Th.P2.5 306 ICTON 2008

978-1-4244-2626-3/08/$25.00 ©2008 IEEE

Performance Comparison of W/T Matrix with Variable Code Parameters for OCDMA System Gurjit Kaur1, Neena Gupta2, Navtej Singh Sahota3

1 University Institute of Engineering and Technology, Panjab University, Chandigarh, India email: gurjeet_kaur@rediffmail.com

2 E&EC Department, Punjab Engineering College, Chandigarh, India email: ng65@rediffmail.com

3 University Institute of Engineering and Technology, Panjab University, Chandigarh, India email:navtej.sahota@gmail.com

ABSTRACT The performance of W/T OCDMA system for W/T Matrix with Variable code parameters for OCDMA System is analyzed for variable weight, length and bit rate. The system has been optimized for permissible BER and number of simultaneous users.

1. INTRODUCTION Optical Code Division Multiple Access (OCDMA) system are getting more attractive in the field of all optical communications as multiple users can access the network asynchronously and simultaneously with high level of transmission security. The main issue of the studies on the OCDMA system is to device a code set of good system performance. In unipolar optical code based OCDMA system , the system performance is determined by the bandwidth efficiency of the optical codes which is closely related with the bit error rate of the optical code in multiple user circumstance as well as the code set size depends on the code parameters e.g. weight, length etc.[1-7].

Performance of the OCDMA system has been analyzed for 3×4, 4×4, 8×4 matrices as input codeword for the bit error rate of 10-9 in this study. The system has been designed in which the users are assigned the codewords with variable length, variable weight. Further, the system performance has also been analyzed for variable bit rate.

2. SYSTEM DESIGN PARAMETERS In this system W/T matrix codes are generated by optimum Golomb ruler. Matrix has been designed with dimensions (W×T), where (W×T) > L. Here, “W” the number of wavelengths, “T” is the number of time slots, and L is the length of the Golomb ruler. There are then (W×T) – L possible shifts; thus the number of new matrices depends on the initial Golomb ruler length L as well as on the number of shifts permitted by the product (W×T). The difference (W×T) – L should be equal to or greater than (W – 1) to assure that the matrix code set size M is equal to the number of rows in the matrices [5], [7].

Table 1. System Parameter for OCDMA system. Parameters Values Matrices 3 ×4, 4 ×4, 8×4 Variable code weight 4,5,6 Variable code length 7,11,25 Variable Data rate 1Gbps, 2Gbps, 2.5Gbps, 3Gbps Variable PRBS 64,160,384,896,2048 Mode locked laser Wavelengths 1554nm -1556.8nm with a difference of .4nm Distance 60Km

In this work the codes for OCDMA system has been designed and then the performance has been evaluated on the simulator Optsim. We use four time slots without any guard with chip period of 100 ps (bit rate = 2.5 Gbps, bit period of 400 ps). For 3×4 matrix the time-slot sequence used is i.e. for user1 (λ1 λ2; λ2; λ1; 0), user2 (λ2 λ3; λ3; λ2; 0), user3 (λ3; λ1; λ1 λ3; 0), user4 (0; λ1 λ2; λ2; λ1) and user5 (0; λ2 λ3; λ3; λ2). For 4×4 matrix OCDMA system optimum again Golomb ruler is used to generate the codes of cardinality 3, weight 5 and length 11.So , for 4×4 matrix sequence used is i.e. for user1 (λ1 λ2 λ4; λ3; λ3; 0), user2 (λ2 λ3; λ1 λ4; λ4; 0), user3 (λ3 λ4; λ2; λ1; λ1), user4 (λ4; λ1 λ3; λ2; λ2) and user5 (0; λ1 λ2 λ4; λ3; λ3). The 8×4 matrix has been designed with cardinality 4, weight 4 and length 25. Here, for user1 (λ1; λ1; λ2; λ1), user2 (λ2; λ2; λ3; λ2), user3 (λ3; λ3; λ5; λ3), user4 (λ4; λ4; λ6; λ4), user5 (λ5; λ5; λ7; λ5), user6 (λ1; λ1; λ3; λ1), user7 (λ7; λ7; 0; λ1 λ7) sequence has been used.

ICTON 2008 307 Th.P2.5

3. RESULTS AND DISCUSSION The system performance has been analyzed with W/T matrix [3×4, 4×4, 8×4] with variable weights .i.e. 4, 5, 6. The results show that as the weight of the code is increased the performance becomes better. For e.g., for 4×4 matrix for 4 simultaneous users the bit error rate is 3.70·10-27 at code weight 4, 4.59·10-35 at code weight 5 and 2.01·10-44 at code weight 6 as shown in the figure 1. Similarly for 8×4 matrix with 14 simultaneous users the bit error rate comes out as 3.04·10-10 at code weight 4, 6.31·10-13 at code weight 5 and 3.04·10-15 at code weight 6. So it is clear from the values that the number of simultaneous users supported by system are more for higher code weights as compared to corresponding lower code weights for BER = 10-9. So this system can support 8,11,16 number of simultaneous users for 3×4,4×4 ,8×4 matrix respectively at data rate 2.5 Gbps with code weight = 6 and BER = 10-9 as shown in figure (1, 2, 3).

1.00E-651.00E-601.00E-55

1.00E-501.00E-451.00E-401.00E-35

1.00E-301.00E-251.00E-201.00E-15

1.00E-101.00E-05

1.00E+000 5 10 15

Number of simultaneous users

BER

Weight = 4Weight = 5Weight = 6

1.00E-58

1.00E-52

1.00E-46

1.00E-40

1.00E-34

1.00E-28

1.00E-22

1.00E-16

1.00E-10

1.00E-04

1.00E+02

0 5 10 15 20

Number of simultaneous users

BER

3x4, CL*=74x4, CL*=118x4, CL*=25

Figure 1. Number of simultaneous users vs. BER for

different code weight (4×4 matrix). Figure 2. Number of simultaneous users vs. BER for

3×4, 4×4 and 8×4 matrices with constant code weight = 4. (*CL means Code Length).

The OCDMA system has further been analyzed for different code length/code weight i.e. 7,11,25 for 3×4, 4×4 and 8×4 matrices respectively. It is evident from the plot i.e. from figure 2 that as the code size is increased from 3×4 matrix to 8×4 matrix the performance of the system is degraded in case of single user. But it is also clear that with increase in the code length, the number of the simultaneous users supported at BER=10-9 are increased. System with 3×4 matrix as input code can support maximum of seven users as compared to 9 and 15 with 4×4 and 8×4 matrix as input codes. In case of 3×4 matrix BER for the single user is 1.29·10-58 and BER for 7th, 9th and 15th user with 3×4, 4×4 and 8×4 matrices is 2.03·10-9, 2.08·10-10 and 3.23·10-9, respectively.

The input data rate in this experiment is generated by PRBS generator. OCDMA system in this experiment has further analyzed for different lengths of the input data. The system performs better with small input pattern length as shown in the figure 3. For example OCDMA system with 64 bits as input PRBS data length has BER 4.38·10-138 as compared to 2.10·10-97, 1.29·10-58, 3.63·10-48 and 1.71·10-33 at 160, 384, 896 and 2048 input data lengths respectively for 3×4 matrix with single user on system. Performance has also been evaluated for different data rates of 1.0 Gbps, 2.0 Gbps, 2.5 Gbps and 3.0 Gbps as represented in figure 4.

1.00E-1381.00E-1291.00E-1201.00E-1111.00E-1021.00E-931.00E-841.00E-751.00E-661.00E-571.00E-481.00E-391.00E-301.00E-211.00E-121.00E-03

1.00E+06

0 1 2 3 4 5 6

n (where patteren length=PL*)

BER

3x44x48x4

1.00E-621.00E-571.00E-521.00E-471.00E-421.00E-371.00E-321.00E-271.00E-221.00E-171.00E-121.00E-071.00E-02

1.00E+03

0 5 10 15 20

Number of simultaneous users

BER

1.0 Gbps2.0 Gbps2.5 Gbps3.0 Gbps

Fig. 3. Plot of BER at different input pattern length of single user for 3×4, 4×4 and 8×4 matrices with code

weight = 4 and data rate = 2.5 Gbps. (pattern length, *PL=2n × n).

Fig. 4. Number of simultaneous users vs. BER for different data rates (8×4 matrix).

Results taken at 1.0 Gbps are better than taken at 3.0 Gbps. The number of simultaneous user supported by the 3×4 matrix are 8,8,7 and 6 for 1.0 Gbps, 2.0 Gbps, 2.5 Gbps and 3.0 Gbps respectively as compared to 9,9,8,6 and 17,15,15,12 supported by 4×4 and 8×4 matrices respectively.

Th.P2.5 308 ICTON 2008

4. CONCLUSION The performance of W/T OCDMA system for 3×4, 4×4, 8×4 matrices is analyzed and optimized for variable weight, length and bit rate. It is concluded that the OCDMA system using 2-D W/T matrix codes should be used according to the requirement of number of simultaneous users. At code weight 6 and data rate 2.5 Gbps for 8×4 matrix, the OCDMA system can supports 16 simultaneous users for BER = 10-9. If there are less number of simultaneous users (< 8), it is recommended to use small size and low code weight as 3×4 matrix at code weight 4 with data rate 2.5 Gbps.

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CDMA system based on 2-D optical orthogonal codes, Journal of Lightwave Technology, vol. 22, no. 11, Nov. 2004.

[2] R. Adams, J. Faucher, L. Thomas, D.V. Plant, L.R. Chen: Demonstration of encoding and decoding 2-D wavelength-time bipolar codes for OCDMA systems with differential detection, IEEE Photonics Technology Letters, vol. 11, no. 10, 2006.

[3] J. Faucher, S. Ayotte, L.A. Rusch, S. LaRochelle and D.V. Plant: Experimental BER performance of 2D (W/T) OCDMA with recovered clock, Electronics Letters, vol.13, no. 4, Apr. 2005.

[4] A.J. Mendez, R.M. Gagliardi, V.J. Hernandez, C.V. Bennett, W.J. Lennon: Design and performance analysis of wavelength/time (W/T) matrix codes for optical CDMA, Journal on Lightwave Technology, (Special Issue on Optical Networks), vol. 21, pp. 2524-2533, Nov. 2003.

[5] D. Lopes, H. Abdalla, A.J.M. Soares: High capacity optical networks using OCDMA techniques, High Frequency Electronics, University of Brasilia, Brazil, 2007.

[6] R.M.H. Kim, L.R. Chen, J. Bajcsy: Design and performance of 2D codes for wavelength-time optical CDMA, IEEE Photonics Technology Letters, vol. 14, no. 5, pp. 714-716, May 2006.

[7] A.J. Mendez, R.M. Gagliardi, V.J. Hernandez, C.V. Bennett, W.J. Lennon: Bit-Error-Rate analysis of 16-user Gigabit Ethernet optical-CDMA technology demonstrator using W/T codes”, IEEE Photonics Technology Letters, vol. 17, no. 2, Feb. 2005.