Performance Analysis in Double-Rayleigh Channels with Diversity Combining Techniques

In this paper, we provide a performance analysis of communication systems over Rayleigh-product channels with two popular diversity combining techniques, namely maximal ratio combining (MRC) and selection combining (SC). We first derive new closed-form expressions for the exact cumulative distribution function (CDF) and probability density function (PDF) of the post-processing signal-to-noise ratio (SNR) for these two schemes. Secondly, we present the first-order asymptotic expansions for these CDF and PDF functions. Performance of MRC and SC techniques, in terms of outage probability, average symbol error rate (SER) and ergodic capacity, is derived using the exact expressions of CDF and PDF. Furthermore, we present new expressions for key metrics characterizing the system performance at the high and low SNR regimes. Thanks to the asymptotic CDF and PDF expressions, we compute the average SER in the high SNR regime and derive the diversity order and array gain parameters. In addition, we provide simple expressions for the ergodic capacity in the asymptotic low and high SNR regimes. Monte-Carlo simulations are conducted and their results agree well with the analytical results.