§ÅÙ» Ç§¨Ãà¢éÒÃËÑÊ

encoder

noise whitening lter

error correction code (ECC) encoder

modulation encoder

sampler detector

Ç§¨ÃµÃÇ¨ËÒ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ

TED (timing error detector)

Ç§¨ÃµÃÇ¨ËÒ¢Õ´àÃÔ Áà»ÅÕ Â¹·Õ äÁèÁÕË¹èÇÂ¤ÇÒÁ¨Ó

memoryless threshold detector

Ç§¨ÃµÃÇ¨ËÒ¢Õ´àÃÔ Áà»ÅÕ Â¹·Õ äÁèÁÕË¹èÇÂ¤ÇÒÁ¨ÓáººËÅÒÂÃÐ´Ñº

multi level memoryless threshold de

peak detector sequence detector

MLSD (maximum likelihood sequence detector)

optimal sequence detector

Viterbi detector

multi level threshold detector

symbol detector opimal detector

decoder

Ç§¨Ã¶Í´ÃËÑÊá¡éä¢¢éÍ¼Ô´¾ÅÒ´ Ç§¨Ã¶Í´ÃËÑÊÁÍ´ÙàÅªÑ¹

error correction code (ECC) decoder

modulation decoder

Ç§¨Ã¡ÃÍ§·Ó¹ÒÂË¹Ö §¢Ñ ¹áººàªÔ§àÊé¹

linear one step predictor

Ç§¨Ãà»ÅÕ Â¹ÊÑÒ³áÍ¹ÐÅçÍ¡à» ¹ÊÑÒ³´Ô¨Ô·ÑÅ

ADC (analog to digital converter)

187

Ç§¨Ãà¿ÊÅçÍ¡ÅÙ»

PLL (phase locked loop)

Ç§¨ÃÀÒ¤ÃÑº

receiver

Ç§¨ÃÀÒ¤Êè§

transmitter

Ç§¨ÃÁÍ´ÙàÅàµÍÃì

modulator

Ç§¨ÃËÒÍ¹Ø¾Ñ¹¸ì

di erentiator

eigenvector

ÊàµªÑ¹à¹ÃÕ Ê¶Ò¹Ð

normalized eigenvector

state

Ê¶Ò¹ÐµèÍä»

next state start state

Ê¶Ò¹ÐàÃÔ Áµé¹

Ê¶Ò» µÂ¡ÃÃÁªèÍ§ÊÑÒ³ÍèÒ¹ Êà»¡µÃÑÁ¤èÒÈÙ¹Âì

read channel architecture

spectral null

ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡ (¡ÒÃ·ÓãËéà» ¹áÁèàËÅç¡) ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡¢Í§Ê× ÍºÑ¹·Ö¡ ÊÀÒ¾ÅºÅéÒ§áÁèàËÅç¡ ÊÀÒ¾ãËé«ÖÁ¼èÒ¹ä´é

medium magnetization

coercivity permeability

ÊÁ¡ÒÃ¹ÍÃìÁÍÅ

normal equation

ÊÁ¡ÒÃ»ÃÑº¤èÒ

update equation

ÊÅÑºà»ÅÕ Â¹ (·ÃÒ¹Êâ¾Ê) ÊèÇ¹»ÃÐ¡Íº

transpose

component

ÊËÊÑÁ¾Ñ¹¸ì

correlation

ÊËÊÑÁ¾Ñ¹¸ì¢éÒÁ ÊÑÒ³

magnetization

cross correlation

signal

ÊÑÒ³äº¹ÒÃÕ (ÊÑÒ³ÊÍ§ÃÐ´Ñº) ÊÑÒ³¾ÑÅÊìä´ºÔµ

dibit pulse

ÊÑÒ³¾ÑÅÊìä¹¤ÇÔµÊìÍØ´Á¤µÔ ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð

ideal Nyquist pulse transition pulse

ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹ÐàÍ¡à·È ÊÑÒ³Ãº¡Ç¹

binary signal

isolated transition pulse

noise

ÊÑÒ³Ãº¡Ç¹¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇ

white Gaussian noise

ÊÑÒ³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇáºººÇ¡ ÊÑÒ³Ãº¡Ç¹¤ÇÒÁÃéÍ¹

transition noise

AWGN (additive white Gaussian noise)

thermal noise

ÊÑÒ³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡

media jitter noise

188

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ÊÑÒ³Ãº¡Ç¹·Õ ¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ

pattern dependent noise

ÊÑÒ³Ãº¡Ç¹·Õ ÍÂÙè¹Í¡á¶º¤ÇÒÁ¶Õ ÊÑÒ³Ãº¡Ç¹áººÊÕ

out of band noise

colored noise

ÊÑÒ³Ãº¡Ç¹ÊÕ¢ÒÇ

white noise

ÊÑÒ³Ãº¡Ç¹Ê× ÍºÑ¹·Ö¡

media noise

ÊÑÒ³áÍ¹ÐÅçÍ¡·Ò§ä¿¿ Ò·Õ ä´é¨Ò¡ËÑÇÍèÒ¹ (ÊÑÒ³ read back) coe cient

ÊÑÁ»ÃÐÊÔ·¸Ô

Ê× ÍºÑ¹·Ö¡ (¨Ò¹áÁèàËÅç¡) àÊ¶ÕÂÃÀÒ¾

media (or medium)

stable

àÊé¹â¤é§ÃÙ»µÑÇàÍÊ

S curve

àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè àÊé¹ÊÒ¢Ò

survivor path

branch

Ë¹èÇ§àÇÅÒ

delay

Ë¹èÇÂ¤ÇÒÁ¨Ó¢Í§ªèÍ§ÊÑÒ³ Ë¹èÇÂ¤ÇÒÁ¨ÓàÊé¹·Ò§

path memory

orthogonality principle

write head

ËÑÇà¢ÕÂ¹ ËÑÇÍèÒ¹

channel memory

read head

àËµØ¡ÒÃ³ì

event

àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´

error event

àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´·Õ â´´à´è¹ áËÅè§µé¹·Ò§

dominant error event

source

áËÅè§»ÅÒÂ·Ò§

destination

ÍÍ¿à«µ·Ò§¤ÇÒÁ¶Õ

frequency o set

ÍÍ¿à«µ·Ò§à¿Ê

phase o set

timing o set gain

ÍÑµÃÒ¡ÒÃªÑ¡µÑÇÍÂèÒ§

sampling rate

ÍÑµÃÒ¡ÒÃªÑ¡µÑÇÍÂèÒ§áººà¡Ô¹¨ÃÔ§ ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ

oversampling rate

convergence rate

ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´ºÔµ

BER (bit error rate)

sampling phase o set

bit rate

asymptotic information rate

density ratio

read back signal

189

ÍÑµÃÒÃËÑÊ

code rate

ÍÑµÃÒÊè§¢éÍÁÙÅ

data rate

auto correlation

ÍÑÅ¡ÍÃÔ·ÖÁ (¢Ñ ¹µÍ¹ÇÔ¸Õ) ÍÑÅ¡ÍÃÔ·ÖÁÇÕà·ÍÃìºÔ

algorithm

Viterbi algorithm inductive

ÍÔ¹´Ñ¡·Õ¿ (»ÃÐàÀ·¢Í§ËÑÇÍèÒ¹) ÍÔ¹¾Øµ (ÃÑºà¢éÒ, ¹Óà¢éÒ) ÍÔ ÁµÑÇ

input

saturated

ÍÕ¤ÇÍäÅà«ªÑ¹áººÊÁºÙÃ³ì ÍÕ¤ÇÍäÅà«ÍÃì

perfect equalization

equalizer

ÍÕ¤ÇÍäÅà«ÍÃìáºº PR

partial response (PR) equalizer

àÎÔÃµ«ì

output channel output

analog

ÎÒÃì´´ÔÊ¡ìä´Ã¿ì

hard disk drive

Hz (hertz)

full response equalizer

SNR (signal to noise

190

ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅç¡·ÃÍ¹Ô¡ÊìààÅÐ¤ÍÁ¾ÔÇàµÍÃìààËè§ªÒµÔ

ºÃÃ³Ò¹Ø¡ÃÁ

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áºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ, 53

¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ, 116, 138,

ÍèÒ¹, 5 8 à¢ÕÂ¹, 5 ¡ÃÐáÊä¿¿ Òà¢ÕÂ¹, 4, 5, 152 ¡ÒÃ¡Å ÓÃËÑÊ¾ÑÅÊì (PCM), 2 ¡ÒÃªÑ¡µÑÇÍÂèÒ§, 11, 18, 21, 36 ¡ÒÃºÇ¡ ¡ÒÃà»ÃÕÂºà·ÕÂº ¡ÒÃàÅ×Í¡, 122 ¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡, 1 áºº¨ÓÅÍ§ªèÍ§ÊÑÒ³, 9 ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §, 3, 44, 54, 96, 103, 147

áººâÁ¹Ô¡ (h0

¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹, 3, 96, 129, 147

áººÊÁºÙÃ³ì, 55, 104, 130, 147 ¡ÒÃà´Ô¹áººÊØèÁ, 20 ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð, 4, 11, 33, 76, 139, 152 ·Õ ´Õ·Õ ÊØ´, 77 ¼ÅµÍºÊ¹Í§, 6, 45 ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡, 5 àÁ·ÃÔ¡«ì, 158 àÍ¡à·È, 6, 55, 104, 130 ¡ÒÃàÅ× Í¹µÓáË¹è§¢Í§¡ÒÃà»ÅÕ Â¹Ê¶Ò¹ÐáººÊØèÁ, 55, 139 ¡ÒÃá·Ã¡ÊÍ´ÃÐËÇèÒ§ÊÑÅÑ¡É³ì (ISI), 6, 65,

ÊÑÒ³¾ÑÅÊìà»ÅÕ Â¹Ê¶Ò¹Ð, 6 àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´, 97

= 1),

¡ÒÃà¢éÒ¨Ñ§ËÇÐ, 18, 22, 34, 67

·ÒÃìà¡çµáºº PR, 13, 44 ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ , 8

¡ÃÐºÇ¹¡ÒÃ

141

h1 = 1,

69, 152 ¡ÒÃá»Å§

24, 28

¡ÒÃá»Å§¿ÙàÃÕÂÃì·Õ µèÍà¹× Í§·Ò§àÇÅÒ, 8

·ÒÃìà¡çµáºº PR, 12, 44 ¼ÅµÍºÊ¹Í§àªÔ§¤ÇÒÁ¶Õ , 8

¢Õ´¨Ó¡Ñ´«Ùà»ÍÃì¾ÒÃÒáÁ¡à¹µÔ¡, 3

¢éÍ¼Ô´¾ÅÒ´

¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹, 44

¡ÓÅÑ§ÊÍ§à©ÅÕ Â (MSE), 47, 119 ºÔµà«ÅÅì, 6, 24, 55, 103, 147 ¡ÓÅÑ§ÊÍ§à©ÅÕ Â·Õ ¹éÍÂÊØ´ (MMSE), 47, 120 ¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ, 47 54 ·Ò§àÇÅÒ, 21, 24, 30, 38 áººÃÒ¡¡ÓÅÑ§ÊÍ§à©ÅÕ Â (RMS), 34

¼ÅµÍºÊ¹Í§, 116 ¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð, 6, 45 ¢Ñ ¹ºÑ¹ä´, 25 ¢éÍ¼Ô´¾ÅÒ´, 26

¤ÇÃ¨Ðà» ¹ÁÒ¡ÊØ´ (ML), 44 ¤ÇÒÁ¶Õ áºº¹ÍÃìÁÍÅäÅ«ì, 8 ¤ÇÒÁ¶Õ ä¹¤ÇÔµÊì, 44

·ÒÃìà¡çµ, 12, 45, 68, 138 ºÒ§ÊèÇ¹ (PR), 12, 43, 68 ÍÔÁ¾ÑÅÊì, 20, 30, 148

¤ÇÒÁË¹Òá¹è¹

ÍÔÁ¾ÑÅÊì¨Ó¡Ñ´ (FIR), 67, 117, 138

¡ÒÃºÃÃ¨Ø, 155

ÍÔÁ¾ÑÅÊìäÁè¨Ó¡Ñ´ (IIR), 117

¢Í§¡ÒÃºÑ¹·Ö¡¢éÍÁÙÅ, 6 ¢Í§¡ÒÃºÑ¹·Ö¡áºº¹ÍÃìÁÍÅäÅ«ì (ND), 6 Êà»¡µÃÑÁ¡ÓÅÑ§, 20, 55, 103, 130, 147

ªèÍ§ÊÑÒ³ÍèÒ¹, 4

àªÔ§¤ÇÒÁ¶Õ , 8, 43 àµçÁ, 67 ä´ºÔµ, 8, 45

¿ §¡ìªÑ¹ ¢Ñ ¹ºÑ¹ä´, 23

·ÒÃìà¡çµ, 53

¢éÍ¼Ô´¾ÅÒ´, 6

·Õ àËÁÒÐ·Õ ÊØ´, 47 »ÃÐÊÔ·¸Ô¼Å, 122

¤ÇÒÁË¹Òá¹è¹¤ÇÒÁ¹èÒ¨Ðà» ¹áººà¡ÒÊìà«ÕÂ¹, 55, 78, 103, 139, 147

áºº GPR, 13, 45 áºº

h1 = 1,

«Ô§¡ì, 20 ¶èÒÂâÍ¹, 13, 24, 46, 117, 138

áºº·ÒÃìà¡çµà©¾ÒÐ, 53 àÅ¢ªÕ ¡ÓÅÑ§, 8 áºº¾ÅÑ§§Ò¹Ë¹Ö §Ë¹èÇÂ, 53 â¤Ãà¹¤à¡ÍÃìà´ÅµÒ, 81 áººâÁ¹Ô¡, 49, 104, 133, 148 áºº PR, 12 ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §, 44

ÀÒÇÐ, 22 ¡ÒÃµÔ´µÒÁ, 22

ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅ, 3

¡ÒÃä´éÁÒ, 22 ¡ÒÃä´éÁÒáººÊÁºÙÃ³ì, 34

áºº¨ÓÅÍ§, 4 ÃÐººÊ× ÍÊÒÃ´Ô¨Ô·ÑÅ, 17

ÃËÑÊ

(0, G/I),

166 167

ÃÙ»áºº NRZI, 4, 151

ÃËÑÊ RLL, 3, 91, 151 167 ÅÓ´Ñº¢éÍ¼Ô´¾ÅÒ´, 93

ISI, 152 ¡ÒÃÍÍ¡áºº, 162 164 ¤ÇÒÁË¹Òá¹è¹¡ÒÃºÃÃ¨Ø, 155 ¤ÇÒÁ¨Ø, 154 155 µÒÃÒ§¤é¹ËÒ, 152, 164

ÍÔ¹¾Øµ·Õ ¶Ù¡µéÍ§, 94

Ç§¨Ã VCO, 18 Ç§¨Ã¡ÃÍ§ ¢éÍ¼Ô´¾ÅÒ´¡ÒÃ·Ó¹ÒÂ, 118

ºÔµÊèÇ¹à¡Ô¹, 153

·Ó¹ÒÂ, 117

¾ÒÃÒÁÔàµÍÃì, 151

·Ó¹ÒÂË¹Ö §¢Ñ ¹áººàªÔ§àÊé¹, 118

ÃËÑÊ

(0, G/I),

166

ÃËÑÊ FM, 164 ÃËÑÊ MFM, 164

¼èÒ¹µ Ó, 4 ¤ÇÒÁ¶Õ µÑ´, 20 ÅÙ», 18

ÃËÑÊ Miller, 164

Ç§¨ÃªÑ¡µÑÇÍÂèÒ§, 4, 18

ÍÑµÃÒ¢èÒÇÊÒÃàªÔ§àÊé¹¡Ó¡Ñº, 155, 160

Ç§¨ÃµÃÇ¨ËÒ, 4

ÍÑµÃÒ¤ÇÒÁË¹Òá¹è¹, 155 156

¢Õ´àÃÔ Áà»ÅÕ Â¹

ÍÑµÃÒÃËÑÊ, 152

·Õ äÁèÁÕË¹èÇÂ¤ÇÒÁ¨Ó, 31

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, 156 158

·Õ äÁèÁÕË¹èÇÂ¤ÇÒÁ¨ÓáººËÅÒÂÃÐ´Ñº, 34

à§× Í¹ä¢ºÑ§¤Ñº

áººËÅÒÂÃÐ´Ñº, 21

¨Ó¹Ç¹ÅÓ´Ñº¢éÍÁÙÅ, 153 154 àÁ·ÃÔ¡«ì¡ÒÃà»ÅÕ Â¹Ê¶Ò¹Ð, 158 159 ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÐÃÕ, 152

áººÍèÍ¹, 38 áººá¢ç§, 38 ¢éÍ¼Ô´¾ÅÒ´·Ò§àÇÅÒ, 18

ÃËÑÊ RS, 3

·Õ àËÁÒÐ·Õ ÊØ´, 69

ÃËÑÊ¤Í¹âÇÅÙªÑ¹, 69

ÅÓ´Ñº·Õ ¤ÇÃ¨Ðà» ¹ÁÒ¡ÊØ´ (MLSD), 77

ÃËÑÊÁÍ´ÙàÅªÑ¹, 151

ÅÓ´ÑºàËÁÒÐ·Õ ÊØ´, 137

ÇÕà·ÍÃìºÔ, 12, 21, 69, 115 ¤ÇÒÁ«Ñº«éÍ¹, 80

¡ÒÃºÑ¹·Ö¡áººá¹Ç¹Í¹, 6 àÍ¡à·È, 55, 104, 130

¤ÇÒÁÅÖ¡¡ÒÃ¶Í´ÃËÑÊ, 80

ä´ºÔµ, 8

¤ÇÒÁ¹èÒ¨Ðà» ¹¢Í§¢éÍ¼Ô´¾ÅÒ´ÅÓ´Ñº, 88

ä¹¤ÇÔµÊì, 20

»ÃÐÊÔ·¸ÔÀÒ¾, 87

ä¹¤ÇÔµÊìÍØ´Á¤µÔ, 12

Ç§¨ÃµÃÇ¨ËÒÅÓ´Ñº, 69

ÊÑÒ³Ãº¡Ç¹, 11, 20, 21, 45, 68, 93

ÍÑÅ¡ÍÃÔ·ÖÁ, 69, 75 80

¡ÒÃ¢ÂÒÂ, 45, 66

à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, 70 72

¡ÒÃ¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ, 138 140

á¼¹ÀÒ¾à·ÃÅÅÔÊ, 70, 72 75

¡ÒÃ·Ó¹ÒÂ, 117, 141

ÊÑÅÑ¡É³ì, 21

¨ÔµàµÍÃì¢Í§Ê× ÍºÑ¹·Ö¡, 55, 61, 103, 107, 138, 139

Ç§¨Ã¶Í´ÃËÑÊ ÁÍ´ÙàÅªÑ¹, 4

·Õ ¢Ö ¹ÍÂÙè¡Ñºáºº¢éÍÁÙÅ, 138

á¡éä¢¢éÍ¼Ô´¾ÅÒ´, 4

·Õ ÍÂÙè¹Í¡á¶º¤ÇÒÁ¶Õ , 11, 20

Ç§¨ÃÁÍ´ÙàÅàµÍÃì, 4, 5

ÀÒÂã¹Ç§¨ÃªÑ¡µÑÇÍÂèÒ§, 18

Ç§¨Ãà¢éÒÃËÑÊ

ÊÕ¢ÒÇ, 60, 119

¡èÍ¹, 91 ÁÍ´ÙàÅªÑ¹, 3

à¡ÒÊìÊÕ¢ÒÇ, 69 à¡ÒÊìÊÕ ¢ÒÇáºººÇ¡, 20, 55, 66, 75, 99, 103, 115, 138

á¡éä¢¢éÍ¼Ô´¾ÅÒ´, 3

áººÊÕ, 93, 99, 116, 138 Ê¶Ò» µÂ¡ÃÃÁªèÍ§ÊÑÒ³ÍèÒ¹, 11

Êà»¡µÃÑÁ¤èÒÈÙ¹Âì, 8, 44, 68

ÊÀÒ¾¤ÇÒÁà» ¹áÁèàËÅç¡, 1, 139, 152 ÊÀÒ¾ÅºÅéÒ§áÁèàËÅç¡, 2, 5 ÊÀÒ¾ãËé«ÖÁ¼èÒ¹ä´é, 3

ÍÍ¿à«µ

ÊÁ¡ÒÃ¹ÍÃìÁÍÅ, 119

·Ò§¤ÇÒÁ¶Õ , 22, 35

ÊÑÒ³¾ÑÅÊì

·Ò§à¿Ê, 21, 22, 33

à»ÅÕ Â¹Ê¶Ò¹Ð, 6, 55, 103, 130, 147 ¡ÒÃºÑ¹·Ö¡áººá¹ÇµÑ §, 6

ÊÁ¡ÒÃ»ÃÑº¤èÒ, 24, 28 ·Ò§àÇÅÒ, 20, 33

ÍÑµÃÒ¡ÒÃªÑ¡µÑÇÍÂèÒ§, 37 áººà¡Ô¹¨ÃÔ§, 37

¨Ø´àÊ¶ÕÂÃÀÒ¾, 32 àËµØ¡ÒÃ³ì¢éÍ¼Ô´¾ÅÒ´, 91

ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ, 22 25, 28, 38

¡ÒÃÇÔà¤ÃÒÐËì, 91 111

ÍÑµÃÒ¢éÍ¼Ô´¾ÅÒ´ºÔµ (BER), 47

¡ÒÃÇÔà¤ÃÒÐËìÃÐÂÐ·Ò§·Õ ¹éÍÂÊØ´, 104 107

ÍÑµÃÒÃËÑÊ, 69, 152, 154, 156

¤ÇÒÁÊÑÁ¾Ñ¹¸ì ÃÐËÇèÒ§

ÍÑµÊËÊÑÁ¾Ñ¹¸ì, 49, 60, 100, 119, 142 ÍÑÅ¡ÍÃÔ·ÖÁ

SNReff

áÅÐ BER,

107 109 ¤ÇÒÁËÁÒÂ, 93

PDNP, 140 144

¹ÔÂÒÁ, 95

PS PDNP, 144 146

ÃËÑÊ RLL, 91

ÇÕà·ÍÃìºÔ, 69 80, 122

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å, 99 103

áºº»ÃÑºµÑÇ, 143

ÃÐÂÐ·Ò§»ÃÐÊÔ·¸Ô¼Å¡ÓÅÑ§ÊÍ§, 101

ÍÕ¤ÇÍäÅà«ÍÃì, 4, 12, 47, 53, 66, 104

·Õ ¹éÍÂÊØ´, 101

ÍÑµÃÒ¡ÒÃÅÙèà¢éÒ, 67

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´, 97 99

áºº zero forcing, 138

ÃÐÂÐ·Ò§ÂØ¤ÅÔ´¡ÓÅÑ§ÊÍ§, 97

áºº¼ÅµÍºÊ¹Í§ºÒ§ÊèÇ¹ (PR), 43, 68, 115

·Õ ¹éÍÂÊØ´, 99 Ç§¨Ãà¢éÒÃËÑÊ¡èÍ¹, 91

áºº¼ÅµÍºÊ¹Í§àµçÁ, 67 áº¹´ìÇÔ´·ì à¤Ã× Í§Ê¶Ò¹Ð¨Ó¡Ñ´, 70, 71 ÃËÑÊ RLL, 156 Ç§¨ÃµÃÇ¨ËÒÇÕà·ÍÃìºÔ, 71 à·¤¹Ô¤¡ÒÃ»ÃÐÁÒ³¤èÒã¹ªèÇ§, 37 à¾Íà«ÍÃìäÇàÇÍÃìä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ, 38 áºº·Ó§Ò¹« Ó, 40

¢Í§ÅÙ», 22, 28 à¡Ô¹à» ¹ÈÙ¹Âì, 20 áºº¢éÍÁÙÅ, 138 áºº¨ÓÅÍ§ ¡ÒÃ·ÓãËéÊÑÒ³Ãº¡Ç¹à» ¹ÊÕ¢ÒÇ, 117 ¡ÒÃ·Ó§Ò¹¢Í§Ç§¨Ã PLL, 23

àÊé¹·Ò§·Õ ÂÑ§ÁÕªÕÇÔµÍÂÙè, 80, 92

¡ÒÃÍÍ¡áºº·ÒÃìà¡çµ, 47

àÊé¹â¤é§ÃÙ»µÑÇàÍÊ, 21, 30 34

ªèÍ§ÊÑÒ³

¨Ø´ÊÁ´ØÅ, 33

GPR áººÊÁÁÙÅ, 93

¡ÒÃºÑ¹·Ö¡ÃÐººáÁèàËÅç¡, 9 ·Õ äÁèµèÍà¹× Í§·Ò§àÇÅÒáººÊÁÁÙÅ, 66 ÍØ´Á¤µÔ, 12 13, 19 àÊÁ×Í¹¨ÃÔ§, 11 12 ÃÐºº¡ÒÃ¨Ñ´à¡çº¢éÍÁÙÅ´Ô¨Ô·ÑÅ, 3 á¼¹ÀÒ¾à·ÃÅÅÔÊ, 70, 72, 91, 115, 141

ä«à¤ÔÅÊÅÔ», 33 ä·ÁÁÔ §¨ÔµàµÍÃì, 18, 20, 39 ä·ÁÁÔ §¿ §¡ìªÑ¹, 30 áºº¹ÍÃìÁÍÅäÅ«ì, 32 ä·ÁÁÔ §ÃÔ¤Ñ¿àÇÍÃÕ, 12, 17 41 ¡ÒÃÍÍ¡áºº¤èÒ¾ÒÃÒÁÔàµÍÃì, 23 34 ÀÒÇÐ¡ÒÃµÔ´µÒÁ, 22 ÀÒÇÐ¡ÒÃä´éÁÒ, 22 áºº´Ô¨Ô·ÑÅ, 37 áºº·Õ ãªé¡Ñ¹·Ñ Çä», 18 23 »ÃÐÊÔ·¸ÔÀÒ¾, 34 37 áºº¹ÔÃ¹ÑÂ, 18 áºº»ÃÐÁÒ³¤èÒã¹ªèÇ§, 37 áººÍØ»¹ÑÂ, 18