| The complexity of an adaptive filtering algorithm is proportional to the tap length of the filter and hence, may become computationally prohibitive for applications requiring a long filter tap. In this thesis, we provide a framework for developing low-complexity adaptive filter algorithms by utilizing the concept of partial-updating along with the technique of finding the gradient vector in the hyperplane based on the Linfinity-norm criterion. The resulting algorithm should have low-complexity not only because of the updating of only a subset of the filter coefficients at each time step, but also from the fact that updating a filter coefficient using the algorithm based on Linfinity-norm requires less number of operations compared to the L2-norm algorithm. Two specific coefficient selection techniques, namely the sequential and M-Max coefficient selection techniques, are considered in this thesis. Statistical analyses of these two algorithms are carried out to derive the evolution equations for the mean and mean-square of the filter coefficient misalignment as well as to obtain stability bounds on the step-size of the two algorithms. Further, these analyses are used to show that the algorithm employing the M-Max coefficient selection technique can achieve a convergence rate that is closest to the full update algorithm. As a consequence, even though there are various ways of selecting a subset of the filter coefficients, the study of the other techniques becomes redundant. Simulations are carried out to validate the results obtained from the statistical analyses of the algorithms. The concept of developing algorithms based on the partial-updating and Linfinity-norm is extended to proportionate adaptive filtering. Finally, the performance of the proposed adaptive filtering algorithms as well as that of the existing ones is studied in echo cancellation. |
