We propose a novel adaptive filtering scheme named metric-combining normalized least mean square (MC-NLMS). The proposed scheme is based on iterative metric projections with a metric designed by combining multiple metric-matrices convexly in an adaptive manner, thereby taking advantages of the metrics which rely on multiple pieces of information. We compare the improved PNLMS (IPNLMS) algorithm with the natural proportionate NLMS (NPNLMS) algorithm, which is a special case of MC-NLMS, and it is shown that the performance of NPNLMS is controllable with the combination coefficient as opposed to IPNLMS. We also present an application to an acoustic echo cancellation problem and show the efficacy of the proposed scheme.

This letter analyses the convergence behaviour of the transform domain least mean square (TDLMS) adaptive filtering algorithm which is based on a well known interpretation of the variable stepsize algorithm. With this interpretation, the analysis is considerably simplified. The time varying stepsize is implemented by the modified power estimator to redistribute the spread power after transformation. The main contribution of this letter is the statistical performance analysis in terms of mean and mean squared error of the weight error vector and the decorrelation property of the TDLMS is presented by the lower and upper bound of eigenvalue spread ratio. The theoretical analysis results are validated by Monte Carlo simulation.