## 1 Introduction
Motivated by the above observation, we will try to fill this gap and provide a comprehensive systematic investigation and certain significant insights about SSC, SEC, and SECps schemes in terms of their potential applications (such as device-to-device, wearable, and Internet of Things applications) over Fisher-Snedecor \(\mathcal{F}\) fading channels. Hence, the main contributions of this paper are summarized as follows:  
1. We derive an exact and novel analytical expression of the probability density function (PDF) for bivariate Fisher-Snedecor \(\mathcal{F}\) distribution with arbitrary fading parameters, along with its compact form, using the generalized Lauricella series function. 2. The analytical expressions of the statistical properties of the output SNR for a dual-branch SSC scheme are deduced in different \(\mathcal{F}\) scenarios, including independent or correlated and identical or non-identical fading cases. To reduce complicated calculations, only the i.i.d. case is considered for SEC and SECps. Noted that some novel analytical expressions of the moment-generating function (MGF) and the \(g\)th \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Research Topic** & **System Models** & **Fading Channels** \\ \hline
[2] & Indoor off-body communication & SSC, SEC, and SECps & Nakagami-m \\
[18] & Outdoor wearable communication & SSC, SEC, and SECps & Nakagami-m \\
[19] & Ultra-ultraviolet communications & SSC & gamma-gamma \\
[20] & Multiuser ultraviolet communication & SSC & gamma-gamma \\
[21] & Low-power ultra-reliable low-latency & PSC and SSC & Nakagami-m \\ downlink communications & & & \\
[22] & Multichannel spectrum sensing & PSC and SSC & correlated Nakagami-m \\
[23] & Indoor millimeter wave communications & SSC and SEC & Rayleigh \\
[24] & Multiuser downlink wiretap networks & SECps & Nakagami-m \\
[25] & Mobile edge computing network & PSC and SSC & Nakagami-m \\
[26] & free space optical communications & distributed 8 SC & generalized Malaga and Gamma-Gamma \\
[27] & Multi-relay networks & SECps & shadowed Rician \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A list of SDC schemes used in some emerging wireless communications applications. moments of the output SNR for the SECps scheme are presented in the context of the multivariate [PERSON]'s H-function. 3. A thorough performance investigation of SSC, SEC, and SECps is presented. The performance metrics of interest comprise the average SNR, amount of fading (AoF), outage probability (OP), average bit error probability and average symbol error probability (ABEP/ASEP), and the average channel capacity. In particular, a novel and exact expression of the ASEP of M-ary quadrature amplitude modulation (MQAM) is also obtained in terms of the multivariate Fox's H-function. Furthermore, the optimal analysis of the performance metrics in the i.i.d. case is discussed in detail. 4. Based on the numerical analysis and simulations, certain significant insights are obtained as follows: (i) the impact of the multipath parameter on the system performance is more than those of the other parameters, including the shadowing parameter, the correlation coefficient, and the average SNR; (ii) to explore the potential gains of the SDC systems, the switching threshold should not be too large or too small compared to the average SNR, and there exists an optimal threshold for optimal performance under certain fading scenarios; (iii) SEC and SECps with more than two branches can provide more benefits than SSC when an appropriate switching threshold is chosen. Note that the above new insights will be meaningful and help to enhance the system reliability in the design and deployment of future communications systems. The remainder of this paper is organized as follows. In Section 2, the statistical properties of the bivariate Fisher-Snedecor \(\mathcal{F}\) composite distribution are studied.