On the Decomposition Parameter of the RLS Algorithm Based on the Nearest Kronecker Product

Decomposition-based algorithms have gained much attention lately, in the context of low-rank system identification problems. These algorithms exploit the nearest Kronecker product (NKP) decomposition of the impulse response (usually of long length) and take advantage of low rank approximations. Among them, the recursive least-squares (RLS) algorithm developed in this framework, namely RLS-NKP, has been found to be very suitable in challenging system identification problems that involve long length impulse responses, e.g., like in acoustic echo cancellation. The performance of the RLS-NKP algorithm depends on its decomposition parameter, which is related to the accuracy of low rank approximation. The current paper focuses on the investigation of this aspect and proposes a simple solution for choosing the decomposition parameter, using a preprocessing stage that relies on a low-complexity algorithm. Experiments are performed in the framework of acoustic echo cancellation and the obtained results support the validity of the proposed solution.