Optimum detection over Rayleigh-fading, dispersive channels, with non-Gaussian noise

The paper discusses the problem of detecting one out of M Gaussian correlated signals in impulsive noise, modeled as a compound-Gaussian, possibly correlated process. We first show that, for uncorrelated noise, the detection problem admits one and the same optimum-in the sense of attaining minimum error probability-solution, independent of the noise statistics: the optimum detector, in fact, amounts to an estimation block, aimed at measuring the short-time noise power spectral density (PSD), whose output is fed to a bank of estimators-correlators, each keyed to one of the M admissible waveforms and to the estimated noise PSD. We also give suggestions for realizing a suboptimum receiver, with reduced complexity, which again is canonical in its structure. As for the performance analysis, we focus on binary frequency-shift keying (BFSK) signaling: we provide numerical results for two particular channel correlations and for Cauchy-distributed noise. These results indicate that, like for the general Gauss-Gauss case, the performance depends on the energy contrast, as well as on the "time-bandwidth" product of the useful signal. Moreover, noise spikiness seems to negatively affect the performance, in the sense that heavier and heavier high-amplitude tails of the noise marginal distribution give rise to higher and higher error probabilities for fixed energy contrast and time-bandwidth signal product.