Efficient evaluation of probabilities of detection and the generalized Q-function (Corresp.)

Abstract

A highly efficient method of evaluating probabilities of detection and the generalized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\cal Q</tex> -function to within an absolute accuracy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> is presented. Many unnecessary computations are avoided when it can be determined by Chernoff bounds that the desired function is within <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> of 0 or 1. When this is not the case, efficient algorithms for the necessary computations are also provided.