Versatile, Accurate, and Analytically Tractable Approximation for the Gaussian Q-Function

The existing approximations for the Gaussian Q-function have been developed bearing in mind applications that require high estimation accuracies (e. g., derivation of the error probability for digital modulation schemes). Unfortunately, the associated mathematical expressions are too complex to be easily employed in many other analytical studies, even if they do not require such a high accuracy. This letter proposes a simple, yet accurate mathematical approximation to the Gaussian Q-function. When compared to other existing approximations, the proposed model provides an adequate balance between accuracy and analytical tractability. Its simplicity enables its application over a wider range of analytical studies at reasonable accuracy levels. As an illustrative example, the proposed approximation is employed to obtain a new and simple closed-form expression for the probability of detection of an energy detector under Rayleigh fading channels.