On the relative error probabilities of linear multiuser detectors

The relative error probability performance of three linear multiuser detectors-the minimum mean-square error (MMSE) detector, the decorrelator, and the conventional matched filter (MF) detector-is investigated under nonorthogonal signaling and additive white Gaussian noise conditions. It is shown that, contrary to the general belief, the MMSE detector does not uniformly outperform the other two detectors. In fact, even for the two-user case, one can find counterexamples where the matched filter is significantly better.