Abstract
This chapter deals with partial-update adaptive filters. It also details several stochastic gradient algorithms with partial coefficient updates. Both time-domain and transform domain adaptive filters are covered. The treatment is focused on the following adaptive filtering algorithms and their partial-update versions: least-mean-square, normalized least mean-square, affine projection algorithm (APA), recursive least squares (RLS), transform-domain LMS, and generalized-subband-decomposition LMS. The computational complexity of each algorithm is examined in detail. The convergence performance of the partial-update algorithms is compared in a channel equalization example. Overall the largest complexity reduction is achieved by periodic partial updates. The method of partial coefficient updates has the most dramatic complexity and convergence impact on LMS and NLMS algorithms. LMS and NLMS employ the simplest approximation to steepest descent algorithm and Newton's method, respectively, and therefore they present more opportunity of performance improvement.
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