Optimum selection combining for M-QAM on fading channels

In this paper, we present the optimum selection combining (SC) scheme for M-QAM which minimizes the average bit error rate (BER) on fading channels. We show that the selection combining scheme, where each bit in a QAM symbol selects the diversity branch with the largest magnitude of the log-likelihood ratio (LLR) of that bit, is optimum in the sense that it minimizes the average BER. In this optimum SC scheme, different bits in a given QAM symbol may select different diversity branches (since the largest LLRs for different bits may occur on different diversity branches), and hence its complexity is high. However, this scheme provides the best possible BER performance for M-QAM with selection combining, and can serve as a benchmark to compare the performance of other SC schemes (e.g., selection based on maximum SNR). We compare the BER performance of this optimum SC scheme with other SC schemes where the diversity selection is done based on maximum SNR and maximum symbol LLR.