Low-Complexity Implementation of the Improved Multiband-Structured Subband Adaptive Filter Algorithm

Previously, we proposed an improved multiband-structured subband adaptive filter (IMSAF) algorithm to accelerate the convergence rate of the MSAF algorithm. When the projection order and/or the number of subbands is increased, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. Thus, this paper proposes several approaches to reduce the complexity of the IMSAF algorithm, both in error vector calculation and matrix inversion operation. Specifically, three approaches are developed to efficiently calculate error vector. The first approach gives an approximate filtering, whereas the other two approaches can provide a fast exact filtering with or without update of the weight vector explicitly based on a recursive scheme. The decorrelation property of IMSAF is determined, and two simplified variants are developed to reduce the complexity as by-products, i.e., the simplified IMSAF (SIMSAF) and pseudo IMSAF algorithms. Then, we discuss the problem of solving a linear system of equations. The performance advantages, limitations, and preferable applications of various methods are analyzed and discussed. Computer simulations are conducted in the context of system identification to determine the principle and efficiency of the proposed fast algorithms.