On subspace methods for blind identification of single-input multiple-output FIR systems

Blind identification of single-input multiple-output (SIMO) FIR systems based on second-order statistics has attracted a great deal of research effort. We focus on subspace estimation procedures, which exploit the structure of the range space of certain matrix-valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations. General subspace identifiability results are obtained, based on properties of minimal polynomial bases of rational subspaces. Several subspace estimation procedures are then derived. These estimators are all based on a weighted least-square solution of an overdetermined system of linear equations. An asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting.