Performance Analysis of RIS-Aided THz Wireless Systems Over α−μ Fading: An Approximate Closed-Form Approach
Ngoc Phuc Le, Mohamed‐Slim Alouini
Abstract
In this article, we study a reconfigurable intelligent surfaces (RISs)-assisted Terahertz (THz) wireless systems with hardware impairments, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \!-\!\mu $ </tex-math></inline-formula> small-scale fading is considered for THz links in accordance with a recent measurement campaign. First, we propose an accurate closed-form approximation of a weighted sum of cascaded nonidentical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \!-\!\mu $ </tex-math></inline-formula> variates based on the Gauss-Laguerre quadrature and a moment-matching method. This approximate approach facilitates analysis of the RIS-THz system over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \!-\!\mu $ </tex-math></inline-formula> fading channels. To demonstrate, we derived closed-form expressions of the outage probability (OP), the ergodic capacity (EC), and the energy efficiency (EE) of the system based on the proposed approximation. Second, we approximately characterize the end-to-end channel of the RIS-THz system when the number of RIS elements is large in scenarios with or without the presence of phase-shift errors. Based on this statistical characterization, the closed-form expressions of the OP, the EC, and the EE of the large-size RIS-THz system are obtained. Furthermore, we devise a low-complexity algorithm that jointly optimizes the transmit power and RIS element activation (i.e., ON/OFF RIS) to maximize the EE in the RIS-THz systems. This algorithm adopts an iterative dynamic programming approach for a maximum subarray problem (i.e., Kadane’s algorithm). Finally, simulations are provided to validate the accuracy of the theoretical analysis as well as demonstrate the efficacy of the devised algorithm.