Performance Analysis of ZF and MMSE Equalizers for MIMO Systems: An In-Depth Study of the High SNR Regime

Abstract

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multi-input multi-output (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of the well-known performance metrics of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff, and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is ρ mmse = ρ zf + η snr , where ρ zf is the output SNR of the ZF equalizer, and that the gap η snr is statistically independent of ρ zf and is a non-decreasing function of input SNR. Furthermore, as snr → ∞, η snr converges with probability one to a scaled F random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better, and significantly so. KeywordsThis work was supported in part by the National Science Foundation Grant CCF-0423842 and CCF-0434410. Zero forcing, minimum mean squared error, MIMO, error probability, V-BLAST, diversity gain, spatial multiplexing gain, tradeoff, outage capacity, outage probability.

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