The wavelet transform-domain LMS adaptive filter employing dynamic selection of subband-coefficients

In this paper, the WTDLMS adaptive algorithm is established based on the multiple-constraint optimization criterion. Furthermore, the WTDLMS with dynamic subband-coefficients update (WTDLMS-DU) is introduced. In this algorithm, the coefficients belonging to a certain subbands are dynamically selected for the update. The optimum selection of the subband-coefficients is derived by the largest decrease of the mean-square deviation. The WTDLMS-DU has a fast convergence speed and a low steady-state error similar to the WTDLMS. In addition, the proposed algorithm has lower computational complexity in comparison to WTDLMS algorithm. The good performance of WTDLMS-DU is demonstrated in various applications such as system identification, linear prediction, and acoustic echo cancellation. Also, a general formalism for the establishment and the theoretical mean-square performance analysis of the family of WTDLMS adaptive algorithms such as WTDLMS, WTDLMS with partial update (WTDLMS-PU), and the proposed WTDLMS-DU are presented. The transient, the steady-state, and the stability bounds of these algorithms are studied in a unified way. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. It is demonstrated through simulations that the results are useful in predicting the performance of the family of WTDLMS adaptive filter algorithms.