Cascaded and Sum of Cascaded Over <inline-formula><tex-math notation="LaTeX">$\boldsymbol{\alpha }$</tex-math></inline-formula>&#x2013;<inline-formula><tex-math notation="LaTeX">$\boldsymbol{\mathcal {F}}$</tex-math></inline-formula> Fading Channels With Pointing Error Impairment

Abstract

In this article, exact expressions are presented for the probability density function, cumulative distribution function, moment generating function, and higher-order moments of the instantaneous signal-to-noise ratio, considering the product and the sum of the products of $N$ $\alpha$-$\mathcal {F}$ variates with pointing errors. New expressions for the outage probability (OP), bit error probability (BEP), ergodic channel capacity, and the area under the receiver operating characteristics (AUC) are deduced, as well as the asymptotic ones. The obtained expressions are used to assess the influence of various channels and system parameters on the system performance. We analyze a scenario considering dual-hop terahertz links and another regarding reconfigurable intelligent surfaces (RIS)-assisted systems. All expressions derived in this work are new, and Monte Carlo simulations corroborate the analytical curves shown.

Keywords

• $\alpha$ - $\mathcal {F}$ fading%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> </named-content>-<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX">$\mathcal {F}$</tex-math> </inline-formula> fading
• AUC
• BEP
• capacity
• OP
• pointing errors