The Asymptotic Cram er - Rao Lower Bound for Blind SignalSeparation

er-Rao Lower Bound for Blind Signal Separation Henrik Sahlin and Ulf Lindgren Chalmers University of Technology, Department of Applied Electronics, S-412 96 Gothenburg, Sweden, [email protected], Telephone +46 31 772 1845 Abstract 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 lter 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) Cram er-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.