Adaptive algorithms for sparse impulse response identification

For some applications such as network echo cancellation, the impulse responses that are modeled and identified by the adaptive filters are sparse in nature. Among the large number of filter coefficients, only a small portion is significantly different from zero. This research is investigating the techniques to improve the performance of the adaptive algorithms, especially the convergence speed and the computational complexity, by taking advantage of the sparseness of the impulse responses, with network echo cancellation as a typical example.; Some highlights of our research results are listed below. (1) Sources, types and characteristics of echoes in communication systems are introduced and the general structure of echo cancellation system is outlined. (2) Typical adaptive filtering algorithms are listed as the starting point of the research. (3) Several state-of-the-art adaptive algorithms especially designed for sparse impulse response identification in current literatures are reviewed. These algorithms provide foundations and directions for this research. (4) By combining the advantages of the sparseness of impulse responses and the partial update techniques, two algorithms are developed in order to achieve faster convergence speed with even less computational complexity. (5) For the steepest descent algorithm, based on reasonable assumptions, the condition under which the fastest overall convergence speed can be reached is presented and proved in the proportionate update framework. How to calculate the optimal stepsize control factors to achieve that condition is also derived. (6) A modified proportionate normalized least mean square (PNLMS) algorithm that has faster convergence than the existing proportionate type algorithms (PNLMS, PNLMS++ etc.) is proposed. Several techniques used to lower the computational complexity are investigated. (7) Several extensions of the MPNLMS algorithm are proposed to improve its convergence for the color input. (8) Extensive simulations and implementation complexity analysis are done for various practical situations.