Analysis of BFSK frequency-hopped spread-spectrum multiple-access over a Rayleigh fading channel

Frequency-hopped spread-spectrum multiple-access over a Rayleigh fading channel is considered when the modulation used is noncoherent BFSK. An expression for the probability of a code symbol error as a function of the number of users, the number of sub-bands and the signal-to-noise ratio is derived. This expression is easily evaluated numerically, and is used to find the code rate that maximizes the throughput for a predetermined error probability when binary BCH codes are employed. The cutoff rate for the random ensemble of codes is also studied, and the result is compared with the performance of specific codes. Further, the effect of background noise, often neglected in this type of problem, is studied and its impact on the performance of the system is found to be severe