Hard-limited versus linear combining for frequency-hopping multiple-access systems in a Rayleigh fading environment

In comparing two proposed frequency-hopping mobile radio systems for digitized speech, Goodman et al. have observed that the system employing multiple frequency-shift keying (MFSK) can accommodate many more users than the one with differential phase-shift keying (DPSK). Besides the difference in modulation methods, the MFSK system uses hard-limited combining while the DPSK one uses linear combining. Upper bounds are obtained on the probability of error for DPSK systems with hard-limited combining and linear combining. These bounds suggest that the DPSK system with hard limiters can support about twice as many users as the original one.