Soft Decision Demodulation to Reduce the Effect of Transmission Errors in Logarithmic PCM Transmitted Over Rayleigh Fading Channels

Abstract

In this paper we investigate soft decision demodulation applied to μ-law Pulse Code Modulated (PCM)-encoded signals transmitted over Rayleigh fading channels by means of coherent phase-shift keying modulation. Each bit in the μ-law PCM word is assigned its own soft decision demodulation erasure threshold. These thresholds are theoretically determined as a function of the input power level, channel s/n, and the relative mean square error power δ that occurs because of the replacement by interpolation or prediction of those samples discarded in the soft decision demodulation process. We find that there is no advantage in applying soft demodulation to more than the first 4 bits of the 8-bit μ-law PCM words, μ = 255. When the input signal level was −17 dB (corresponding to peak overall speech s/n in the absence of transmission errors), the gains in overall speech s/n compared to basic μ-law PCM and fixed weighted μ-law PCM were 7 and 3.5 dB, respectively, when the channel s/n was 30 dB. More significantly, when the input signal level was reduced to −40 dB, the corresponding gains in overall speech s/n were 18 and 12 dB. Simulations were performed using four concatenated speech sentences and a fading channel that was obtained from a mobile radio Rayleigh fading hardware simulator. The simulations were in reasonable agreement with our theoretical results.