# Approximate Expression of Bit Error Rate in Uplink MC-CDMA Systems with Equal Gain Combining

• Develi, Ibrahim (Department of Electrical & Electronics Engineering, Faculty of Engineering, Erciyes University) ;
• Akdagli, Ali (Department of Electrical & Electronics Engineering, Faculty of Engineering, Mersin University)
• Received : 2011.12.16
• Accepted : 2012.07.31
• Published : 2013.02.28

#### Abstract

Uplink multicarrier code-division multiple-access (MC-CDMA) with equal gain combining (EGC) over Nakagami fading channels is considered. An improved expression which is a feasible alternative for the bit error rate (BER) performance evaluation of MC-CDMA signals is proposed. Simulated annealing algorithm is employed to obtain the optimum value of the coefficients belonging to the proposed expression. Numerical examples show that the performance curves computed by the improved expression are in good agreement with the results obtained by the exact expression. Thus, the proposed expression can improve the accuracy of BER performance evaluation that has been realized by the approximate expression.

#### References

1. K. Fazel, S. Kaiser, and M. Schnell, "A flexible and high performance cellular mobile communications system based on orthogonal multi-carrier SSMA," Wireless Per. Commun., vol. 2, no. 1&2, pp. 121-144, Mar. 1995. https://doi.org/10.1007/BF01099534
2. S. Hara and R. Prasad, "Overview ofmulticarrier CDMA," IEEE Commun. Mag., vol. 35, no. 12, pp. 126-133, Dec. 1997.
3. S. Hara and R. Prasad, "Design and performance of multicarrier CDMA system in frequency-selective Rayleigh fading channels," IEEE Trans. Veh. Technol., vol. 48, no. 5, pp. 1584-1595, Sept. 1999. https://doi.org/10.1109/25.790535
4. T. Mueller, K. Brueninghaus, and H. Rohling, "Performance of coherent OFDM-CDMA for broadband mobile communications," Wireless Per. Commun., vol. 2, no. 4, pp. 295-305, 1996. https://doi.org/10.1007/BF01099337
5. E. A. Sourour and M. Nakagawa, "Performance of orthogonal multicarrier CDMA in a multipath fading channel," IEEE Trans. Commun., vol. 44, no. 3, pp. 356-367, Mar. 1996. https://doi.org/10.1109/26.486330
6. L. Vandendorpe, "Multitone spread-spectrum multiple-access communications system in a multipath Rician fading channel," IEEE Trans. Veh. Technol., vol. 44, no. 2, pp. 327-337, May 1995. https://doi.org/10.1109/25.385926
7. T. T. Liu and C. Y. Yang, "Equivalent signal-alignment-based frequencydomain equalization forMC-CDMA two-way relay systems," IEEE Trans. Veh. Technol., vol. 61, no. 1, pp. 237-248, Jan. 2012. https://doi.org/10.1109/TVT.2011.2175952
8. W. Yang, J. Y. Liu, C. L. Xu, and S. X. Cheng, "Joint carrier frequency offset estimation and compensation for downlink group-orthogonal multicarrier CDMA," Wireless Per. Commun., vol. 62, no. 1, pp. 107-116, Jan. 2012. https://doi.org/10.1007/s11277-010-0041-5
9. C. C. Lin, W. C. Chen, and C. D. Chung, "Spectral sidelobe decaying property of Walsh-Hadamard code in MC-CDMA systems," IEEE Trans. Wireless Commun., vol. 10, no. 10, pp. 3151-3157, Oct. 2011. https://doi.org/10.1109/TWC.2011.081611.102086
10. Y. Meng, M. L. You, H. W. Luo, and G. Liu, "The subspace-based linear conjugate CMA in BPSK-modulated MC-CDMA systems," Wireless Per. Commun., vol. 56, no. 4, pp. 761-777, Feb. 2011. https://doi.org/10.1007/s11277-009-9846-5
11. F. Zabini, B. M. Masini, A. Conti, and L. Hanzo, "Partial equalization for MC-CDMA systems in non-ideally estimated correlated fading," IEEE Trans. Veh. Technol., vol. 59, no. 8, pp. 3818-3830, Oct. 2010. https://doi.org/10.1109/TVT.2010.2060217
12. L. L. Yang and L. Hanzo, "Multicarrier DS-CDMA: A multiple access scheme for ubiquitous broadband wireless communications," IEEE Commun. Mag., vol. 41, no. 10, pp. 116-124, Oct. 2003.
13. C. L. Chang, P. S. Huang, and T. M. Tu, "Performance comparison of MRC and EGC on a MC-CDMA system with synchronization errors over fading channels," Wireless Per. Commun., vol. 43, no. 2, pp. 685-698, Oct. 2007. https://doi.org/10.1007/s11277-007-9273-4
14. G. L. Stuber, Principles of Mobile Communications. Kluwer Academic Publisher, 1996.
15. J. I. Z. Chen and C. W. Liou, "Performance evaluation of MC-CDMA systems with EGC diversity over correlated selective fading channels," in Proc. IEEE WCNC'07, (Hong Kong, China), Mar. 2007, pp. 4186-4190.
16. Y. Feng and J. Qin, "BER of MC-CDMA systems with MRC in correlated Nakagami-m fading," Electron. Lett., vol. 41, no. 19, pp. 1069-1071, Sept. 2005. https://doi.org/10.1049/el:20052050
17. Y. Feng and J. Qin, "BER of MC-CDMA systems with EGC in correlated Nakagami-m fading," IEEE Commun. Lett., vol. 10, no. 10, pp. 689-691, Oct. 2006. https://doi.org/10.1109/LCOMM.2006.060379
18. A. B. Djebbar, A. Djebbari, M. Bouziani, and J. M. Rouvaen, "Derivation of new expressions of bit error rate for MC-CDMA system in Nakagami fading channel," $AEi?{\frac{1}{2}}$ Int. J Electron. Commun., vol. 57, no. 6, pp. 395-402, 2003. https://doi.org/10.1078/1434-8411-54100191
19. M. Bouziani, A. Djebbari, A. B. Djebbar, M. F. Belbachir, and J. M. Rouvaen, "MC-CDMA with exponential power profile in Nakagami fading channel," $AEi?{\frac{1}{2}}$ Int. J Electron. Commun., vol. 59, no. 6, pp. 359-361, 2005. https://doi.org/10.1016/j.aeue.2004.11.010
20. A. E. El-Mahdy, "Error probability analysis of multicarrier direct sequence code division multiple access system under imperfect channel estimation and jamming in a Rayleigh fading," IET Signal Process., vol. 4, no. 1, pp. 89-101, Feb. 2010. https://doi.org/10.1049/iet-spr.2009.0038
21. M. Nakagami, "The m-distribution: A general formula of intensity distribution of rapid fading," in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, Ed. Oxford, U.K.: Pergamon, 1960.
22. N. Yee, J. P. Linnartz, and G. Fettweis, "Multi-carrier CDMA in indoor wireless radio networks," in Proc. IEEE PIMRC, (Yokohoma, Japan), Sept. 1993, pp. 109-113.
23. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Sci., vol. 220, no. 4598, pp. 671-680, May 1983. https://doi.org/10.1126/science.220.4598.671
24. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of the state calculations by fast computing machines," J Chem. Phys., vol. 21, no. 6, pp. 1087-1092, 1953. https://doi.org/10.1063/1.1699114
25. D. Turgut, B. Turgut, R. Elmasri, and T. V. Le, "Optimizing clustering algorithm in mobile ad hoc networks using simulated annealing," in Proc. IEEE WCNC, New Orleans, USA, Mar. 2003, pp. 1492-1497.
26. C. Ciftlikli, A. Kalinli, and I. Develi, "An improved formula obtained by simulated annealing for the computation of maximum SINR for DSCDMA receiver with exponentially weighted despreading function," Euro. Trans. Telecommun., vol. 17, no. 1, pp. 143-150, Jan./Feb. 2006. https://doi.org/10.1002/ett.1045