Bounds on the pairwise error probability of coded DS/SSMA communication systems in Rayleigh fading channels

Abstract

Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh fading channel are derived. A new set of probability density functions (PDFs) and cumulative distribution functions (CDFs) of the multiple-access interference (MAI) statistic is derived, and a modified bounding technique is proposed to obtain the bounds. The upper bounds and lower bounds together specify the accuracy of the resulting estimation of the PEP, and give an indication of the system error performance. Several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability (APEP) values. The approach can be used to accurately study the multiple-access capability of the coded DS/SSMA system without numerical integrations.