Optimum diversity detection over fading dispersive channels with non-Gaussian noise

We consider the problem of M-ary signal detection over a single-input-multiple-output (SIMO) channel affected by frequency-dispersive Rayleigh-distributed fading and corrupted by additive non-Gaussian noise, modeled as a spherically invariant random process. We derive both the optimum detection structure and a suboptimal, reduced-complexity receiver, based on the low-energy-coherence approach. Interestingly, both detection structures are canonical, i.e., they are independent of the actual noise statistics. We also carry out a performance analysis of both receivers, with reference to the case that the channel is affected by a frequency-selective fading and for a binary frequency-shift-keying signaling format. The results obtained through both a Chernoff-bounding technique and Monte Carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non-Gaussian noise. Interestingly, it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum (unrealizable) receiving structure