On the relative output SINR of the full and partial decorrelators

We investigate the relative output SINR performance of two linear multiuser detectors - the full decorrelator and the partial decorrelator. For each detector, we consider two implementations that are equivalent under perfectly known input statistics. The first implementation utilizes the signature matrix while the second implementation is based on the eigendecomposition of the ideal input covariance matrix. While the full decorrelator aims at decorrelating the complete multiple-access-interference, the partial decorrelator aims at decorrelating only a part of it by excluding one or more user-signatures or eigenvectors from the corresponding implementation method. We derive necessary and sufficient conditions on the signal energy and signature cross-correlation levels under which the partial decorrelator outperforms the full decorrelator in the output SINR sense. Numerical results demonstrate the validity of the above conditions and simulation studies illustrate the relative SINR and BER performance of the full and partial decorrelators under sample-average-estimated input statistics.