Evaluation of the Q Function

A convenient method of evaluating the Q function over the parameter space quarter plane is presented. The Q function is first expressed as an infinite series. The N term truncated series Q_{N}(a, b) is used to approximate Q(a, b) for a^{2} + b^{2} \leq R where the choice of N depends on the accuracy desired and R is determined by considerations such as computer bit capacity, computational time, and accuracy. For a^{2} + b^{2} > R , alternate expressions are used. When b - a \geq d , we approximate Q by 0, and when b - a \leq d , we approximate Q by 1. The accuracy is dependent on the choice of the constant d . In the reniainder of the quarter plane, a^{2} + b^{2} > R and | b - a , and an efficient expression is used, but it is of limited accuracy (from 10-5to 10-9) near the line a = b .