Robust Variable Step-Size Decorrelation Normalized Least-Mean-Square Algorithm and its Application to Acoustic Echo Cancellation

In this paper, we present a robust variable step-size decorrelation normalized least-mean-square (RVSSDNLMS) algorithm. A new constrained minimization problem is developed by minimizing the l
₂
norm of the a decorrelated posteriori error signal with a constraint on the filter coefficients in the l
₂
norm sense. Solving this minimization problem gives birth to the efficient RVSSDNLMS algorithm. The convergence performance and computational complexity of RVSSDNLMS algorithm are analyzed. Finally, simulations show that the proposed RVSSDNLMS considerably outperforms the normalized least-mean-square (NLMS), robust variable step-size NLMS, and pseudoaffine projection algorithms in terms of convergence rate and steady-state error in Gaussian noise and impulsive noise environments.