Optimized Selection Diversity for Rayleigh Fading Channels

This paper considers the choice of the number of diversity branches for minimizing the bit error rate of a selection diversity system using noncoherent binary frequency-shift keying modulation for transmission over a Rayleigh fading Gaussian channel. An exact expression for the optimum number of branches, , is given. The resulting probability of bit error decreases exponentially with the square root of the energy per bit.