Accurate Approximation to Channel Distributions of Cascaded RIS-Aided Systems With Phase Errors Over Nakagami-<i>m</i> Channels
Zhandos Zhakipov, Khaled M. Rabie, Xingwang Li, Galymzhan Nauryzbayev
Abstract
Reconfigurable intelligent surfaces (RISs) are a promising technology foreseen to drive the development of beyond-fifth-generation (B5G) wireless networks. This letter proposes a novel accurate approximation to the channel distribution of cascaded RIS-aided wireless networks, with a reasonable assumption of phase errors, over Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> fading channels. Using the approximation, the probability density function (PDF) and outage probability (OP) expressions are derived for the end-to-end cascaded RIS-aided communication. Obtained PDF and OP formulas are valid for any number of cascaded RISs, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> , and reflecting elements per individual RIS, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> . The approximation accuracy is validated using the Kolmogorov-Smirnov goodness-of-fit test. Analytical results are verified by Monte Carlo simulations under different system parameters. Finally, derived expressions have been used to illustrate the impact of various important system parameters on the outage performance of the proposed system.