Signal detection over Rayleigh-fading channels with non-Gaussian noise

The authors deal with the problem of the detection of waveforms over fading channels with impulsive noise, modelled as a compound-Gaussian, possibly correlated process. Starting with the optimum detector, which is actually unsuited to real-time implementation, they propose a sub-optimum scheme, with reduced complexity. Moreover, they show that such a scheme can be further simplified for the important case of binary frequency shift keying signalling. For this case, a thorough performance assessment is also presented. In particular, the authors consider the case of slowly fading, frequency selective channel, and give closed-form formulas for the performance: as a case study, they focus on Laplacian noise, and assess the impact of the noise spikiness on the performance. The 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; the sub-optimum detector turns out to suffer a very limited loss, as compared to the optimum one, even for extremely low probabilities of error. Additionally, noise spikiness negatively affects the performance of both the optimum and the sub-optimum receiver, in the sense that the more impulsive the noise (i.e. the more its statistics deviate from those of Gaussian noise), the worse the performance.