Identification and deconvolution of multichannel linear non-Gaussian processes using higher order statistics and inverse filter criteria

This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and spatially independent non-Gaussian vector sequence (which is not observed). An iterative, inverse filter criteria-based approach is developed using the third order or the fourth-order normalized cumulants of the inverse filtered data at zero lag. Stationary points of the proposed cost functions are investigated. The approach is input iterative, i.e., the input sequences are extracted and removed one by one. The matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. Strong consistency of the proposed approach is also briefly discussed. Computer simulation examples are presented to illustrate the proposed approaches.