Linear System Identification Based on a Kronecker Product Decomposition

Linear system identification is a key problem in many important applications, among which echo cancelation is a very challenging one. Due to the long length impulse responses (i.e., echo paths) to he identified, there is always room (and needs) to improve the performance of the echo cancelers, especially in terms of complexity, convergence rate, robustness, and accuracy. In this paper, we propose a new way to address the system identification problem (from the echo cancelation perspective), by exploiting an optimal approximation of the impulse response based on the nearest Kroneeker product decomposition. Also, we make a first step toward this direction, by developing an iterative Wiener filter based on this approach. As compared to the conventional Wiener filter, the proposed solution is much more attractive since its gain is twofold. First, the matrices to be inverted (or, preferably, linear systems to be solved) are smaller as compared to the conventional approach. Second, as a consequence, the iterative Wiener filter leads to a good estimate of the impulse response, even when a small amount of data is available for the estimation of the statistics. Simulation results support the theoretical findings and indicate the good results of the proposed approach, for the identification of different network and acoustic impulse responses.