Second Order Statistics of -Fisher-Snedecor Distribution and Their Application to Burst Error Rate Analysis of Multi-Hop Communications

Abstract

An advantage of using the composite fading models (CFMs) is their ability to concurrently address the impact of multi-path and shadowing phenomena on the system performance in wireless communications. A Fisher-Snedecor (FS) F CFM has been recently proposed as an experimentally verified and tractable fading model that can be efficiently applied for 5G and beyond 5G wireless communication systems. This paper provides second-order (s-order) performance analysis of the product of N independent but not identically distributed (i.n.i.d) FS F random variables (RVs). In particular, accurate and closed-form approximations for level crossing rate (LCR) and average fade duration (AFD) of the product of N i.n.i.d FS F (N-FS F) RVs are successfully derived by exploiting a general property of a Laplace approximation method for evaluation of the N-folded integral-form LCR expression. Based on the obtained s-order statistical results, the burst error rate and maximum symbol rate of the N-FS F distribution are addressed and thoroughly examined. The numerical results of the considered performance measures are discussed in relation to the N-FS F multi-path and shadowing severity parameters. Moreover, the impact of the number of hops (N) of the N-FS F CFM on the s-order metrics, the burst error rate and maximum symbol rate are numerically evaluated and investigated. The derived s-order statistical results can be used to address the cooperative relay-assisted (RA) communications for vehicular systems. Monte-Carlo (M-C) simulations for the addressed statistical measures are developed in order to confirm the provided theoretical results.

Effective Energy Efficiency under Delay–Outage Probability Constraints and F-Composite Fading

“…Likewise, ref. [23] assessed the second-order statistics of the Fisher-Snedecor distribution, notably in their application in burst error rate analysis of multihop communications, while [24] assessed the receiver switched diversity combining schemes under the same distribution. These studies are significant contributions with innovative models and analytical frameworks for understanding and mitigating fading effects in IoT networks, thus building reliable and efficient communication systems.…”

On the second order statistics of the ratio of two Fisher-Snedecor random variables and its application to interference limited communications

“…The second order statistics (SO-S) in terms of level crossing rate (LCR) and average fade duration (AFD) of FS-F distribution are provided in (Yoo et al, 2019) while the LCR and AFD of the product of two FS-F RVs are provided in (Stefanovic et al, 2021a). SO-S of N-FS-F fading model and their application to multihop communications are provided in (Stefanovic et al, 2021b(Stefanovic et al, , 2022b. Moreover, SO-S over cascaded N-Gamma-gamma (N-GG) fading channels are investigated in (Stefanović et al, 2021).…”