A Recursive Least-squares Algorithm Based on the Nearest Kronecker Product Decomposition

The recursive least-squares (RLS) adaptive filter is an appealing choice in system identification problems, mainly due to its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of high length impulse responses, like in echo cancellation. In this paper, we focus on a new approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. Thus, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are tensorized together. Simulations performed in the context of echo cancellation indicate the good performance of the RLS algorithm based on this approach.