A New Accurate Approximation of the Gaussian Q-Function with Relative Error Less Than 1 Thousandth in a Significant Domain

The approximations of the Gaussian Q-function found in the literature have been often developed with the goal of obtaining high estimation accuracies in deriving the error probability for digital modulation schemes. Unfortunately, the obtained mathematical expressions are often too complex, even difficultly tractable. A new approximation for the Gaussian Q-function is presented in the form of the standard normal density multiplied by a rational function. The rational function is simply a linear combination of the first 5 integer negative powers of the same term, linear in x, using only 4 decimal constants. In this paper we make some considerations about the significant interval where to consider the Q-function in telecommunication theory. The relative error in absolute value of the given approximation is less than 0.06% in the considered significant interval.