Asymptotic SER Analysis of EGC and SC in Fading and Non-Gaussian Noise and Interference

In this paper, we present a unified asymptotic symbol error rate (SER) analysis for linearly modulated signals with equal gain combining (EGC) and selection combining (SC) at the receiver. Our analysis is general enough to encompass all commonly used fading models and (possibly) non-Gaussian noise (and interference). We show that for high signal-to-noise ratios (SNRs) the SER of EGC and SC depends on the Mellin transform of the probability density function (pdf) of the noise. Since the Mellin transform can be readily obtained for all commonly encountered noise pdfs, the provided SER expressions are easy and fast to evaluate. Furthermore, we show that the diversity gain of EGC and SC only depends on the fading statistic and the number of diversity branches, whereas the coding gain depends on the modulation format, the type of fading, the number of diversity branches, the type of noise, and the combining scheme. Therefore, in a log-log scale for high SNR the SER curves of EGC and SC for different types of noise are parallel and their relative shift depends on the Mellin transforms of the noise pdfs.