Blind MIMO identification using the second characteristic function

We propose a new approach for the blind identification of a multi-input-multi-output (MIMO) system. As a substitute to using "classical" high-order statistics (HOS) in the form of time-lagged joint cumulants, or polyspectra, we use the estimated Hessian matrices of the second joint generalized characteristic function of time-lagged observations, evaluated at several preselected "processing-points." These matrices admit straightforward consistent estimates, whose statistical stability can be finely tuned (by proper selection of the processing-points)-in contrast to classical HOS. Transforming the obtained matrix sequence into the frequency-domain, we obtain (and solve) a sequence of frequency-dependent joint diagonalization problems. This yields a set of estimated frequency response matrices, which are transformed back into the time domain after resolving frequency-dependent phase and permutation ambiguities. The performance of the proposed algorithm depends on the choice of processing-points, yet compares favorably with other algorithms, especially at moderate signal-to-noise ratio conditions, as we demonstrate in simulation results.