Performance analysis of coherent equal gain combining over Nakagami-m fading channels

We study the exact average output signal-to-noise ratio (SNR) and symbol error rate (SER) of M-ary phaseshift-keying (PSK) signals with coherent equal gain combining reception. The analysis assumes independent Nakagami-m (1960) fading paths, which are not necessarily identically distributed. On one hand, we use geometric summations to obtain closed-form expressions for the average output SNR over diversity paths with an exponentially decaying power delay profile. On the other hand, capitalizing on an alternative integral representation of the conditional SER along with Gauss-Hermite quadrature integration, we derive an average SER expression in the form of a single finite-range integral and an integrand composed of tabulated functions. We also present a simpler but approximate approach for the closed-form evaluation of the SER of these signals over independent identically distributed Nakagami-m fading paths.