134 by International Journal

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in

Two Dimensional Optical CDMA Network with Incoherent Detection Technique Satyasen Panda . Associate professor, Department of Electronics Engineering, SIT, Bhubaneswar, India Abstract: In this paper, we have proposed and analyzed novel two-dimensional (2-D) matrices of wavelength hopping and time spreading code for optical code division multiple access (OCDMA) networks with incoherent detection mechanism. The 2-D codes are constructed by integrating one dimensional modified quadratic congruence (MQC) code with one dimensional modified prime (MP) code. The respective encoders and decoders are designed using fiber Bragg gratings and optical delay lines to minimize the bit error rate (BER). The performance analysis of 2-D OCDMA system is based on measurement of signal to noise ratio (SNR), BER and eye diagram for different number of simultaneous users. Also, in the analysis various noises and multiple access interference (MAI) effects are considered. The results obtained with incoherent NAND detection technique are compared with those obtained with OR and AND subtraction techniques. The comparison results proved that the NAND detection technique with MQC\MP code can accommodate more number of simultaneous users for longer distances of fiber with minimum BER as compared to OR and AND subtraction techniques. The optical power is also measured at various transmission distances to analyze the effect of attenuation. Keyword: Cross Correlation (CC), Two dimensional Optical Code Division Multiple Access (2-D OCDMA), Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA), Multiple Access Interference (MAI), Phase Induced Intensity Noise (PIIN) and Two Dimensional Modified Quadratic Congruence/Modified Prime (2-D MQC/MP) code.

1. Introduction The optical CDMA technique is one of the most advanced techniques in recent times for optical access networks which support large number of active users by using available frequency with less time delay, providing flexible provisioning, higher data rate transmission, lower bit error rate (BER) and security [1]. But the OCDMA systems always suffer due to the influence of various types of noises like thermal noise, shot noise, phase induced intensity noise (PIIN) and most importantly multiple access

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interference (MAI) [2]. In OCDMA systems different types of codes have been proposed like onedimensional (1-D) codes which spread in time or frequency and two-dimensional (2-D) codes which spread in both time and wavelength. With the increase in number of active users in the OCDMA network, the MAI increases which degrades system performance. To minimize MAI, the number of chip collisions in the receiver should be less, the length of the code should be increased and the weight of the code chips should be reduced. By increasing the length of the one dimensional uni-polar code, the complexity of the encoder and decoder increases which reduces the data transmission rate. To nullify the above system limitations, we have constructed 2D OCDMA code (MQC/MP) by combining 1-D modified quadratic congruence (MQC) code [3] and 1-D modified prime (MP) code [4]. In 2-D OCDMA coding, pulses are placed in various chips of different wavelength across the bit period, making a wavelength hopping pattern which performs increased code design flexibility and better coding performance. Here, all simultaneous users share the exact wavelength and time domain space achieving better division of wavelength, synchronous access and easier network control and management. To improve the system performance of OCDMA systems by decreasing MAI, various detection mechanisms have been adopted by modifying designs of transmitters and receivers. The basic detection techniques are coherent detection techniques and incoherent detection techniques. Coherent detection techniques are executed in a bipolar behavior with the coding operation and also have the knowledge of phase information of the carrier while sending the detection signal but it requires phase synchronizations and complex hardware. However, Incoherent detection technique does not require phase synchronization, complex hardware and it is performed in a uni-polar environment to improve the system performance. There are various types of incoherent detection techniques like complementary subtraction technique, AND subtraction technique [5], spectral detection technique (SDD) [6], OR detection technique. These detection techniques can minimize MAI but the performance degrades due to poor signal quality. Taking into account these limitations Page 818

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in with AND and SDD detection techniques, we devised NAND subtraction detection of MQC/MP 2D code to improve system performance. We have analyzed the overall system performance by mathematical analysis and simulation analysis to obtain results by experimenting MQC/MP 2-D code with NAND detection technique which is compared with those as obtained by AND and complementary detection techniques. The comparison results prove that the system performance improved a lot by using MQC/MP code with NAND detection technique compared to other detection techniques in terms of better signal quality and easier implementation. The remaining paper is organized as follows. The section 2 provides the construction mechanism of MQC/MP 2-D OCDMA code. The section 3 shows the procedures of NAND subtraction technique. The system performance analysis is provided in section 4. Section 5 presents the simulation setup for implementing the 2-D MQC/MP code with NAND subtraction technique. Section 6 contains the discussion on theoretical and simulation results. Finally, conclusions are drawn in section 7.

2. The proposed 2-D MQC/MP code design

Where c  {1, 2.........., p-1} and 2.........., p-1} Every sequence

b, i, j

 {0, 1,

ti , j (k ) has p+1 elements and

p 2 different code sequences for every pair of parameters c and b by modifying parameters i and j to generate p (p-1) code families. Stage 2:

To construct a sequence of binary numbers (0, 1) x(l ) based on original sequence ti , j (k ) the

following mapping method is used.

if l  kp  ti , j (k ) 1 x(l )  { 0 otherwise Where l=0, 1, 2, 3.......,

(2)

l  p 2  1 and k     p

representing highest number less than or equal to the value of (l/p). The following MQC code sequences can be generated by using the parameters p=3, c=1 and b=2.

x(0)  1 0 0 0 1 0 0 1 0 0 0 1 ,

The two dimensional MQC/MC code is constructed by combining the features of wavelength hopping MQC codes and temporal spreading Prime codes (MP). The 2-D MQC/MP code with X as number of wavelengths and Y as the temporal code length, a and c are auto-correlation and crosscorrelation values referred as (X  Y,W, a , C ).

x(1)  0 1 0 0 0 1 0 0 1 0 0 1 , x(2)  0 0 1 0 0 0 1 0 0 1 0 1 ,

x(8)  1 0 0 0 0 1 1 0 0 0 1 0 , Each of the MQC code sequence contains

The following steps describe the construction of 2-D MQC/MP code for various orders.

2.1 MQC code construction

p 2  p elements that can be subdivided into p+1 groups where each group contains one “1” and (p-1) “0”s.

2.2 MP code construction

The modified quadratic congruence (MQC) codes can be constructed using the following stages.

The modified prime (MP) codes can be constructed using the following stages.

Stage 1: In this stage, At first, we have to construct a sequence of integer numbers as ti , j (k ) that are

Stage 1: The construction of modified prime (MP) code starts with considering Galois field GF (p) of a prime number p. A modified prime sequence y ,  ( z ) is

elements of a Galois finite field GF (p) over an odd prime p (p > 2) by using the following equation:

c(k  i)2  j  (mod p), k  0,1, , p  1  ti, j (k )  { kp i  b (mod p),

y , ( z )  {

(1)

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(   z )



p , z  0,1, 2, , p  1 ,

z p

(3)

Page 819

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in Where

 0,1,2,

 0,1,2,

, p 1 .

, p 1

and

By using the equation 3, a prime code family of

p 2 sequences can be generated for different values of parameters  and  .

Here

, p2  p 1 and   0,1,

, p2 1 .

Here, each number represents the position of ‘1’ in a string of 5 bits where other four bits are ‘0’. Modified Prime code (MP) has maximum correlation of one as represented in table 3.

A prime code set of PC for p=5 is established by the table 1. TABLE 1 A prime code set of PC for p=5

s  0,1,2,

TABLE 3 A Modified prime code set of MP for p=5

d(0)

10000

d(1)

10000

01000

00100

00010

00001

y(0)

d(3)

10000

00100

00001

01000

00010

y(1)

d(4)

10000

00010

01000

00001

00100

y(2)

d(5)

10000

00001

00010

00100

01000

y(3)

y(4)

2.3 MQC/MP code construction The MQC/MP code matrices

Considering each number in the above code set in table 1 consisting of p time slots, the value of the number plus ‘1’ is the location of the optical pulse . So the table 1 can be modified to get the Prime code set as shown in table 2. TABLE 2 A prime code set for p=5

y(0)

y(1)

y(2)

y(3)

y(4)

ml ,

can be

generated using the following expression.

 d (0) x(l )    d (1) x(l )   ml ,   d (2) x(l )       d ( p 2  p  1) x(l )    

p 2  1 and   {0, 1, 2.........., p 2  1 }.

Where l= 0, 1, 2, 3.......,

3. NAND subtraction technique To generate a modified prime (MP) code set from the prime code sequence, each sequence is mapped into a binary form (0, 1). The modified prime code sequence will be

y  d (0), d (1), d (2),

Where

d ( s )  {

, d ( p 2  p 1) (4)

1, where s  zp  y ,  ( z ) 0, otherwise

Imperial Journal of Interdisciplinary Research (IJIR)

In digital electronics, NAND gate performs the complementary operation of AND gate. In our proposed analysis, the concept of NAND is used as an operation for NAND subtraction detection technique to improve the system performance in the receiver side because the mobility of electrons inside NAND gate is three times greater than AND ,OR and NOR gates . In this technique, the cross-correlation ( AB ) (k ) represents NAND operation between A and B sequence. If we take A=1 0 1 0 and B=1 1 0 0, than NAND of A and B is ( AB ) =0 1 1 1. Since NAND subtraction technique identifies similar Page 820

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in spectral position of chips in a much better way, the code weight is increased which further increases Signal power and Signal to Noise ratio (SNR). So the OCDMA system performance is highly improved by using the NAND subtraction technique. Table 4 provides the comparison between NAND, AND and OR subtraction technique. TABLE 4 Comparison between NAND, AND and OR Subtraction technique

AND

NAND

For the analysis of our system, Gaussian approximation is used for the calculation of BER. Since, 2-D MQC/MP code has zero to one cross correlation property, there is no overlapping in the spectra of different users, which reduces the multiple access interference improving the overall system performance. In this paper, for 2-D MQC/MP code, thermal noise (  t ), phase induced intensity noise (PIIN) and shot noise (  sh ) in the photo detector are considered. The performance of an optical receiver depends on the signal to noise ratio (SNR). The SNR of an electrical signal is defined as the average signal



), where 

defined as the variance of different noise sources, I is 2

the average photo current and I is the power spectral density of I. For MQC/MP, the composite noise variance [8] can be 2 2  2   shot   t2   PIIN  2eI shot B 

4K BTn B RL

2  I PIIN Btc

bMk , N is related to

temporal spreading.

b1,k N  ck ,1 , ck ,2 , k Where c , N  1,0

, ck , N 

 1, 2,

, M

 b1,k N   k  b k ci , j   2, N     k  bM , N 

4. System performance analysis

Cik, j is a

matrix of M row vectors and

Here emitted wavelengths of

Spectral position S1

power to noise power (SNR=

The i-th user of 2-D MQC/MP code

(5)

Where e is the electronic charge, B is the noise equivalent of electrical bandwidth of the receiver, K B is Boltzmann’s constant, Tn is the absolute

tc is coherent time of light incident to photo diode, RL is the receiver load

receiver temperature, resistance.

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(6)

The MQC/MP 2-D code cross-correlation using NAND detection technique is much lower than other detection techniques. Since, this technique provides better system performance by reducing PIIN noise, shot noise, signal to noise ratio (SNR) and bit error rate (BER), it has become the most preferred detection technique. This NAND detection technique on MQC/MP 2-D code is described in the following equation.

 (c i 1

c )c { W  1

k l i, j i, j

l i, j

for

k l

for

k l

(7)

0 otherwise

Since shot noise, phase induced intensity noise (PIIN) and thermal noises obey negative binomial distribution, the following assumptions are used to analyze the system with transmitter and receiver without much difficulty and for mathematical straightforwardness. The assumptions [9] are a)

Each light source is ideally unpolarized and its spectrum is flat over the

 v , v0  v  . Where 2 2 v0 the central optical frequency is and v is

bandwidth v0



the optical source bandwidth expressed in Hz. b) Each power spectral component has equivalent spectral width. c) Each user has equal power at the receiver. d) Bit streams from different transmitters are synchronized e) The effect of PIIN, Shot Noise, Beat Noise and Thermal Noise obey Gaussian distribution.

Page 821

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in Using the above assumptions, the system performance is analyzed using Gaussian approximation. The Power Spectral density (PSD) of the received optical signal is described [10] as below

 k   bk   b1  b2  b3   k 1 

 bk   W (12)

The photo detector current I is represented as

P r v  r vks

 b  c k 1

i 1 j 1

i, j

(w)rect (v, i )

(8)

Pr is the effective power of a broadband source at the receiver, ci , j ( w) is the element of w-th user’s codeword, k is the number of active users, M is the spectral code sequence length, N is the temporal code sequence length, k s is the spatial code sequence code weight, bk is the data bit of the k-th user. The rect(v,i) function is given by rect(v,i)= v v     u v  v0  (M  2i)   u v  v0  (M  2i  2)  2M 2M    

(9)

The aggregate power spectral density at the input of photo detector one (PD1) in figure 3 is given by 

P1   G1 (v)dv  0

[

Pr k M N k  bk  ci, j (w)cil, j (w)rect (v, i)]dv (10) vks k 1 i 1 j 1



Pr k  bk MN  1 k 1

Pr (2W  2) (13) MN  1

Where  is the Responsivity (=  e

) of photo

diode. The aggregate signal power is represented as

 Pr (2W  2)  Ps  I 2    MN  1 

(14)

The thermal noise power can be expressed as

Where u(v) represents unit step function.



I  I 2  I1  [ P2  P1 ] 

The Power spectral density at the input of photo detector two (PD2) in figure 3 is given by

2 Pther  I thermal 

4 K BTn B RL

(15)

The aggregated shot noise obtained at photo detectors in the receiver part can be expressed as 2  2eB ( I1  I 2 ) Pshot  I shot

2eBPr  W 2  2W    MN  1  2  

(16)

The total PIIN noise obtained at photo detectors in the receiver part can be expressed as 2 PPIIN  I PIIN  BI12  ck  BI 22  ck

B2 Pr2 kW W 2  2W    ( MN  1) 2 v  2 



c



(17)

kW . MN  1

P2   G2 (v)dv 

Where



Since probability of sending either “1” or “0” is 0.5, the PPIIN can be simplified as

Pr k M N k [ [(ci , j ( w)cil, j ( w)).cik, j ( w)]rect (v, i)]dv (11) 0 vks k 1 bk  i 1 j 1

k P  r [W  (W  1) bk ] MN  1 k 1

Here

bk is the data bit of the k-th user that

represents the value either “1” or “0”.

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2 PPIIN  I PIIN  BI12  ck  BI 22  ck



B2 Pr2 kW W 2  2W   ( MN  1)2 v  4 

(18)

When a broadband pulse is source input to a group of fiber Bragg gratings, the incoherent light fields are mixed and applied to the photo detector, and the phase noise of the fields appear in the photo Page 822

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in detector output. The coherence time of the thermal source



 tc  is expressed as below [11].





G 2 (v)dv

  G (v)dv   0 

(19)

Where, G(v) is the single sideband power spectral density (PSD) of the source. Taking into consideration aggregate signal power and various noise powers, the signal to noise ratio (SNR) for the NAND detection technique is expressed as

SNR 

Ps Pther  Pshot  PPIIN

Figure 1. Source of the transmitter of 2-D MQC/MP OCDMA network

 Pr (2W  2)   MN  1   4K BTn B 2eBPr W 2  2W  B2 Pr2kW W 2  2W    RL MN  1  2  (MN  1)2 v  4  2

(20)

Now using the Gaussian approximation, the bit error rate (BER) can be expressed as [12]

BER  Pe 

 1 erfc  2 

SNR 8

  

(21)

Where, SNR represents signal to noise ratio and “erfc” is the error complementary function.

5. Network simulation setup

As shown in figure1, in the encoder side continuous wave (CW) lasers are used as optical source with the input power varying from 0 dBm to 10 dBm, which produces pulses with a repetition rate equal to the bit rate of the system. The code chips for different users are given as input through the user defined bit sequence generators and are encoded to the equivalent non return to zero (NRZ) signals. A Mach-Zehnder modulator modulates the signals/data. The Encoder consists of 3 sets of Bessel optical filters (BOF) implemented using fiber Bragg gratings (FBG) and time delay (TD) circuits. The broad band light source is sliced using splitter produces sliced chips having spectral width of 0.8 nm modulated by pseudo random bit sequence(PRBS).

The simulation set up for OCDMA system based on 2-D MQC/MP code using NAND subtraction technique consisting 3 users is implemented using simulation software Opti-system version 14.0 consisting of transmitter, receiver and single mode fiber. In the schematic diagram of 2-D W/T OCDMA network employing MQC/MP code various transmitters, receivers and couplers are used. The transmitter first encodes the radio signals with its corresponding code word and broadcasts the encoded data to the receiver via optical fiber. The structure of the transmitter is shown in figure 2 composed of pseudo random bit sequence (PRBS) generator, NRZ pulse generator, CW laser array, WDM multiplexer, MZM modulator, power splitter, power combiner and encoder. Figure 2. Transmitter of 2-D MQC/MP OCDMA Network

The output of the encoder provides the MQC/MP coded data, which is sent to the power combiner for

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Page 823

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in feeding the transmission.

single

mode

fiber

(SMF)

nature and un-correlated. The system performance is estimated by referring to SNR and BER.

for

The structure of the receiver as shown in figure 3, composed of multiplexer (MUX), de-multiplexer (DEMUX), 3 sets of photo detectors (PDs), low pass Bessel filters, Regenerators, NAND subtractors and eye diagram analyzers. The Encoder consists of 6 sets of Bessel optical filters (BOF) and time delay (TD) circuits.

6. Simulation results For this part of the paper, we have evaluated the OCDMA system performance based on theoretical analysis and simulation results according to the typical system parameters as listed in the table 5. TABLE 5 System parameters used in simulation

Figure 3. Receiver of 2-D MQC/MP OCDMA Network

The received data from the transmitter is amplified and demultiplexed at the beginning of the receiver. The demultiplexed data is decoded by the sets of Bessel optical filters and inverse time delay (ITD) circuits. The six sets of PIN photo detectors (PDs) used to convert optical data to electrical signal which is then transmitted through NAND subtractors for efficient detection. Eye diagram analysers are connected at the end to analyze the received signal. The generated noise at the receiver side is random in

Sl. No. 1

Parameters

Quantity

Line encoding

NRZ

Effective Power at the source

0 to -10 dBm

Number of users

20 to 120

Operating Wavelength

1550 nm

Fiber length

10 to 50 km

Data rate

Received power

622 Mbps to 1 Gbps 0 to -35 dBm

Fiber attenuation

0.2 dB/km

Dispersion

16.75 ps/nm/km

PMD coefficient

0.5 ps/sqrt(km)

The bit error rate (BER) performance of 2-D MQC/MP code using AND, OR and NAND subtraction technique for various numbers of active users is shown in figure 4.

-10

-20

BER

OR AND

-30

NAND

-40

-50

100

Number of users

Figure 4. BER vs. Number of active users

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Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in

It is seen from the figure 4 that the NAND subtraction technique is much more effective in reducing the multiple access interference and bit error rate than other detection techniques. Also, the

BER level is lower for higher number of users in NAND detection technique employed for 2-D MQC/MP code.

1000 900 OR 800 AND 700

NAND

SNR

600 500 400 300 200 100 0 10

100

Number of users

Figure 5. SNR vs. Number of active users

Figure 5 shows the signal to noise ratio (SNR) versus the number of active users. It is observed that the 2-D MQC/MP codes provide much better SNR value using NAND detection technique compared to OR and AND detection techniques for higher effective signal power.

Figure 6 (b). Eye diagram at 622Mbps for OR detection technique in receiver.

Figure 6 (c). Eye diagram at 622Mbps for AND detection technique in receiver. Figure 6 (a). Eye diagram at 622Mbps for NAND detection technique in receiver.

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The eye diagrams of the received signals for various detection techniques are shown in figure 6(ac). It is observed that the system produces higher signal quality with NAND detection technicque compared to other detection techniques like AND and OR for 2-D MQC/MP codes.

Page 825

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in 0

-10

-20

BER

2-D MQC (p1=7, p2=3) -30

2-D PDC (M=73 , N=7) 2-D MQC/MP(M=80, N=9)

-40

-50

100

150

200

250

300

350

400

450

Number of active users Figure 7. BER vs. number of active users for various types of 2-D codes

The BER variation against number of active users for different types of 2-D codes is demonstrated in figure 7. It is observed that BER performance is much better for 2-D MQC/MP code in comparison to

2-D perfect difference (PDC) [13] code and 2-D modified quadratic congruence (MQC) code for a given number of simultaneous users.

2-D MQC (p1=7, p2=3) 2-D PDC (M=73 , N=7)

2-D MQC/MP(M=80, N=9)

BER

-2

-4

-6

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

Effective transmitted power(dBm) Figure 8. BER vs. Effective transmitted power (dBm) for various types of 2-D codes

The BER variation against effective transmitted power (dBm) for various types of 2-D codes is demonstrated in figure 8. It is observed that the proposed 2-D MQC/MP code requires lowest optical transmission power compared to other codes like 2-D MQC and 2-D PDC codes because of effective suppression of PIIN noise.

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7. Conclusions In this paper, we have proposed a new 2-D MQC/MP optical CDMA code for enhancing the system performance by suppressing various types of noises like thermal noise, shot noise and PIIN noise. The system architecture of the 2-D code is also explained in detail which achieves higher cardinality, better BER performance and lower effective Page 826

Imperial Journal of Interdisciplinary Research (IJIR) Vol-3, Issue-2, 2017 ISSN: 2454-1362, http://www.onlinejournal.in transmitted power compared to other two dimensional OCDMA codes. The performance degradation due to PIIN noise can be minimized by lowering cross-correlation and BER [14]. We have also analyzed the OCDMA system performance for 2-D MQC/MP code for three different detection techniques like NAND, OR and AND subtraction techniques. The analysis result obtained by NAND detection technique with 2-D MQC/MP code found to be supporting more number of simultaneous users and it can improve the system performance by minimizing the MAI significantly in comparison to other detection techniques like OR and AND subtraction technique.

[8]

[9]

[10]

8. Acknowledgment The author would like to extend their sincere appreciation to the All India Council of Technical Education (AICTE) for the funding of this research through the research project number 20/AICTE/RIFD/RPS (POLICY-II) 2/2012-13.

[11]

[12]

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