Multichannel system identification and deconvolution: performance bounds

We consider the problem of estimating the parameters of an unknown multi-input multi-output (MIMO) linear system and the related problem of deconvolving and recovering its inputs. Only the system outputs are assumed to be observable. The system inputs are assumed to be non-Gaussian. We derive simple closed-form asymptotic expressions for the Cramer-Rao lower bound (CRLB) for the system parameters, as well as lower bounds on the signal reconstruction performance. These show that the identification/deconvolution performance depend on the accuracy with which the location (mean) and the scale (standard deviation) parameters of the input probability density functions can be identified from observation of the input signals.