On the relative output SINR of full and partial decorrelators

We investigate the relative output signal-to-interference-plus-noise ratio (SINR) performance of two linear direct-sequence code-division multiple-access multiuser detectors: the full decorrelator and the partial decorrelator. We derive necessary and sufficient conditions on the system parameters under which the partial decorrelator outperforms the full decorrelator in the output SINR sense. As a side study, we consider a blind implementation of the full decorrelator that is based on eigendecomposition of the interference-plus-noise autocovariance matrix and can be easily modified to provide a partial decorrelator. Simulation studies illustrate the relative SINR and bit-error rate performance of the full and partial decorrelator under perfectly known and sample-average-estimated input statistics.