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Performance Analysis in Double-Rayleigh Channels with Diversity Combining Techniques

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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 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.

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Notes

  1. For the definition of slowly varying function, please see [23, 24].

  2. We note that the unconditional \(\beta ^i\) are dependent. Hence, the order statistics analysis of the unconditional SNRs is complicate.

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Authors and Affiliations

  1. NOCCS Laboratory, National Engineering School of Sousse, University of Sousse, 4002, Sousse, Tunisia

    Mohamed Lassaad Ammari

  2. Department of Electrical and Computer Engineering, University of Sherbrooke, Québec, Canada

    Sébastien Roy

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  1. Mohamed Lassaad Ammari
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  2. Sébastien Roy
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Correspondence to Mohamed Lassaad Ammari.

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Ammari, M.L., Roy, S. Performance Analysis in Double-Rayleigh Channels with Diversity Combining Techniques. Wireless Pers Commun 114, 2529–2550 (2020). https://doi.org/10.1007/s11277-020-07488-8

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