Improved PNLMS algorithm employing wavelet transform and sparse filters

The proportionate normalized least mean-square algorithm (PNLMS) has been proposed with the objective of improving the adaptation convergence rate when modeling high-order sparse finite impulse response systems. Whereas fast initial adaptation convergence rate is obtained with the PNLMS algorithm for white-noise input, slow convergence is observed for colored input signals. In this paper, we derive a new proportionate-type NLMS algorithm which employs a wavelet transform and sparse adaptive subfilters, and results in better convergence rate than the PNLMS algorithm for colored input signals. Simulation results for the digital network echo canceler application illustrate the convergence improvement obtained with the proposed approach when compared to the NLMS, PNLMS and other recently proposed proportionate-type algorithms.