Adaptive filtering algorithms with selective partial updates

In some applications of adaptive filtering such as active noise reduction, and network and acoustic echo cancellation, the adaptive filter may be required to have a large number of coefficients in order to model the unknown physical medium with sufficient accuracy. The computational complexity of adaptation algorithms is proportional to the number of filter coefficients. This implies that, for long adaptive filters, the adaptation task can become prohibitively expensive, ruling out cost-effective implementation on digital signal processors. The purpose of partial coefficient updates is to reduce the computational complexity of an adaptive filter by adapting a block of the filter coefficients rather than the entire filter at every iteration. In this paper, we develop a selective-partial-update normalized least-mean-square (NLMS) algorithm, and analyze its stability using the traditional independence assumptions and error-energy bounds. Selective partial updating is also extended to the affine projection (AP) algorithm by introducing multiple constraints. The new algorithms appear to have good convergence performance as attested to by computer simulations with real speech signals.