Computing probability of errors of linear multiuser detectors in white Gaussian noise and Rayleigh fading channels

We present a tool for rapidly computing the bit error rate of linear multiuser detectors. Computing bit error rates of linear multiuser detectors involves averaging the probability of error over the bits of all the users which is an exponentially complex operation. The technique presented in this paper is based on computing the Laplace inversion integral of the moment generating function of the variate which determines the probability of error of a user. We apply this technique for computing the probability of error of an arbitrary linear multiuser detector operating in an additive white Gaussian noise and in a Rayleigh fading channel