Transmission errors in companded PCM over Gaussian and Rayleigh fading channels

Transmission errors in mu-law pulse-code-modulated systems are capable of inflicting considerable distortion in the recovered analog signals. This distortion is analyzed for the case when the transmission is over radio channels, and when either noncoherent frequency shift keying or coherent phase shift keying (CPSK) modulation is employed. Both Gaussian and Rayleigh fading channels are considered, and for the latter, the effect of bit scrambling prior to transmission and two types of diversity are investigated. 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 is determined. In addition to the theoretical results, computer simulations are presented of mu-law pulse-code-modulated encoded speech transmitted over the same channels, using CPSK modulation, bit scrambling, and diversity where appropriate.