Analysis of an Approximate Decorrelating Detector

In this paper an approximate decorrelating detector is analyzed on the basis of a rst order ap proximation 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 at fading and also speci cally for the case of random signature waveforms The detector outperforms the conventional matched lter 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 o regions are identi ed which characterize the signi cant advantage that the approximate decorrelator provides over the matched lter receiver The reduced complexity of the approximate decorrelator and performance gains over the conven tional matched lter makes it a viable alternative for implementation in practical CDMA systems in particular in those where the signature waveforms span many symbol intervals This work was presented in part at the rd Annual Allerton Conference on Communication Control and Computing Allerton IL October It was partially supported by a grant from NSF and ARO DAA G The Approximate Decorrelator Conventionally demodulation of DS CDMA signals is achieved with a matched lter receiver These receivers are optimum only when there is no multiple access interference in additive Gaussian noise channels and not only do they su er from the near far problem but they have inferior performance even with perfect power control Several multiuser detection schemes have been proposed e g however these are more complex than the matched lter detector and may require explicit knowledge or estimates of various parameters To overcome this inconvenience adaptive detectors have been proposed recently see and references therein that are still more complex than the matched lter detector to varying degrees Our approach here is to analyze a simpli ed multiuser detector that is only slightly more complex than the matched lter detector while still retaining some of the performance advantages of multiuser detectors We consider a linear multiuser detector namely the decorrelating detector and analyze an approximation for it which was proposed in for both the synchronous and asynchronous cases For simplicity in illustration we will consider the case of synchronous reception of the users bits In this case the output of the matched lter for the k user can be written as yk Akbk X j k Ajbj jk nk where Ak and bk f g are the amplitude and the bit of the k user respectively and nk R T n t sk t dt with sk t being the signature waveform of the k th user which is assumed to have unit energy The crosscorrelation between the signature waveforms is de ned as