Combined-step-size Proportionate Decorrelation NLMS Algorithm for Adaptive Echo Cancellation

Due to the highly correlated speech input signal and sparse echo path in echo cancellation application, the conventional least mean square (LMS) algorithm will suffer from slow convergence rate. In this paper, we firstly develop an improved proportionate weight-constraint decorrelation normalized least mean square (IPDNLMS) algorithm, which makes use of decorrelation and proportionate methods to increase the convergence rate. Then, to solve the conflict between fast convergence rate and small steady-state error, a combined-step-size IPDNLMS (CSS-IPDNLMS) algorithm is proposed, which combines two different step-sizes of one IPDNLMS filter adaptively via a modified sigmoidal activation function. The stability analysis is also carried out. Finally, simulation results indicate the proposed CSS-IPDNLMS algorithm is efficient and outperforms the normalized least mean square (NLMS), improved proportionate NLMS (IPNLMS), weight-constraint decorrelation NLMS (WCDNLMS), proportionate decorrelation NLMS (PDNLMS), and IPDNLMS algorithms.