Subspace methods for blind identification of SIMO-FIR systems

Blind identification of single-input multiple-output (SIMO) FIR systems based on second order statistics has attracted a lot of research efforts. 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 the properties of minimal polynomial bases of rational subspaces. Several subspace estimation procedures are then derived. These estimators are all based on the (possibly weighted) least-square solution of an overdetermined system of linear equations and are thus well-suited for practical implementations.