Transmission Errors in Companded PCM Over Gaussian and Rayleigh Fading Channels

Abstract

Transmission errors in μ-law pulse-code-modulated systems are capable of inflicting considerable distortion in the recovered analog signals. We analyze this distortion when the transmission is over radio channels, and when either noncoherent frequency shift keying or coherent phase shift keying (CPSK) modulation is employed. We consider both Gaussian and Rayleigh fading channels, and for the latter we investigate the effect of bit scrambling prior to transmission and two types of diversity. We determined the gain in overall signal-to-noise ratio due to using the minimum distance code compared to the conventional folded binary code for low values of input signal power. In addition to the theoretical results, we present computer simulations of μ-law pulse-code-modulated encoded speech transmitted over the same channels, using CPSK modulation, bit scrambling, and diversity where appropriate, i.e., for the same conditions as employed in the derivation of our theory.