A proof that uncorrelated branch SNRs yield the lowest error rate for MRC receivers operating over Nakagami-m-fading channels

We analyze the symbol error rate of a multiple-branch predetection maximal ratio combiner for correlated Nakagami-m-fading channels. Focusing on the correlations between diversity branches, we provide a simple analytic proof, applicable to different modulation schemes, that uncorrelated branches result in the lowest symbol error probability. First, we present a proof assuming that all branches have the same fading severity m, where m can be a noninteger. We then present a proof for the case where the branches have different but, integer-valued fading severities (ms).