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Using Log Likelihood Relation for BER Analysis of QAM in Space Diversity

Md.Zahangir Alam 1, Chowdhury Sajadul Islam 2, and M. Abdus Sobhan 2
1. Dept. of Electronics and Telecommunication Engineering, Prime University, Bangladesh
2. School of Engineering and Computer Science, Independent University, Bangladesh (IUB)

Abstract— The bit error rate (BER) performance for quadrature amplitude modulation (QAM) with different diversity combining scheme is derived for Rayleigh fading channel using Log-likelihood ratio (LLR). In this paper, four diversity combining techniques such as, Maximal Ratio Combiner (MRC), Selection Combiner (SC), Equal Gain Combiner (EGC), and Switching Combiner (SCC) are considered for the BER analysis of QAM symbol through a Raykeigh fading channel. The average BER performance of QAM symbol through a flat fading channel is derived from the individual bits forming the QAM symbol with MRC, SC, EGC, and SCC space diversity. The analytical and simulated result of the BER performance of the QAM symbol through the same channel with MRC, SC, EGC, and SCC diversity combiner is shown and compared to each other to find which combiner provides better BER performance. . The both analytical and simulation result shows that the probability of bit error decreases with the order of diversity for all the cases of MRC, SC, EGC, and SCC. It is also seen from the results that MRC provides better BER performance than the other combiners (such as SC, EGC, and SCC). It is observed from the results that LLR-space diversity based formulation gives the best BER performance among all. 

Index Terms— Rayleigh fading channel, QAM, Diversity, Diversity combiner, LLR

Cite:Md.Zahangir Alam, Chowdhury Sajadul Islam and M. Abdus Sobhan, "Using Log Likelihood Relation for BER Analysis of QAM in Space Diversity," Journal of Communications, vol. 4, no.6, pp.371-379, 2009.