Optimum selection combining for M-ary signals in frequency-nonselective fading channels

We present the optimum selection-combining (SC) rule for M-ary signals based on the log-likelihood ratio (LLR) in frequency-nonselective, independent and nonidentically distributed fading channels. The motivation for using the LLR in selecting the diversity branch is that it provides the reliability information of the maximum a posteriori probability decision which minimizes the probability of symbol error. We present coherent and noncoherent optimum SC rules with and without fading information that minimize the probability of symbol error. It is shown that the optimum SC rule provides a significant power gain over the conventional signal-to-noise ratio-based SC rule, and the power gain increases with an increasing number of available diversity branches and decreasing alphabet size. We also present suboptimum SC rules that require less computation, but provide a power gain close to that provided by the optimum SC rule.