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We analyze the mean squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation when the covariance matrix is estimated using a finite number of samples. The conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the WL estimator. We derive accurate closed-form expressions for the MSE of the two estimators under four ambiguity resolution scenarios. In the first three scenarios, the receiver resolves the ambiguity using some clairvoyant knowledge about the channel. The first scenario, used as a reference, is the ideal case of optimal resolution. The second scenario assumes that one of the channel coefficients is known and the third assumes knowledge of the coefficient with the largest magnitude. The fourth scenario considers the more realistic case where pilot symbols are employed for ambiguity resolution. Our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of WL and conventional subspace-based estimators, showing that the WL estimator performs better when partial or inaccurate channel information is employed for ambiguity resolution.

Widely Linear versus Conventional Subspace-Based Estimation of SIMO Flat-Fading Channels: Mean Squared Error Analysis