Performance Analysis of RIS-Aided THz Wireless Systems over α-μ Fading: An Approximate Closed-Form Approach

In this paper, we study a reconfigurable intelligent surfaces (RIS)-assisted Terahertz (THz) wireless systems with hardware impairments, where α-μ small-scale fading is considered for THz links in accordance with a recent measurement campaign. Firstly, we propose an accurate closed-form approximation of a weighted sum of cascaded non-identical α-μ variates based on the Gauss-Laguerre quadrature and a moment-matching method. This approximate approach facilitates analysis of the RIS-THz system over α-μ 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. Secondly, 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.