Weighting Strategies for Companded PCM Transmitted Over Rayleigh Fading and Gaussian Channels

Abstract

We present three methods of weighting N-bit μ-law Pulse Code Modulation (PCM) with binary modulation, and evaluate their performances theoretically for transmission over Rayleigh fading and Gaussian channels. The digital modulation methods considered are noncoherent frequency shift keying and coherent phase shift keying. Ideal selection combining and ideal maximal ratio combining diversity techniques are employed when the transmission is over fading channels. Weighting System 1 is the conventional weighted pulse code modulated system, where the bits in every PCM word have the same weighting profile. Weighting System 2 has 2N 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 signal-to-noise ratio (s/n) over unweighted μ-law PCM of 3, 4.5, and 6 dB for Systems 1, 2, and 3, respectively. When the systems were used in conjunction with Gaussian channels, the corresponding gains were 10, 12, and 17 dB, for a channel s/n of 10 dB. In addition to the theoretical results, we conducted computer simulations using four concatenated speech sentences transmitted via our weighted μ-law PCM systems over mobile radio channels. The simulation performances were in good agreement with our theoretical results, which were based on input signals having an exponential distribution.