Novel Range Wise Optimization of the Exponential Bounds on the Gaussian Q Function and its Applications in Communications Theory

This paper presents a novel and highly effective method for improving the accuracy of approximations for the Gaussian Q function. By rigorously optimizing the coefficients of the approximations using the interior point optimization technique, significantly tighter bounds are achieved with simplicity intact. The proposed approach, which is applicable to a wide range of scenarios, focuses on enhancing the simple exponential bounds proposed in the literature. Through a comprehensive analysis based on the relative error, the superiority of the optimized coefficients compared to the existing bounds and approximations available in the open literature is demonstrated. Moreover, an insight into the generic applicability of the optimized coefficients is provided, which exhibits excellent performance in terms of the absolute error as well. The Gaussian Q function plays a crucial role in evaluating the performance of diverse wireless communication systems under various challenging fading distributions. Therefore, the proposed research significantly contributes to advancing the accuracy of the approximations of the Gaussian Q function, enabling improved error performance for coherent digital modulation techniques. The findings presented herein offer valuable contributions to the state-of-the-art and set a new standard for accuracy in the work related to Gaussian Q function approximations.