Constrained Cramer-Rao bounds on source separation

Constrained Cramer-Rao bounds (CRBs) are developed for multiple-input multiple-output (MIMO) scenarios, including both instantaneous and convolutive mixing. We find the convolutive MIMO Fisher information matrix (FIM) and study its properties. While this FIM is generally rank deficient, we establish equality constraints to achieve regularity. We employ the constrained CRB formulation of Gorman and Hero (1990) and Stoica and Ng (see IEEE SPL, vol.6, no.7, p.177-79, 1998), allowing the incorporation of side information into the bounds. This framework provides bounds on many algorithms proposed in the literature for MIMO channel and source estimation that exploit various kinds of side information, including semi-blind, constant modulus, and others.