Vol.:(0123456789) Wireless Personal Communications https://doi.org/10.1007/s11277-020-07488-8 1 3 Performance Analysis in Double‑Rayleigh Channels with Diversity Combining Techniques Mohamed Lassaad Ammari 1  · Sébastien Roy 2 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract 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 expres- sions for the exact cumulative distribution function (CDF) and probability density func- tion (PDF) of the post-processing signal-to-noise ratio (SNR) for these two schemes. Sec- ondly, 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 con- ducted and their results agree well with the analytical results. Keywords MIMO systems · Performance analysis · Rayleigh-product channels 1 Introduction Spatial diversity, which combines multiple replicas of the received signal, has long been recognized as an effective technique to mitigate fading and its impact on the performance of communication systems [1, 2]. Receiver diversity combining methods such as maximal ratio combining (MRC), equal gain combing (EGC) and selection combing (SC) are often used to combine available diversity branches [1–3]. It is well known that, in the ideal case of independent diversity branches, MRC is the optimal technique in terms of maximizing * Mohamed Lassaad Ammari mlammari@gel.ulaval.ca Sébastien Roy sebastien.roy13@usherbrooke.ca 1 NOCCS Laboratory, National Engineering School of Sousse, University of Sousse, 4002 Sousse, Tunisia 2 Department of Electrical and Computer Engineering, University of Sherbrooke, Québec, Canada