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

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2 Author(s)
Qinghua Shi ; Dept. of Electron. Eng., Univ. of Electro-Commun., Chofu, Japan ; Karasawa, Y.

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.

Published in:

Communications Letters, IEEE  (Volume:15 ,  Issue: 5 )