Analysis of an Approximate Decorrelating Detector

In this paper an approximate decorrelating detector is analyzed on the basis of a first order approximation to the inverse crosscorrelation matrix of signature waveforms. The approximation is fairly accurate for systems with low crosscorrelations and is exact in the two-user synchronous case. We present an exact as well as approximate analysis of the bit-error-rate performance of this detector on a channel that is subject to flat fading, and also specifically for the case of random signature waveforms. The detector outperforms the conventional matched filter receiver in terms of BER. The approximate decorrelator (while not being near-far resistant like the decorrelating detector) is fairly robust to imperfections in power control. Power trade-off regions are identified which characterize the significant advantage that the approximate decorrelator provides over the matched filter receiver. The reduced complexity of the approximate decorrelator and performance gains over the conventional matched filter makes it a viable alternative for implementation in practical CDMA systems, in particular in those where the signature waveforms span many symbol intervals.