Acct 14 ig 56

IJEEE, Vol. 1, Spl. Issue 1 (March 2014)

e-ISSN: 1694-2310 | p-ISSN: 1694-2426

Capsulization of Existing Space Time Techniques 1

Maninder singh, 2Dr.Hardeep singh Saini

Indo Global College of Engineering, Punjab, India 1

md_singh1989@yahoo.com, 2hardeep_saini17@yahoo.co.in

Abstract— In this paper, we explore the fundamental concepts behind the emerging field of space-time coding for wireless communication system. A space–time code (STC) is a method which employed to increase the reliability of data transmission in the wireless communication systems using multiple transmit antennas. Space–time code (STC) depends on transmitting multiple, redundant copies of a data stream to the receiver in the hope that at least some of them may live the physical path between transmission and reception section with reliable decoding.

used widely and division algebras over for making or constructing codes[6,5],fig1.1 Space time code diagram.[7]

Keywords— STC; STTC; BLAST; 1. INTRODUCTION With the increase in demand of increasingly sophisticated communication services available any-time, anywhere, wireless communications has emerged as one of the largest and most rapid and steadfastness sectors of the global telecommunications industry. A quick look at the status quo reveals that second and third generation cellular systems supporting data rates of 9.6 Kbps to 2 Mbps uses by a 700 million people around the world subscribe to existing. More recently, in wireless LAN networks IEEE 802.11, which provided 11 Mbps rate and attracted more than $1.6 billion (USD) in equipment sales [1]. The capabilities of both of these technologies over the next ten years, are expected to move toward the 100 Mbps – 1 Gbps range [2] and subscriber numbers to over 2 billion [3]. One of the most significant technological developments of the last decade, that promises to play a key role in realizing this tremendous growth, is wireless communication using MIMO antenna architectures.

A space time code (STC) which is used in the wireless communication to improve the reliability of data transmission. Space Time Code depends on transmitting multiple, redundant copies of a data beam to the receiver.

The receiver which in the hope that at least one of them may live the physical path between both transmission and reception section. Space time code may be further divided according to coherent STC and non coherent STC. When the receiver section the channel impairment through training called coherent STC[4] and in the non coherent is totally opposite to the coherent STC .Coherent STC basically is

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Fig 1.1Space time code diagram [7] Space time techniques divide into two main parts (see in the fig) -: 1) Transmit diversity 2) Spatial multiplexing

Fig 1.2 Classification of space time technique [3] 2.SPACE TIME TECHNIQUES 2.1Transmit diversity 2.1.1 Space time block codes –: The term Space-Time Code (STC) originally got into existence in 1998 by Tarokh et al. to describe a new two-

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dimensional way of encoding and decoding signals transmitted over wireless fading channels using multiple transmit antennas.

In this technique, data stream of a multiple copies are transmits across the number of antennas (MIMO) and this technique improves the reliability of data transfer. Also, the transmitted signal must transverse a potentially difficult environment with scattering, reflection, refraction and then it effects by thermal noise which effects the information or data in the receiver section. So, space- time coding basically add all the copies of the received signal, so in this way it can easily get the information.

It is divided into three sections. First one is flat quasi-static fading channel is used in communication system operating under narrow band conditions, second is frequency selective fading channel which is used in wideband communication system[8].

Fig2.1: Transmit 2 Receive Alamouti STBC The Alamouti space-time block coding is a simple MIMO technique which can be used to reduce the BER of a system with a specific SNR and without any loss on the data rate/information. The presented decoding technique is called hard decision-based zero forcing and it is easily to implement in hardware slot. [9]

2.1.1.1 Flat quasi-static channel-: This is further divided into the first one is the Alamouti code and second is extended version of Alamouti work on which accommodates large number of transmit antennas, proposed

by Tarokh et al under the name of orthogonal designs. Lately is linear depression code of Hassibi et al, which address the capacity limitation of both of these codes and also support arbitrary number of transmit antenna.

(b)STBC based orthogonal design-: It is basically advanced version of Almouti`s work. It removes the capacity limitations. It also provides full diversity gain. Example: the code N=U, transmit antenna is given by

(a)Almouti Block Code-: It is introduced to improve link-level performance based on diversity. It is proposed a simple scheme for a 2*2 matrix system that achieves a full diversity gain with a simple maximum likelihood decoding algorithm. It is designed from the view of diversity gain to increased the multiple antenna transmission scheme in order to achieve the good performance. Let in the case where these two transmit antenna by arranging the input symbols (�1 ,�2 ) and input their complex conjugates in a special 2*2 matrix. �=

đ?‘Ľ1 đ?‘Ľ2

�1 � � = �2 3 �4

−đ?‘Ľ2 đ?‘Ľ1 −đ?‘Ľ4 đ?‘Ľ3

−đ?‘Ľ3 −đ?‘Ľ4 đ?‘Ľ4 −đ?‘Ľ3 đ?‘Ľ2 đ?‘Ľ2 −đ?‘Ľ2 đ?‘Ľ1

We seen that each column of S differ from the first by permutation reflection. Next, we consider a generalized real orthogonal design, for N=3 transmit antenna. �1 � = �2 �3

−đ?‘Ľ2∗ đ?‘Ľ1∗

Each column of � contains the symbols transmitted from the pair of antennas during a particular symbol period. We see that second column is a permutation and a reflection of the complex conjugate of the first. Then � over flat fading channel, written as: where P is the appropriate permutation reflection matrix.

−đ?‘Ľ2 đ?‘Ľ1 −đ?‘Ľ4

−đ?‘Ľ3 −đ?‘Ľ4 đ?‘Ľ4 −đ?‘Ľ3 đ?‘Ľ1 đ?‘Ľ2

It views like a counter intuitive at first complex orthogonal design only exist for N=2 , namely the Almounti`s STBC .

Therefore generalized complex orthogonal design is derived and various codes are constructed. So, generalized design for N=4 is given by �1 �2 � = �3 �4

ℎ−đ?‘‡ đ?‘† = [ℎ−đ?‘‡ x ℎ−đ?‘‡ Pđ?‘Ľ ∗ ] [(ℎ−đ?‘‡ đ?‘†)1 (ℎ−đ?‘‡ đ?‘†)∗2 ] = ℎ−đ?‘‡ (ℎ−đ?‘‡ P)∗ ]x The principle of space time block coding with 2 transmit antenna and one receive antenna is explained in the post on Alamouti STBC. With two receive antenna’s the system can be modeled as shown in the figure below (fig2.1).

−đ?‘Ľ2 đ?‘Ľ1 −đ?‘Ľ4 đ?‘Ľ3

−đ?‘Ľ3 −đ?‘Ľ4 đ?‘Ľ1∗ −đ?‘Ľ2∗ −đ?‘Ľ3∗ −đ?‘Ľ4∗ đ?‘Ľ4 −đ?‘Ľ3 đ?‘Ľ2∗ đ?‘Ľ1∗ đ?‘Ľ4∗ −đ?‘Ľ3∗ đ?‘Ľ2 đ?‘Ľ2 đ?‘Ľ3∗ −đ?‘Ľ4∗ −đ?‘Ľ2∗ đ?‘Ľ2∗ đ?‘Ľ1∗ −đ?‘Ľ2 đ?‘Ľ1 đ?‘Ľ4∗ đ?‘Ľ3∗ −đ?‘Ľ2∗

L=8 symbol periods are required to transmit Q=4 symbols, resulting in a significantly reduced rate but increased the capacity offered by competitive MIMO scheme such as BLAST [10,11]. STBC based on amicable designs, which provide higher rates than those based orthogonal design for some numbers of transmit and receive antennas [12] and quasi-orthogonal STBC, which sacrifice diversity to achieve rate 1 for some condition with more than two transmit antennas.[13] (c)Linear dispersion code-:

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This is used to realize rates higher than 1 sym\s\hz\ using STBC transmission, Hassibi et.al. Study the effective capacity of code based on orthogonal design. It basically develops a new class of block code designed to maximize the mutual information between the transmitted and received signals. The resulting designs are called linear dispersion codes. Codes for using a set of 2Q dispersion matrices �=

đ?‘„ đ?‘ž=1 (đ?‘Ľđ?‘…đ?‘ž

đ??´1 =

1 0 1 0 0 −1 0 1 , đ??ľ1 = , đ??´2 = , đ??ľ2 = 0 1 0 −1 1 0 1 0

đ??ż , data columns where complex conjugation is applied in the underlying code are transmitted in time-reversed order, hence the name given to the code. The accompanying guard blocks are also conjugated and time-reversed. The transmitted signal matrix has the following general structure:

đ??´đ?‘ž + jđ?‘Ľđ??źđ?‘ž đ??ľđ?‘ž ) (1) Where R stand for real part of complex valued structure and it is imaginary part. For instance if Q=2 and

then the linear combination of (1) gives �=

đ?‘Ľđ?‘…1 đ?‘Ľđ?‘…2

+ đ?‘—đ?‘Ľđ??ź1 + đ?‘—đ?‘Ľđ??ź2 =

đ?‘Ľ1 đ?‘Ľ2

−đ?‘Ľđ?‘…2 −đ?‘Ľđ?‘…1

+ đ?‘—đ?‘Ľđ??ź2 − đ?‘—đ?‘Ľđ??ź1

−đ?‘Ľ2∗ đ?‘Ľ1∗

The limitation of LDC is that good designs are not known to follow systematic or algebraic rules.[14] 2.1.1.2 Frequency Selective Fading Channel: It is used in STBC for transmission over frequency selective or multipath fading channel. In this there are two main parts, in the first class are those techniques for single-carrier modulation techniques systems that focus on reducing equalization complexity and this techniques known as time – reversal approach by LindsKog et al. that takes benefit of space- time code structure to decrease the dimensionality of the equalization step.

The second classes of techniques are built around block processing operations that effectively convert the frequency selective channel into a set of flat fading sub-channels. These may employ OFDM with multi-carrier modulation or Frequency Domain Equalization with single-carrier modulation. (a)Time Reversal (TR) STBC-: This technique is used for single-carrier modulation system which focuses on reducing equalization complexity. The proposal in this area is a time-reversal approach by Zindskog.et.al that takes advantage of the space time code structure to decrease the dimension of the equalization step.

It is flat fading channel based on orthogonal design. They are designed for use with single-carrier modulation in which it simplifying the equalization by decoupling the problem from LN dimension to N L-dimensional tasks which may be executed in parallel. The TR-STRC involves protecting data symbol columns by enclosing each of them between guard columns of known symbols.

They will refer to these guard blocks as the prefix and suffix, both must be of length at least K - 1, and denote by the net length of the protected data block. It is clear that there is some rate loss associated with the guard blocks, which can be reduced by increasing the size of the data block.

However, the maximum size of the data blocks is also limited by the coherence time of the channel 2 In addition www.ijeee-apm.com

It have seen that channel be slowly fading so that đ??ż = đ??ż0 [đ??ż + 2(K-1)] symbol periods, whereas before đ??ż denotes the gross block length including guard symbols and đ??ż0 is the block length of the underlying STBC design for flat fading.

The main limitation of the TR-STBC is its limited rate compared to the potential multiplexing gain available in the MIMO channel. [15,16] (b)STBC with frequency domain processing-: A number of researchers have also considered extensions of the Alamouti scheme to systems using frequency domain processing. One of the first proposals for combining STBC with OFDM and multi-carrier modulation was put forward

by Mudulodu et al. Subsequently, two works based on single-carrier transmission systems with frequency domain processing at the receiver were presented by Al-Dhahir and Zhou et al. All three approaches share substantially similar signal matrix structures and thus we will follow [17] here.

In this work STBC over frequency selective fading channels is proposed in combination with FDE. As we shall see, it exhibits a structure that bears some resemblance to timereversal, and thus shares many properties of the TR-STBC. The transmitted signal matrix is of the form

We note that the rate achieved by this transmission scheme is fractionally higher than that of the TR-STBC because it does not require a guard suffix block. [19, 18] 2.1.2 Space time trellis codes (STTC)-: It is used in the multiple antenna wireless communication. It International Journal of Electrical & Electronics Engineering

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transmits multiple redundant copies of a convolutional code or trellis code distributed over time and with a number of antennas (MIMO). Then receivers use these multiple, 'diverse' copies of the data to reconstruct the actual transmitted data. In space time block code, they are able to provide both coding gain and a better bit error rate performance. But in space time trellis code they are more complex than STBCs to encode and decode. They depend on a viterbi decoder at the receiver where STBCs need only linear processing. STTC were proposed by Vahid Tarokh et al. in 1998. Just as trellis codes impose structure within each code word (cover the code space) and also between code words transmitted in sequence (over time) the diversity gain of STTCs is determined via a PEP argument. The PEP expresses the probability of transmitting đ?‘†đ?‘? and deciding in favour of đ?‘†đ?œ€ at the decoder. Defining the code word difference matrix B = đ?‘†đ?‘? − đ?‘†đ?œ€ with SVD B = U đ?‘‰ + and r = rank B

6. Loses capacity with two or more receive antennas.

2.2 Spatial multiplexing –: In view of the narrowband nature of the transmission, each data stream follows only one route to the receiver and there are no multipath experienced by the individual data streams.

In SM system, the maximum number of modulation symbols that can be transmitted per symbol, maximum (đ?‘&#x;đ?‘ ) is given by max(đ?‘&#x;đ?‘ )) =đ?‘ đ?‘Ą which implies that the maximum spectral efficiency of an SM system given by đ?œ‚đ?‘šđ?‘Žđ?‘Ľ =đ?‘ đ?‘Ą đ?‘&#x;đ?‘Ą đ?‘™đ?‘œđ?‘”2 (M)bps/Hz Where đ?‘&#x;đ?‘Ą s the rate of any conventional coding used in the spatial multiplexing system and M is the modulation order.In general, spatial multiplexing is achieved using a concept called layered space-time (LST) coding.[21]

đ?‘?

đ?&#x2018;&#x20AC; P(đ?&#x2018;&#x2020;đ?&#x2018;? â&#x2020;&#x2019; đ?&#x2018;&#x2020;đ?&#x153;&#x20AC; ) < đ?&#x153;&#x2039;đ?&#x2018;&#x2013;=1 đ?&#x153;&#x2039;đ?&#x2018;&#x2014;đ?&#x2018;&#x;=1 (đ?&#x153;&#x17D;đ?&#x2018;&#x2014;2 )â&#x2C6;&#x2019;1 4

đ?&#x2018;?

=(det[đ??ľđ??ľ +])â&#x2C6;&#x2019;đ?&#x2018;&#x20AC; ( )â&#x2C6;&#x2019;đ?&#x2018;&#x20AC;đ?&#x2018;&#x; 4

(2)

2.2.1 Layered space time (LST)-: Spatial multiplexing is achieved by raising a concept of layered space time (LST) coding. Foschini proposed LST architecture. In LST method, SM can also be achieved using Eigen beam forming, it is a practical SM technique that is used in most modern wireless communication system. They are three main approaches are-: Bell Laboratory layered space-time (BLAST) family of techniques-: a) V-Blast (Vertical-Blast) b) H- Blast (Horizontal Blast) c) D-Blast (Diagonal Blast

above equation(2) is coding gain of approximately, 1 đ?&#x203A;ž = [detâ Ą(đ??ľđ??ľ +)]đ?&#x2018;&#x; is achieved.

The type of decoding algorithm that is used is an important consideration for LST coded SM system. Four decoding schemes are-: 1) Zero Forcing (ZF) 2) Zero Forcing with interference cancellation (ZF-IC) 3) Linear minimum mean square error estimation (LMMSE) 4) LMMSE with interference cancellation (LMMSE-IC)

Fig 2.2: Space time trellis codes It has high complexity so this is it main limitation. [20] Comparison between STBC and STTC-: STBC STTC 1. It has no coding gain.

1. It has coding gain.

2. Easily decodable by maximum likelihood decoding via linear processing.

3. STBC is simple to design based on orthogonal sequences.

2.

Conserve capacity irrespective of the number of antennas.

4.For one receive antenna and state code, performance is similar to STTC

4. STTC outperforms with increasing antennas and trellis states.

5. Easily lends itself to industrial applications because of its simplicity.

5. Complex to organize.

(a) VERTICAL BLAST-: In V-Blast the information bit stream is processed by an optional conventional error encoder and then split into đ?&#x2018; đ?&#x2018;&#x; data stream, each of which is separately modulation before being passed to its respective antenna for transmission. The use of the adjective vertical in v-blast is a reference to the fact that the input is split into parallel streams that are depicted vertically in most diagrams encoder employs its own modulator the V-blast architecture is capable of accommodating applications where different data rates are applied to different layers. Layer with higher data rates might use higher order modulation schemes so that each layer would have the same bandwidth (fig 2.2 a).

3. STTC is difficult to design.

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6.Conserve capacity irrespective of the number of antennas.

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Fig2.2 (a) V-Blast encoding architecture [21] Since distinct data stream are applied to each of the đ?&#x2018; đ?&#x2018;Ą layer, during each use of the channel there are đ?&#x2018; đ?&#x2018;Ą different modulation symbols transmitted. Therefore the space-time code rate associated with the V-BLAST encoder is đ?&#x2018;&#x2026;đ?&#x2018; =đ?&#x2018; đ?&#x2018;Ą and the spectral efficiency is đ?&#x2018; đ?&#x2018;Ą đ?&#x2018;&#x2026;đ?&#x2018;Ą (M)bps/HZ; where M is the modulation order. In the case of V-BLAST, Loyka and Gagnon prove that the diversity order varies from (đ?&#x2018; đ?&#x2018;&#x; -đ?&#x2018; đ?&#x2018;Ą +1) up to đ?&#x2018; đ?&#x2018;&#x; , depending on which layer is being decoded. We see that N*N V-BLAST only achieves a maximum diversity gain equal to 1, compared with đ?&#x2018; đ?&#x2018;Ą đ?&#x2018; đ?&#x2018;&#x; for system with full diversity. [22, 23]

basically similar with H-BLAST but only difference is it includes a block after the modulator that performs stream rotation. Let we take a example we assume that đ?&#x2018; đ?&#x2018;Ą =4 and output are divided into blocks consisting of đ?&#x2018; đ?&#x2018;Ą consecutive segments, the output of the four convential encoders are vectors denoted by a, b, c and d and then output of four encoded segments out of convential encoder 1 by đ?&#x2018;&#x17D;1 ,đ?&#x2018;&#x17D;2 ,đ?&#x2018;&#x17D;3 , and đ?&#x2018;&#x17D;4 ,the next set of four encoded segments by a 5 , a 6, a7, anda 8 Rather than simply passing the modulated outputs from each encoder onto its respective antenna, the stream rotator rotates the modulated segments in a roundrobin fashion by performing two operation: a) it distributes consecutive sequences of đ?&#x2018; đ?&#x2018;Ą segments from each encoder onto each of the antenna; b) the order of the encoders that it operated on is chosen in a circularly rotated manner rather than simply sequentially from encoder 1 to đ?&#x2018; đ?&#x2018;Ą .

In D-BLAST, each diagonal layer constitutes a complete code word then decoding is done layer by layer. The advantage of this type of BLAST techniques is that the outputs from each conventional encoder are distributed over space which provides a grater spatial diversity (fig2.2 c).

[26]

(b) HORIZONTAL-BLAST (H-BLAST) The H-BLAST encoding architecture shown in fig 2.2 b , it is basically similar with V-BLAST but only difference is it includes separate conventional error encoder on each of the transmit data stream. In this â&#x20AC;&#x153;horizontalâ&#x20AC;? suggest that the encoder on each layer perform coding in the time domain, which can be pictured as being horizontal in the picture, compared with the space dimension that is depicted being vertical(fig2.2 b).[24]

Fig2.2(c) D-Blast encoding architecture [21, 25]

Fig 2.2(b) H-Blast encoding architecture[21,25] (c) DIAGONAL-BLAST (D-BLAST) The D-BLAST encoding architecture shown in fig 2.2 c, it is www.ijeee-apm.com

2.2.2 THREADED SPACE-TIME ENCODING (TSTE)-: TST proposed by El Gamal et al. It was developed to enable the construction of full rates and full diversity MIMO transmission by combining layering ideas with constituent space time codes. it is based on partitioning the space time signal matrix into non-overlapping threads .In this method mixes the signal more thoroughly across the antennas than does the D-BLAST diagonal system. The last block is a spatial interleave, which interleaves the symbols as shown in fig2.3 in the space time matrix and each shade shows a thread. We have one code word per thread, in the first International Journal of Electrical & Electronics Engineering

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[6] V. Tarokh and H. Jafarkhani (July 2000). "A Differential Detection Scheme for Transmit Diversity". IEEE Journal on Selected Areas in Communications 18 (7): 1169â&#x20AC;&#x201C;1174.

[7] http://en.wikipedia.org/wiki [8] S.M. Alamouti (October 1998). "A simple transmit diversity technique for wireless communications". IEEE Journal on Selected Areas in Communications 16 (8): 1451â&#x20AC;&#x201C;1458.

[9] Siavash M. Alamouti. A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications, 16(8):1451{1458, October1998.

[10] Vahid Tarokh, Hamid Jafarkhani, and A. Robert Calderbank.

Space-time block codes from orthogonal designs. IEEE Transactions on Information Theory, 45(5):1456{1467,July 1999.

[11] Vahid Tarokh, Hamid Jafarkhani, and A. Robert Calderbank.

Space-time block coding for wireless communications: Performance results. IEEE Journal on Selected Areas in Communications, 17(3):451{460, March 1999.

[12]Girish Ganesan and Petre Stoica. Space-time diversity using orthogonal and amicable orthogonal designs. Wireless Personal Communications, 18(2):165{178, August 2001.

[13]Hamid Jafarkhani. A quasi-orthogonal space-time block code.

IEEE Communications Letters, 49(1):1{4, January 2001.

[14] Babak Hassibi and Bertrand Hochwald. High-rate codes that are linear in space and time. IEEE Transactions on Information Theory, 48(7):1804{1824, July 2002.

[15] Erik G. Larsson, Petre Stoica, Erik Lindskog, and Jian Li. Space-time block coding for frequency-selective channels. In IEEE International Conference on Acoustics, Speech and Signal Processing, volume 3, pages 2405{2408, May 2002.

[16] Erik Lindskog and Arogyaswami J. Paulraj. A transmit diversity scheme for channels with intersymbol interference. In IEEE International Conference on Communications volume 1, pages 307{311, June 2000.

[17] Naofal Al-Dhahir. Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels. IEEE Communications Letters, 5(7):304{306, July 2001.

[18] Shengli Zhou and Georgios B. Giannakis. Space-time coding with maximum diversity gains over frequency-selective fading channels. IEEE SIgnal Processing Letters,8(10):269{272, October 2001.

[19] Sriram Mudulodu and Arogyaswami J. Paulraj. A transmit diversity scheme for frequency selective fading channels. In IEEE Global Telecommunications Conference,volume 2, pages 1089{1093, November 2000.

[20] Vahid Tarokh, Nambi Seshadri, and A. Robert Calderbank.

Space-time codes for high data rate wireless communication: Performance criterion and code construction. IEEE Transactions on Information Theory, 44(2):744{765, March 1998.

[21] INTRODUCTION TO MIMO COMMUNICATIONS BY JERRY R. HAMPTON CAMBRIDGE UNIVERSITY PRESS, 28-NOV-2013 [22] Gerard J. Foschini, Glen D. Golden, Reinaldo A. Valenzuela, and Peter W. Wolniansky. Simplifed processing for high spectral efficiency wireless communication employing multi-element arrays.

IEEE Journal on Selected Areas in Communications,17(11):1841{1852, November 1999.

[23] Peter W. Wolniansky, Gerard J. Foschini, Glen D. Golden, and Reinaldo A. Valenzuela.V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel. In International Symposium on Signals, Systems, and Electronics,pages 295{300, September 1998.

[24] Gerard J. Foschini, Dmitry Chizhik, Micahel J. Gans, Constantinos B. Papadias, and Reinaldo A. Valenzuela. Analysis and performance of some basic space-time architectures. IEEE Journal on Selected Areas in Communications, 21(3):303{320, April2003.

[25] SPACE -TIME CODES AND MIMO SYSTEMS BY M OHINDER JANKIRAMAN ARTECH HOUSE, 01-JAN-2004.

[26] Gerard J. Foschini. Layered space-time architecture for wireless communication in a fading environment when using

columns the symbols of each layer are not shifted and in second columns they are shifted once in a cyclic manner. In the third column they are shifted twice and so on. The đ?&#x2018;&#x20AC;đ?&#x2018;Ą *matrix A contains the symbols transmitted over the Mt transmit antennas for l symbol periods. We can describe each layer in general by specifying a set of elements from A. Let L= (đ??ż1 , đ??ż2 ,.. đ??żđ?&#x2018;&#x161;đ?&#x2018;Ą ) be set of indices specifying the elements of A. Mathematically LI is defined as[27,28] đ??żđ?&#x2018;&#x2013; = { ([t+i-1]đ?&#x2018;&#x20AC;đ?&#x2018;&#x2021; + 1,l): 0â&#x2030;¤ đ?&#x2018;Ą â&#x2030;¤ đ?&#x2018;&#x2122;}

Fig2.3Threaded Space-Time encoding architecture [21, 25]

3. CONCLUSION We have study the various types of the space-time codes techniques in which every techniques it own advantages and limitation like generally, in the interest of coding gain, we prefer to use trellis codes instead of block codes within the space-time architecture, trellis codes provides higher coding gain but come at the cost of increased decoding complexity.

We have also study that TLST codes yielded the maximum transmit diversity. The V-BLAST which has gained a lot of popularity because of its simplicity.

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[2] Ari Hottinen, Olav Tirkkonen, and Risto Wichman. Multiantenna transceiver techniques for 3G and beyond. John Wiley & Sons, 2003.

[3] Theodore S. Rappaport, A. Annamalai, R. M. Buehrer, and William H. Tranter. Wireless communications: Past events and a future perspective.

IEEE Communications Magazine, 40(5):148{161, May 2002.

[4] B.A. Sethuraman, B. Sundar Rajan, and V. Shashidhar (October 2003). "Full-diversity, high-rate space-time block codes from division algebras". IEEE Transactions on Information Theory 49 (10) [5]Marzetta, T.L. and Hochwald, B.M. (January 1999). "Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading". IEEE Transactions of Information Theory 45 (1): 139â&#x20AC;&#x201C;157.

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multiple antennas. Bell Labs Technical Journal,1(2):41{59, September 1996.

[27] Hesham El Gamal and Jr. A. Roger Hammons. A new approach to layered space-time coding and signal processing. IEEE Transactions on Information Theory, 47(6):2321{2334, September 2001.

[28] Hesham El Gamal and Mohamed Oussama Damen. Universal space-time coding. IEEE Transactions on Information Theory, 49(5):1097{1119, May 2003.

AUTHORS Maninder Singh is following M.Tech from Indo Global College of Engineering, India. He has completed B.Tech from IGCE, Mohali (Punjab), India in the year 2011. He has two year of educational expertise.

Working as Assistant Professor (ECE) at indo global college of Engineering, Abhipur (Mohali) since June-2012.His areas of interest are wireless and mobile communication, Optical communication.

Communication Engineering in 2012. He holds Masterâ&#x20AC;&#x2122;s degree in Electronic and communication from Punjab technical university, jalandhar passed in 2007. His total experience is 15 year, presently, working as Professor (ECE) and Associate Dean Academic at Indo Global college of Engineering, Abhipur (Mohali), PUNJAB (INDIA) since June-2007. He is author of 5 books in the field of communication Engineering. He has presented 21 papers in international /national conferences and published 30 papers in international journals. He is a fellow and senior member of various prestigious societies like IETE (India), IEEE, UACEE, IACSIT and he is also editorial member of various international journals.

Hardeep Singh Saini obtained his Doctorate degree in Electronics and

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