Remarks on the Performance of the Linear Detectors in MIMO Spatial Multiplexing Systems

Abstract

Linear minimum mean square error (MMSE) detector has been shown to alleviate the noise amplification problem associated with the conventional zero-forcing (ZF) detector. In this paper, we analyze the performance improvement by the MMSE detector in terms of the condition number of its filtering matrix, the post-processing signal to noise ratio (SNR) improvement, and the variance of the postprocessing SNRs. To this end, we derive explicit formulas for the condition numbers of the filtering matrices and the post-processing SNRs. Analytical and simulation results demonstrate that the improvement achieved by the MMSE detector over the ZF detector does not only depend on the noise variance and the condition number of the channel matrix, but also on how close the smallest singular values are to the noise variance. This conjecture is also proven correct via analyzing the post-processing SNR of both detectors.