A unified treatment is presented for the problem of detecting binary data transmitted over an L-fold diversity complex non-Gaussian channel further disturbed by additive white Gaussian noise. The data is extracted using a quadratic form detector driven by the outputs from a cross-correlation detector matched to the transmitted signals. By employing a probability density function (PDF) expansion technique, the bit error probability is decomposed into a Gaussian and a non-Gaussian component. Our results, being valid for the doubly dispersive (space and time) channels, are reduced to expressions which characterize the performance for other channel types, viz., the wide-sense stationary uncorrelated scattering (WSSUS), the temporally-dispersive spatially-nondispersive, the temporally-nondispersive spatially-dispersive, and the totally nondispersive channel. A coherence matrix is defined which allows us to treat three types of diversity reception, vis., noncoherent, partially coherent, and coherent detection with a noisy phase reference. Detailed performance analysis of the noncoherent case is presented and used to numerically evaluate system performance over a non-Gaussian channel modeled by the Middleton (1977) class A PDF.>

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.>

Decision variables in numerous practical systems can frequently be characterized using a Hermitian quadratic form in complex Gaussian variates. Performance analysis involving these variates requires a complete description of the statistical distribution of the quadratic form. Such a complete description is presented. The method used is based on inverting the characteristic function of the quadratic form by solving a number of convolution integrals. The results presented include two forms for the probability density function (PDF), an expression for the cumulative distribution function (CDF), and expressions for the distribution moments and cumulants. These results are shown to reduce to previously known results for some special cases. Relations of the quadratic form and its CDF to the noncentral chi /sup 2/ (chi-square) and the complex noncentral Wishart distributions are exposed. Evaluation of the CDF at the origin is shown to reduce to the doubly noncentral F-distribution due to R. Price (1962, 1964). A generalization of the Marcum Q-function is also identified and suggested.>