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Minimum error-probability diversity detection over fading dispersive channels with non-Gaussian noise

In this work we consider the problem of M-ary signal detection over a single-input-multiple-output channel affected by time- and/or frequency-dispersive Rayleigh-distributed fading and in the presence of non-Gaussian noise, modeled as a spherically invariant random process (SIRP). We derive the optimum (minimum error-probability) detector, and show that its structure is canonical, i.e. it is independent of the actual noise statistics. Finally, the performance analysis of the receiver highlights that the adoption of diversity represents a suitable means to restore performance also in the presence of dispersive fading and impulsive non-Gaussian noise.