Optimum selection combining for M-ary signals in fading channels

We present the optimum selection combining for M-ary signaling based on the log-likelihood ratio that minimizes the probability of symbol error. Then, we present the noncoherent optimum selection combining that does not require knowledge of the signal phases on each branch. Numerical results indicate that a significant gain over the SNR-based selection combining can be provided by the proposed optimum selection combining. Finally, we present a suboptimum selection combining that requires a lower complexity, but provides a power gain close to that of the optimum selection combining.