Influence of Code Size Variation on the Performance of 2D Hybrid ZCC/MD in OCDMA System

Transcription

1 MATEC Web of Conferences 5, 68 (8) MUCET 7 Influence of Code Size Variation on the Performance of D Hybrid ZCC/MD in OCDMA System Rima Matem,*, S A Aljunid, M N Junita, C B M Rashidi, Israa Shihab Ahmed Advanced Communication Engineering Centre of Excellence School of Computer and Communication Engineering (ACE CoE -SCCE), Universiti Malaysia Perlis (UniMAP),Perlis, Malaysia, Abstract Several two dimensional OCDMA have been developed in order to overcome many problems in optical network, enhancing cardinality, suppress Multiple Access Interference (MAI) and mitigate Phase Induced Intensity Noise (PIIN) This paper propose a new D hybrid ZCC/MD code combining between D ZCC spectral encoding where M is its code length and D MD spatial spreading where N is its code length The spatial spreading (N) code length offers a good cardinality so it represents the main effect to enhance the performance of the system compared to the spectral (M) code length according to the numerical results Introduction In OCDMA system, each user has its own code word rather of the specific wavelength or time slot which is provided by Wavelength Division Multiple Access (WDMA) and Time Division Multiple Access (TDMA) respectively [] This property provides that to users can access the same channel simultaneously and asynchronously [] Many D coding have been proposed and investigated as [], [4], [5], [6] Several classifications has been investigated in OCDMA system such as temporal OCDMA encoding and spectrumamplitude coding (SAC) OCDMA, spectral-phase encoding (SPE), frequency hopping (FH) OCDMA, and D hybrid coding approach [7] The D OCDMA depicts an enhanced performance compared to D OCDMA system in term of low power lost, high cardinality, minimum cross-correlation, high data rate and high autocorrelation with side[8] Several challenges affect the performance of OCDMA system in the implementation level [9-] The main challenges are due to the Multiple Access Interference (MAI) of the overlapping chips and Phase Induced Intensity Noise (PIIN) where PIIN is due to the desired signal mixed with the unwanted signal simultaneously at the same wavelength incident on the same photo-detector [-] In the other side, an important factor can be impact the performance of OCDMA system is the code length where it represents one of the essential characteristic to design the system [-4] The main obstacle of increasing the code length is that growing complexity and cost, reducing the data transmission and bandwidth efficiency [5-6] In this paper, combining between one dimensional Zero Cross Correlation code (D ZCC) [7] and one dimensional Multi Diagonal code (D MD) [8] where the both represent zero cross correlation property The new D hybrid ZCC/MD code used to eliminate MAI and mitigate PIIN The increment of spatial code length N significantly influences the system performance compared to the spectral code length M this paper is organized as follow: section II represents code construction, then section III shows the system performance, section IV depicts on the analytical results and discussion, finally the conclusion D hybrid ZCC/MD code construction The derivation of the D hybrid ZCC/MD is based on the Zero Cross Correlation (D ZCC) code and Multi Diagonal (D MD) code This new code is characterized by (MM, NN, ww, λλ aa, λλ cc ) where MM is spectral code length, NN is spatial code length,ww is the code weight, λλ aa represents auto-correlation and λλ cc is the cross-correlation The code size of the D hybrid code represented by MM NN D Zero Cross Correlation (ZCC) code The Zero Cross Correlation (ZCC) code for SAC OCDMA was developed by [7] ZCC is designed with zero cross correlation property between its code words to improve the performance of SAC OCDMA system ZCC is characterized by a matrix of KKKKKK where KK represents number of active users and LL represents the minimum code length The number of active user KK and code length LL are given as: KK = ww + () LL = ww(ww + ) () The construction of the code is designed from the modified double weight (MDW) code [] where the matrix is generated as follow with the basic ZCC code (w=): ZZZZZZ(ww = ) = [ ] * Corresponding author: rymann9@hotmailcom The Authors, published by EDP Sciences This is an open access article distributed under the terms of the Creative Commons Attribution License 4 (

2 MATEC Web of Conferences 5, 68 (8) MUCET 7 According to the following maps, the increase of the number of users is occurred: ZZZZZZ(ww = ) = [ ZZ ZZ ] ZZZZZZ(ww = ) = [ ZZ ZZ ] The number of code weight can be increased by the general transformation below: ZZZZZZ ww = [ AA BB CC DD ] Where: AA: is [, ww(ww )] matrix of zeros ww BB: represents ww replication of the matrix jj= jj[,] CC: contain of the duplication of the matrix from ww DD: is the diagonal pattern of [mm nn] with exchange column of zeros matrix [mm nn] An example for the transformation code from ww = ww = ww = as follow: Step: A sequence of diagonal matrix can be constructed using the value of the weight (ww) and number of user (KK), according to these value the ii(ii =,,, KK) is the index of rows in each matrix and jj(jj =,,,, ww)where j is the number of diagonal matrix Step: The MD sequences can be computed for each diagonal matrix using the equation below: SS ii,jjww = { (ii nn + ii), jj ww = eeeeeeee () SS ii, = ii [ KK], SS ii, = ffffff jj ww = oooooo KK, SS ii, = [ ] [ KK], Each element of the SS ii,jj matrices represents the position of one in TT ii,jj matrices with KKKKKKdimensions Where TT ii, = [SS ii, ] KK KK, TT ii, = [SS ii, ] KK KK,, TT ii,ww = [SS ii, ] KK KK ZZZZZZ ww= = AA ZZZZZZ ww= = [ CC BB ] AA DD BB TT ii, = [ ], TT ii, = [ ] TT ii,ww = [ ] KK KK KKKKKK KK KK,, Step: The construction of the matrix of MD code of power KKKKKK is based on the combination of diagonals matrices In a matrix each row is a single code sequence ZZZZZZ ww= = [ ] D Multi Diagonal (MD) code CC One-dimensional Multi Diagonal (D MD) was been developed by [9] It is characterized by NN(code length), ww(code weight) and λλ cc (in phase cross correlation) For the code sequence XX = {xx, xx,, xx NN }, YY = {yy, yy,, yy NN } The cross correlation expression can be expressed by λλ cc = NN ii xx ii yy ii DD MMMM (Multi Diagonal) possesses zero cross correlation λλ cc = The matrix of D MD code consists of KKKKKK where KK is the number of user, NNis the code length The choice of the weight value is free and NN = KKKK The D MD code can be designed as below: DD MMMM = TT ii, TT ii, TT ii,ww KKKKKK aa, aa, aa,nn aa, aa, aa, MMMM = aa, aa, aa,nn [ aa iinn, aa iinn, aa iinn,nn] The following table give an example of MD code with KK = 4, ww = Table I: The MD code with KK = 4, ww = ii 4 Code sequence

3 MATEC Web of Conferences 5, 68 (8) MUCET 7 TABLE II: D Hybrid ZCC/MD Code for kk = and kk = AA gg,h [] [] [] [ ] [ ] [ ] [ ] The cross correlation of newly code can be obtained using four characteristics are given as follow: AA = YY TT XX (4) AA = YY TT XX (5) AA = YY TT (6) AA = YY TT XX (7) Where A(d), d (,,,) has been given in [9] represents the characteristic matrices Where parameters XX and YY are the complementary of XX and YY respectively The cross correlation of hybrid D ZCC/MD code AA (dd) and AA gg,h is formulated as: RR (dd) (gg, h) =) MM NN NN= aa iiii (dd) MM= aa (ii+gg)(jj+h) (8) Where aa (dd) iiii depicts the (ii, jj) tth of AA (dd) and aa (ii+gg)(jj+h) is the (ii, jj) tth of AA gg,h Table III shows the cross correlation between any two codes AA (dd) and AA gg,h of D Hybrid ZCC/MD code produced from the equation (8) Table III: Cross Correlation of D ZCC/MD hybrid code RR () RR () RR () RR () gg =, h = kk kk gg =, h kk kk gg, h = kk kk Where BB is the electrical bandwidth, II is the average photocurrent, ee is the electron charge, KK bb is Boltzmann's constant, TT nn is the absolute temperature, is the load resistance and ττ is the coherence time of the light By applying the same method as [9], the PIIN, shot noise and thermal noise can be expressed as follow: = BB RR PP ssss ww kk ii PPPPPPPP ii sshoooo ii ttheeeeeeeeee () vvvv = eeee RRRR ssssww WW () = 4KK bbtt nn BB () Note that the probability of sending bit at any time for each user is ½ so: = RR PP ssss ww kk ii nnnnnnnnnn + eeeeeeee ssssww vvvv WW + 4KK bbtt nn BB (4) where RR is the responsivity of the photo-diode given by RR = ηηηη/hvv, ηη is the quantum efficiency of the photo-diode, and h is Plank's constant PP ssss is the effective source power at the receiver, kk is the code weight of spectral encoding, WW is the number of active users, NN and MM are the code lengths of spatial and spectral code sequences respectively SSSSSS = II = [ RRRRssssww WW ] ii RR PP nnnniissss ssssww kk vvvv (5) +eeeeeeee ssssww + 4KK bb TT nnbb WW The BER can then be calculated from SNR as follows []: Where BBBBBB = eeeeeeee ( SSSSSS 8 ) eeeeeeee = ππ exp ( yy )dddd Results and Discussion (6) (7) Table IV: Parameters used in analytical calculations gg, h kk kk The cross correlation of AA, and AA gg,h can be calculated as follows: MM NN RR () (gg, h) = aa () ii,jj aa ii,jj (gg, h) ii= jj= = { kk kk ffffff gg =, h = ooooheeeeeeeeeeee (9) In performance analysis there types of noise are considered Phase Induced Intensity Noise (PIIN), Shot Noise and Thermal Noise In addition the BER is calculated using Gaussian approximation The general form of the photocurrent noise from the photodiodes can be written as below: ii nnnnnnnnnn = ii PPPPPPPP + ii sshoooo + ii ttheeeeeeeeee = BBII ττ + eeeeee + 4KK bbtt nn BB () PD quantum efficiency Spectral width of broadband light source Operating wavelength Electrical bandwidth Data transmission rate Receiver noise temperature Receiver load resistor Boltzmann s constant Electron charge Light velocity RR = 75 λλ = nnnn ( λλ = 75 TTTTZZ) λλ = 55μμμμ BB = MMMMMM RR bb = 6MMMMMMMM TT nn = KK = Ω KK bb = 8 WW/KK/HHzz ee = cccccccccccccccc CC = 8 mm/ss

4 MATEC Web of Conferences 5, 68 (8) MUCET 7 The analysis of the code is based on the parameters shown in the Table IV where the numerical results are exhibited in following figures BER Number of users Figure : BER versus the number of simultaneous users for D ZCC/MD with the fixed value number of time spreading N Figure illustrates the relation between the BER and the number of simultaneous users for D ZCC/MD with the fixed number of time spreading N to and the effective source power, Psr is fixed at -dbm with variation of wavelength M (M=, M=4, M=7) It can be seen that this variation of M makes a small difference in the number of simultaneous users The respective number of simultaneous users for groups of (M=, N=), (M=4, N=) and (M=7, N=) are 8, 45 and 5 respectively when the BER at 9 BER -5 - D ZCC/MD (M=7,N=) D ZCC/MD (M=4,N=) D ZCC/MD(M=,N=) D ZCC/MD(M=,N=) D ZCC/MD (M=,N=9) D ZCC/MD (M=,N=6) Number of users Figure: BER versus the number of simultaneous users for D ZCC/MD with the fixed number of wavelength M The figure represents the plot of BER versus the number of users for D ZCC with the fixed number of wavelength M to and the time spreading N varies at 6, 9 and at Psr=- dbm According to the figure, the curves are separately each from other comparing with the Figure The changing of the values of N results the variation of cardinality From the figure, at BER equal to 9 the number of simultaneous users for N=6, 9, 9 is 5, and 75 respectively Note that the increases of N causes that the code can accommodate a higher number of simultaneous users but for the lowest number of N offer the lower cardinality in the system 4 Conclusion This study is focused to analyze D hybrid ZCC/MD code in term of impact size including D ZCC a spectral encoding and D MD a spatial spreading From the numerical results it can be seen that the improvement of the cardinality is related to the spatial spreading N where is present the principal role to ameliorate the performance of the system The large number of N offers the capability to provide a high cardinality in the system at standard acceptable BER when the number of spectral encoding is fixe The variation of M and fixed value of N makes a small difference in the number of simultaneous users can be obtained This paper clarifies and defines the relationship between the code size and the system performance References Paul R Prucnal, CRC Press, Florida, (6) Keraf, N Din, et al Electronic Design (ICED), nd International Conference on IEEE, (4) AR Arief, SA Aljunid, MS Anuar, MN Junita, RB Ahmad and F Ghani, IEEE International Conference on Control System, Computing and Engineering, pp , () 4 Hongxi Y, Le Ma, Hongbin Li and Lixin Zhu, Photon New Communication, () 5 Cheing-H L, Jingshown Wu and Chun-L Y Journal of Lightwave Technology, vol, no, pp , December (5) 6 Preeti M and Shalini D International Journal of Computer Science & Engineering Technology IJCSET, pp -5, () 7 Arief, A R, Aljunid, S A, Anuar, M S, Junita, M N, & Ahmad, R B Optik-International Journal for Light and Electron Optics, 4(9), () 8 Kadhim, R A, Fadhil, H A, Aljunid, S A, & Razalli, M S Journal of Theoretical and Applied Information Technology, 8(), 589 (5) 9 Abdullah, A R A J, Aljunid, S A, Safar, A M, Nordin, J M, & Ahmad, R B Optical Engineering, 5(6), 657- () Keraf, N Din, et al Photonics (ICP), 4 IEEE 5th International Conference on IEEE, 4 Chang, Yao-Tang, et al Optical Fiber Technology 6: 4- () Keraf, N Din, et al Advanced Computer and Communication Engineering Technology Springer, Cham 9-4 (5) Keraf, N Din Malaysia University Conference Engineering Technology (4) 4 Jellali, Nabiha, et al Optical Fiber Technology 6: 6- (7) 5 Dexter, Karl J, Douglas Alexander Reid, and Liam P Barry IEEE photonics technology letters : (9) 4

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