Optimal step size control for acoustic echo cancellation

Depth and speed of convergence are important metrics for the performance of acoustic echo cancellers (AECs). The LMS (Least Mean Square) or NLMS (normalized LMS) algorithms constitute the core of many AEC implementations. This paper presents an optimal step size control strategy for the NLMS algorithm when the input signal is white. This strategy gives the deepest convergence in the shortest amount of time. The optimum step size turns out to be the solution of a Riccati equation. Simulation results are presented to confirm the analysis. Practical considerations for colored signals and time varying echo impulse responses are also discussed.