High Order Algorithms for Adaptive Filters

Faster convergence of adaptive filters has been of particular interest in the areas of adaptive equalizers and adaptive antennas. The algorithm most frequently suggested is some variation of the firstorder gradient-descent LMS algorithm. This paper investigates a general procedure for the design of higher-order algorithms. Convergence of the mean weight vector and the variance is compared for three typical algorithms. Results indicate that high order convergence of the mean weight vector can easily be achieved, and this in itself can be useful. However, the variance response of the high order algorithms can tend to have an offsetting effect which may preclude their use in some applications.