Widely linear vs. conventional subspace-based estimation of SIMO flat-fading channels

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 closed-form expressions for the MSE of the two estimators under four different scenarios which vary in the amount and accuracy of the information available for ambiguity resolution. Our work demonstrates that the relative performance of WL and conventional subspace-based estimators is strongly related to the accuracy of ambiguity resolution and shows that the less information available about the actual channel for ambiguity resolution, or the lower the accuracy of this information, the more favorable the WL estimator becomes.