Binary communications through noisy, non-Gaussian channels

New and unifying analytical tools are developed and used to evaluate the bit error probability, false alarm and detection probabilities that result when binary information is communicated through a random channel further disturbed by additive white Gaussian noise. The class of channels modeled here are those which envelop the received electric field with an arbitrary space-time complex envelope. The complex Gaussian envelope, being a special case, yields the Rayleigh and Rice fading statistics. Considerable insight into the problem of communicating through a complex non-Gaussian fading channel is obtained by decomposing the performance measures into the sum of two terms, viz., one attributable to the usually assumed complex Gaussian envelope plus a residual performance term expressed as a series expansion in terms of multidimensional Hermite polynomials whose coefficients are the channel quasi-moments. Finally, a numerical example is presented in which the theory is applied to a specific non-Gaussian channel.>