Log-likelihood ratio based generalized selection combining for M-ary signaling

We present a generalized selection combining (GSC) of M-ary signals that selects K out of L diversity branches based on the log-likelihood ratio (LLR). The motivation for using the LLR in selecting diversity branches is that the magnitude of LLR provides the reliability of hard decision and the LLR-based hard decision minimizes the bit error probability. It is shown that the proposed LLR-based GSC rule provides a significant power gain over the conventional SNR-based GSC rule, and the power gain increases with decreasing alphabet size and decreasing number of selected branches. We also present suboptimum LLR-based GSC rules that require a less computation, but provide virtually identical performance as the LLR-based GSC rule.