Optimum detection of fading signals in impulsive noise

This paper deals with the synthesis and the analysis of optimum receivers to detect one out of M equally likely, equi-energy, fading signals in impulsive noise, modelled as a compound Gaussian, possibly correlated process. We show that the conventional coherent and incoherent detectors are still optimum, independent of the noise as well as the fading probability density functions. The performance analysis has been carried on with reference to the general case of arbitrarily distributed disturbance: in order to simplify the analysis, asymptotical expressions have been developed for high signal-to-noise ratios as well as high signal space dimensionality. Interestingly enough, this allows separating the effect of the noise spikyness from that of the fading law. Results indicate that, for deep fading, the noise marginal distribution does not dramatically affect the error probability, nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions. For non-fluctuating signals, instead, the noise distribution plays a primary role: spiky noise usually produces performance impairment; moreover, the limit performance in impulsive disturbance may exhibit marked deviations from the well-known stepwise shape which is typical of Gaussian channels