Subspace methods for blind identification of SIMO-FIR systems

Blind identification of single-input multiple-output (SIMO) FIR systems based on second order statistics only 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 (possibly weighted) least-square solution of an overdetermined system of linear equations and are thus well-suited for practical implementations.