Tighter bounds on the Gaussian Q-function based on wild horse optimization algorithm

The Gaussian Q-function (GQF) is widely used in various scientific and engineering fields, especially in telecommunications and wireless communication. However, the lack of a closed-form expression for this function has led to considerable research efforts to achieve more accurate approximations. This study introduces a new approximate method that provides high accuracy for the boundaries of the GQF. The proposed approach utilizes parametric functions for both the lower and upper bounds of the GQF. The parameters of these functions are estimated using the Wild Horse Optimization (WHO), a meta-heuristic optimization algorithm, with the aim of minimizing the distance between the proposed functions and the actual GQF. The optimization process targets the minimization of the maximum absolute error and the mean absolute error, ensuring that the proposed bounds provide a tight and accurate approximation of the GQF. Numerical experiments and comparisons with existing bounds demonstrate the superior accuracy of the proposed method. The new lower and upper bounds achieve significantly lower maximum absolute error and mean absolute error values compared to previous approaches. Furthermore, the study evaluates the effectiveness of the proposed bounds in estimating the symbol error probability (SEP) for various digital modulation schemes, showing that the new bounds provide more accurate estimates of the SEP compared to the existing bounds. The results highlight the practical significance of the proposed method in enhancing the reliability of error probability estimation in communication systems.