Weighting strategies for companded PCM transmitted over Rayleigh fading and Gaussian channels.

Three methods of weighting N-bit mu-law PCM with binary modulation are presented, and their performances theoretically evaluated for transmission over Rayleigh fading and Gaussian channels. The digital modulation methods considered are non-coherent frequency shift keying (NCFSK) and coherent phase shift keying (CPSK). Ideal selection combining (ISC) and ideal maximal ratio combining (IMRC) diversity techniques are employed when the transmission is over fading channels. Weighting System 1 is the conventional weighted PCM system where the bits in every PCM word have the same weighting profile. Weighting System 2 has 2(N) unique weighting profiles, while System 3 has an addendum to System 2 where every bit in a particular word is further weighted by a unique multiplicative factor. For Rayleigh fading channels and the encoder operating at an input level that provided maximum signal-to-quantization noise- ratio we obtained gains in overall S/N over unweighted mu- law PCM of 3, 4.5 and 6 dB for Systems 1, 2 and 3, respectively.