Decomposition-Based Wiener Filter Using the Kronecker Product and Conjugate Gradient Method

The identification of long-length impulse responses represents a challenge in the context of many applications, like echo cancellation. Recently, the problem has been addressed in the framework of low-rank systems, using a decomposition of the impulse response based on the nearest Kronecker product and low-rank approximations. As a result, the original system identification problem that involves a long-length finite impulse response filter is reshaped as a combination of two (much) shorter filters, which leads to significant advantages. In this context, the benchmark Wiener filter can be formulated in terms of an iterative algorithm, where the estimates of the two component filters are sequently updated. However, matrix inversion operations are required within this algorithm. In this article, we develop a new version of the decomposition-based iterative Wiener filter, which relies on the conjugate gradient (CG) method and avoids matrix inversion. Simulations performed in the framework of echo cancellation indicate the good performance of the proposed solution, which outperforms the conventional Wiener filter (implemented using CG updates) and inherits the advantages of the decomposition-based approach.