Combined coding and quadratic detection for DS/CDMA systems operating in Rayleigh fading channels

We present the true union bound of a DS/CDMA system that employs convolutional coding and a quadratic detector. In our study, the total bandwidth expansion factor caused by coding and spreading is fixed and the channel is assumed to exhibit Rayleigh flat fading. The objective is to assess the performance of various quadratic detectors as a function of the spreading factor and the fade rate. Specifically, four detectors were considered: chip level differential detection, chip level maximum likelihood sequence estimation, noncoherent detection, and perfect coherent detection. It was found that in the presence of fast Rayleigh fading, different detectors behave differently when the spreading factor varies. For example, the chip level differential detector and the ideal coherent detector favour a small spreading factor and a low rate code, while the MLSE prefers a high rate code and a high spreading factor. For the noncoherent detector, there actually exists an optimal system configuration at certain fade rates.