A Family of Adaptive Decorrelation NLMS Algorithms and Its Diffusion Version Over Adaptive Networks

In order to increase the convergence rate of the normalized least mean square (NLMS) algorithm for highly correlated signals, a family of adaptive decorrelation NLMS variants is proposed in this paper. First, an adaptive decorrelation NLMS algorithm is presented to reduce the computational complexity of the existing decorrelation NLMS scheme. Then, by introducing a norm constraint on the decorrelation filter taps, the weight-constraint decorrelation NLMS (WCDNLMS) method is proposed. Third, on the WCDNLMS basis, a combination scheme of two weight-constraint decorrelation filters is developed to obtain an appropriate decorrelation parameter in different stages, i.e., large norm at transient state and small norm upon convergence. In addition, by extending the filter combination to adaptive networks, the diffusion combined weight-constraint decorrelation NLMS algorithm is devised for distributed estimation with colored inputs, and its theoretical performance is also analyzed. Finally, computer simulations are conducted to demonstrate the efficiency of the proposed algorithms and agreement with theoretical calculations.