Gradient vector driven variable step size least mean square algorithm

A gradient vector driven variable step size least-mean-square (GVD-VSS-LMS) algorithm is proposed in the context of under-modeling acoustic echo cancellation (AEC). The cost function is the mean square error. The gradient vector which takes into account the under-modeling noise and ambient noise is derived by differentiating the cost function with respect to the weight vector of the adaptive filter. The variable step size is driven by the gradient vector. The updating equation for the weight vector is derived. The stability analysis of the proposed algorithm is provided and the convergent condition is obtained. The proposed algorithm does not require any additional information about the acoustic environment, which makes it practical in real-world AEC applications. The simulation results show that in the context of under-modeling AEC, the algorithm proposed has good convergence speed and convergence precision, good tracking ability and robustness to the increment of the ambient noise power.