Optimum threshold diversity reception of binary noncoherent frequency shift keying

The optimum diversity rule for reception of binary noncoherent frequency-shift keying in slow and nonselective Rayleigh fading (multipath) and additive non-Gaussian noise is derived for the critically important threshold case (of small nonvanishing signals and large sample size). The relevant expression for the probability of error illustrates the significant improvement achieved, even with a small number of diversity channels, i.e. 20-30 dB gain from two to five channels for 10^-5 error probability.