The asymptotic Cramer-Rao lower bound for blind signal separation

This paper considers some aspects of the source separation problem. Unmeasurable source signals are assumed to be mixed by means of a channel system resulting in measurable output signals. These output signals can be used to determine a separation structure in order to extract the sources. When solving the source separation problem the channel filter parameters have to be estimated. This paper presents a compact and computationally appealing formula for computing a lower bound for the variance of these parameters, in a general many inputs many outputs scenario. This lower bound is the asymptotic (assuming the number of data samples to be large) Cramer-Rao lower bound. The CRLB formula is developed further for the two-input two-output system and compared with the results from a recursive prediction error method.