Diversity reception of fading signals in spherically invariant noise

The problem of noncoherent diversity reception of one out of M equally likely signals is addressed. The signal on each diversity channel is affected by slow and nonselective fading with an arbitrary distribution law, and is subject to additive correlated non-Gaussian noise modelled as a spherically invariant random process. An asymptotically (i.e. for large sample size) optimum receiver is synthesised, whose structure depends on the noise on each diversity channel only through its correlation function, but is otherwise independent of the noise distribution. With reference to Rayleigh fading on each channel, the performance, in terms of bit-error rate, of the proposed asymptotically optimum receiver is assessed, via computer simulations, by considering the transmission of an orthogonal signal set and adopting the generalised Cauchy model for the univariate distribution function of the noise. It is shown that the performance degradation with respect to the fully optimum performance is scarcely significant even for low values of the sample size. Moreover, in highly non-Gaussian noise the proposed receiver significantly outperforms the fully optimum receiver synthesised under a Gaussian noise assumption, which exhibits the same implementation complexity