The $α$-$η$-$\mathcal{F}$ and $α$-$κ$-$\mathcal{F}$ Composite Fading Distributions

Abstract: In this paper, we present the $\alpha$-$\eta$-$\mathcal{F}$ and $\alpha$-$\kappa$-$\mathcal{F}$ composite fading distributions. The two distributions generalize the two well-known composite fading distributions, namely the $\eta$-$\mu$/inverse gamma and the $\kappa$-$\mu$/inverse gamma distributions. For both distributions, we derive new exact closed-form expressions for the probability density function (PDF) and cumulative density function (CDF) of the instantaneous signal-to-noise ratio (SNR). Additionally, the outage probabilities (OPs) of a wireless communication system operating over the new composite fading channels are obtained. Moreover, we derive asymptotic OPs, in the high SNR regime, to gain more insight into the influence of fading parameters. Some numerical results on the envelope PDFs and OPs are provided and compared with Monte-Carlo simulation results to validate the analyses.