An LMS style variable tap-length algorithm for structure adaptation

• Published in: IEEE transactions on signal processing Vol. 53; no. 7; pp. 2400 - 2407
• Main Authors: Yu Gong, Cowan, C.F.N.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; Algorithms; Applied sciences; Complexity; Computer simulation; Convergence; Detection, estimation, filtering, equalization, prediction; Equivalence; Exact sciences and technology; filter length; Information, signal and communications theory; Least mean squares; Least squares approximation; Noise cancellation; Numerical simulation; Optimization; Partitioning algorithms; Performance analysis; Searching; Signal and communications theory; Signal, noise; Steady-state; Stochastic processes; Studies; tap-length variation; Telecommunications and information theory; Performance evaluation; filter length; Adaptive filters; tap-length variation; Numerical method; Adaptive filter; Stochastic method; Algorithm; Steady state; Algorithm complexity; Descent method; Gradient method; Least mean squares methods
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2005.849170

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.