Gaussian Q Function Approximation in Wireless Communication System’s Design: A Gradient-Based Optimization Approach

This paper proposes a novel iterative gradient-based optimization approach aimed at achieving more precise and streamlined approximations for the Gaussian Q function—an essential element in communication system’s design. Our optimization strategy involves determining optimal weights for exponential functions within a defined range of the argument (x) of the Gaussian Q function. The primary goal is to iteratively minimize the error or cost function, progressively refining local minima across successive iterations. The results strikingly highlight the exceptional accuracy of our proposed approach in approximating the Gaussian Q function, positioning it as a robust contender for real-world communication system’s design. Importantly, our method showcases a clear superiority in accuracy over prevailing techniques. Moreover, to comprehensively evaluate the efficacy of our approach, we simplify the key metrics like symbol error probability (SEP) of various coherent digital modulation techniques over a versatile multi-cluster fluctuating two-ray fading model, which includes majority of the classical fading models like Rayleigh, Nakagami- $m,q$ , Rician, Rician-shadowed, fluctuating two-wave, two-wave with diffused power, etc. As an application example, the numerical results of the SEP of square quadrature amplitude modulation (SQAM) are validated against the exact results obtained via MATHEMATICA software package. In addition, a comparative analysis on the time required to compute the exact and proposed SEP values is also highlighted in this paper. The asymptotic SEP is also derived which gives an idea on the diversity order of the system. Lastly, extensive Monte-Carlo simulations have also been carried out to validate the proposed work.