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 recently attracted a lot of research efforts. In this contribution, 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 covariance coefficients of the observations, General subspace identifiability results are obtained in a first part, 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 in a second part to evaluate the potential of these methods and the impact of the weighting.