A UNIFIED APPROACH FOR GENERATING OPTIMUM GRADIENT FIR ADAPTIVE ALGORITHMS WITH TIME-VARYING CONVERGENCE FACTORS

Abstract

In this paper, a unified approach for generating fast block- and sequential-gradient LMS FIR tapped delay line (TDL) adaptive algorithms is presented. These algorithms employ time-varying convergence factors which are tailored for the adaptive filter coefficients and updated at each block or single data iteration. The convergence factors are chosen to minimize the mean squared error (MSE) and are easily computed from readily available signals. The general formulation leads to three classes of adaptive algorithms. These algorithms. ordered in a descending order of their computational complexity and performance. are: the optimum block adaptive algorithm with individual adaptation of parameters (OBAI), the optimum block adaptive (OBA) and OBA shifting (ODAS) algorithms, and the homogeneous adaptive (HA) algorithm. In this paper, it is shown how each class of algorithms is obtained from the previous one, by a simple trade-off between adaptation performance and computational complexity. Implementation aspects of the generated algorithms are examined and their performance is evaluated and compared with several recently proposed algorithms by means of computer simulations under a wide range of adaptation conditions. The evaluation results show that the generated algorithms have attractive features in the comparisons due to the considerable reduction in the number of iterations required for a given adaptation accuracy. The improvement, however. is achieved at the expense of a relatively modest increase in the number of computations per data sample.