Dual-Hop Relaying Communications Over Fisher-Snedecor F-Fading Channels

In this paper, we present a comprehensive framework for the performance analysis of dual-hop relaying communications with variable gain amplify-and-forward (AF) relays and operating in the presence of both multipath fading and shadowing, modeled by the Fisher-Snedecor <inline-formula> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula>-distribution. Novel closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) of the considered system subject to hardware impairments are first derived. Single-integral expressions for the numerical evaluation of the <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-th moment of the end-to-end SNR, the outage probability (OP), the ergodic capacity under different adaptive transmission schemes, the effective capacity and the average bit error rate (ABER) of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary modulation schemes are further presented. The proposed analytical expressions are valid for most of the well-known fading distributions, provided that the moment generating function (MGF) of the inverse SNR of each hop is readily available. For the special case of ideal hardware, it is shown that the above performance metrics can be expressed in closed-form. It is worth pointing out that the proposed analysis is valid even when the destination node is equipped with multiple antennas and maximal ratio combining (MRC) is employed. The correctness of the proposed mathematical analysis is validated through extensive numerically evaluated results accompanied with Monte-Carlo simulations.

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