A Kronecker Product RSOR Algorithm Applied to Acoustic Echo Cancellation

Acoustic echo is a common challenge in modern communication systems, particularly in applications such as hands-free and conferencing systems. Several adaptive algorithms have been proposed to mitigate this issue. Among them, the recursive successive over-relaxation (RSOR) algorithm offers convergence properties comparable to the recursive least squares (RLS) algorithm. However, its computational cost becomes prohibitive for high-order filters, as required in acoustic echo cancellation (AEC) systems. Recently, new adaptive algorithms based on the nearest Kronecker product (NKP) decomposition have emerged to reduce computational complexity, potentially allowing the development of efficient AEC systems integrated into portable devices. In this work, we propose for the first time the RSOR algorithm based on the NKP strategy. Simulation results show that the proposed algorithm achieves convergence rates similar to RSOR and RLS algorithms while reducing computational cost by 89% compared to conventional RSOR algorithm, making it suitable for efficient AEC implementations in embedded and portable devices.