Perturbation analysis of subspace-based semi-blind MIMO channel estimation approaches

In this paper, a perturbation analysis of two subspace-based semi-blind MIMO channel estimation approaches is conducted. Our analysis shows that, in the noise-free case, the whitening-rotation (WR)-based algorithm is subject to a signal perturbation error, while the nulling-based algorithm is a signal perturbation free scheme with an ideal nulling constraint imposed on the channel matrix. This explains why the WR-based method is efficient only in the low SNR case, and concludes that the nulling-based approach is better for moderate to high SNRs. A novel closed-form mean square error (MSE) expression is also derived for the nulling-based blind estimation method, in which an appealing scheme for the determination of the weighting factor is presented. The nulling-based method with the proposed weighting scheme is validated via computer simulations, showing a very high estimation accuracy of our semi-blind solution in terms of the MSE of the channel estimate.