Iterative Wiener Filter Using a Kronecker Product Decomposition and the Coordinate Descent Method

In this paper, we present an iterative Wiener filter suitable for the identification of long-length impulse responses that own the low-rank feature. Many real-world systems have these characteristics, e.g., like the network and acoustic echo paths. The proposed algorithm relies on the nearest Kronecker product decomposition of the impulse response and reformulates the original system identification problem (that involves a single long-length filter) into a combination of two much shorter filters. Besides, we use the coordinate descent method to solve the two resulting normal equations. Simulations performed in the context of echo cancellation indicate that the proposed iterative Wiener filter achieves good performance, especially in challenging cases, e.g., less accurate statistics’ estimates and noisy conditions.