Diversity Reception Through Complex Non-Gaussian, Noisy Channels

In this paper, 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, viz., 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 Class A pdf.