Real-Time Implementation of the Exact Block NLMS Algorithm for Acoustic Echo Control in Hands-Free Telephone Systems

Abstract

Adaptive filter algorithms that employ a block processing approach converge slower for colored excitation signals like speech than their sample by sample counterparts. Furthermore, the block processing introduces a signal delay which increases with rising block length. If the error signal of a block adaptive filter is corrected in such a way that the corrected error signal equals the error signal of the sample-by-sample version of the adaptive filter, then both algorithms are mathematically identical. This error correction method is applied to many algorithms such as the NLMS, the affine projection, and the fast Newton algorithm. In this contribution, the exact block NLMS algorithm is examined in detail. To reduce the signal delay and the numerical complexity, the error signal correction method is combined with a partitioning of the filter and with the overlap save implementation method. The resulting algorithm has a low numerical complexity, a moderate signal delay, and the same convergence behavior as the NLMS algorithm. Finally, real-time implementation aspects of the algorithm are discussed.