On identification of FIR multichannel models using higher-order statistics

The problem of estimating the impulse response function of an FIR multiple-input multiple-output (MIMO) system given only the noisy measurements of the vector output of the system, is considered. The system is assumed to be driven by a spatially and temporally i.i.d. non-Gaussian vector sequence (which is not observed). The model order is unknown. The FIR N/spl times/M (N/spl ges/M) MIMO transfer function is assumed to have full column rank on the unit circle; there are no other assumptions. Higher-order cumulant matching is used to consistently estimate the MIMO impulse response via nonlinear optimization. Although it is known that the system impulse response is identifiable up to certain square matrix, no algorithm has yet been proposed in the literature without making additional restrictive assumptions. A previously proposed inverse filter criteria based approach (which yields biased estimates in noise) is used to obtain initialization for the cumulant matching approach. A simulation example is presented to illustrate the two approaches.