Binary Error Rate Caused by Intersymbol Interference and Gaussian Noise

The probability of error in a binary signal owing to intersymbol interference and Gaussian noise is computed by approximation of the expression for the probability of error by a finite sum of squareintegrable functions. The approximating functions should be chosen so that their averages over all bit combinations can be easily determined. The projection of the error function on the subspace of polynomials results in a series which converges more rapidly to the exact error rate than does the Taylor series expansion used previously. The negative exponential functions have the same general form as the error function and, as expected, also result in rapid convergence to the average error rate.