In this paper we quantify theoretically the effect of the desired-signal power level on the mean square filter estimation error and the normalized output signal-to-interference-plus-noise-ratio (SINR) of sample matrix inversion (SMI)-type estimates of the minimum mean-square-error (MMSE) and the linearly constrained minimum variance (LCMV) filters. We prove that in finite data support situations filters that utilize a sample average estimate of the desired-signal-absent input correlation matrix exhibit superior normalized filter output SINR and mean square filter estimation error when compared to filters that utilize a sample average estimate of the desired-signal-present input correlation matrix. Finally, we investigate pilot-assisted and decision-directed adaptive filter implementations that exhibit near desired-signal-absent SMI-filtering performance while they are trained using desired-signal-present data/observations.
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