An Accurate and Efficient Approximation to the Gaussian Q-Function and its Applications in Performance Analysis in Nakagami-m Fading

Based on the semi-infinite Gauss-Hermite quadrature rule defined in [0, ∞), we present an accurate and efficient approximation to the Gaussian Q-function, which is expressed as a finite sum of exponential functions. We then extend to address the problem of a product of Gaussian Q-functions averaged over Nakagami-m fading, ending up with a closed-form solution applicable for any real m ≥ 0.5. Numerical examples show that the proposed method with only N = 2 terms can give error probabilities (in closed form) that are virtually indistinguishable from the exact results obtained by numerical integration.