A framework for Gaussian Q approximation with BSA and its application to RIS-assisted systems

Abstract

This paper proposes a novel and improved Chiani approximation for the Gaussian Q-function by employing the backtracking search optimization algorithm (BSA). The proposed approximation includes only exponential terms which are comfortable for the mathematical functionality. Then, a wireless communication application of reconfigurable intelligent surface (RIS) structures, which are anticipated to play a crucial role in integrated sensing and communication (ISAC), has been presented. In the considered wireless communication scenario, the link between the source and RIS node is Nakagami-m fading, while the link between RIS node and the destination is Rayleigh fading. The received probability density function (PDF) expression of instantaneous signal to noise ratio for this system has been derived analytically. Using this derived PDF, the error expression ($P_e$) for the RIS-assisted communication system employing the rectangular quadrature amplitude modulation (RQAM) technique has been obtained with the assistance of the proposed improved Chiani approximation in this study. The obtained RQAM error figures are presented comparatively, and the results clearly show that the $P_e$ expression by obtained the proposed approximation with BSA for the RIS-assisted communication system, which is an important aspect for ISAC, is in excellent agreement with computer simulations.