A variable step size and variable tap length LMS algorithm for impulse responses with exponential power profile

Step size and tap length play critical roles in balancing the complexity and steady-state performance of an adaptive filter. For an impulse response with an exponential power decay profile, which models a wide range of practical systems, such as an acoustic echo path, this paper proposes a new variable step-size and tap-length least mean square (LMS) algorithm. In each iteration, the optimal step-size and tap-length are derived by minimizing the mean square deviation (MSD) between the true and the estimated filter coefficients. The proposed algorithm performs better in terms of both convergence rate and steady-state performance than the existing ones. Effectiveness of the proposed algorithm is demonstrated through computer simulations.