On the achievable improvement by the linear minimum mean square error detector

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Linear minimum mean square error (MMSE) detector has been shown to alleviate the noise amplification problem, resulting in 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, and in terms of the post-precessing signal to noise ratio (SNR) improvement. 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 is not only dependent 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.