Analysis of the hierarchical LMS algorithm

• Published in: IEEE signal processing letters Vol. 10; no. 3; pp. 78 - 81
• Main Author: Nascimento, V.H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Computational efficiency; Convergence; Councils; Equivalence; Error analysis; Estimates; Filters; Least squares approximation; Least squares methods; Mathematical models; Optimization; Robustness; Signal processing; Steady-state; Stochastic systems
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2002.807863

We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the hierarchical structure to be equivalent to the optimal (full-length) Wiener solution. When these conditions are not satisfied, we show that HLMS will compute biased estimates. Our analysis also shows that even when these conditions hold, the MSE obtained using HLMS may be much larger than that obtained using LMS, since the potentially large MSEs at the subfilters in the first hierarchical level directly affect the output MSE.