Existence and performance of Shalvi-Weinstein estimators

The Shalvi-Weinstein (1990) criterion has become popular in the design of blind linear estimators of i.i.d. processes transmitted through unknown linear channels in the presence of unknown additive interference. Here, we analyze SW estimators in a general multiple-input multiple-output (MIMO) setting that allows near-arbitrary source/interference distributions and noisy noninvertible channels. The main contributions of this paper are (i) simple tests for the existence of SW estimators for the desired source and (ii) bounding expressions for the MSE of SW estimators that are a function of the minimum attainable MSE and the kurtoses of the source and interferers.