Performance of optimum threshold incoherent diversity in non-Gaussian noise and fading

The optimum diversity receiver in arbitrary non-Gaussian noise and Rayleigh fading statistics is derived for binary narrowband correlated symmetric incoherent signalling in the threshold regime, i.e. for small signals and independent noise samples. Its performance is obtained in terms of the error probability P_e for various values of a specific signal crosscorrelation coefficient rho and multichannel order, when fading in the channel is assumed to be slow, nonselective Rician or Rayleigh. This expression for P_e is shown to be a generalisation of a recent performance result in optimum threshold detection of incoherent narrowband signals in narrowband non-Gaussian noise. It is graphically demonstrated that the best signalling in Rayleigh fading is orthogonal ( rho =0) and that performance significantly improves as the diversity order increases for fixed sample size N(>>1) and second-order noise statistic L⁽²⁾(>or=1). A novel by-product of the analysis is the error probability expression of the single-channel threshold incoherent receiver with Rician fading, which is used to graphically demonstrate that the signalling scheme which optimises, i.e. gives the minimum possible value of, P_e is also orthogonal.