An analytically tractable approximation for the Gaussian Q-function

In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics. The approximation enables derivation of closed-form expressions for metrics such as average symbol, bit and block error probabilities which are known to be analytically involved as they require computation of the expectation of Q-function and its integer powers, for any m of Nakagami-m fading. The tightness of the approximation is verified by simulations. The usefulness of the approximation is demonstrated by obtaining a simple closed-form expression for the average symbol error probability of differentially encoded QIPSK in Nakagami-m fading.