Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation

Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA. APSM asymptotically minimizes a sequence of non-negative convex functions in a real-Hilbert space. On the other hand, the exponentially weight...

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Vydáno v:Proceedings of the ... European Signal Processing Conference (EUSIPCO) s. 1 - 5
Hlavní autoři: Yukawa, Masahiro, Yamada, Isao
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.09.2006
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Adaptation models
Hilbert space
Indexes
Signal processing algorithms
Vectors
ISSN:2219-5491, 2219-5491
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Abstract Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA. APSM asymptotically minimizes a sequence of non-negative convex functions in a real-Hilbert space. On the other hand, the exponentially weighted stepsize projection (ESP) algorithm has been reported to converge faster than APA in the acoustic echo cancellation (AEC) problem. In this paper, we first clarify that ESP is derived by APSM in a real Hilbert space with a special inner product. This gives us an interesting interpretation that ESP is based on iterative projections onto the same convex sets as APA with a special metric. We can thus expect that a proper choice of metric will lead to improvement of convergence speed. We then propose an efficient adaptive algorithm named adaptive quadratic-metric parallel subgradient projection (AQ-PSP). Numerical examples demonstrate that AQ-PSP with a very simple metric achieves even better echo canceling ability than ESP, proportionate NLMS, and Euclidean-metric version of AQ-PSP, while keeping low computational complexity.
AbstractList Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA. APSM asymptotically minimizes a sequence of non-negative convex functions in a real-Hilbert space. On the other hand, the exponentially weighted stepsize projection (ESP) algorithm has been reported to converge faster than APA in the acoustic echo cancellation (AEC) problem. In this paper, we first clarify that ESP is derived by APSM in a real Hilbert space with a special inner product. This gives us an interesting interpretation that ESP is based on iterative projections onto the same convex sets as APA with a special metric. We can thus expect that a proper choice of metric will lead to improvement of convergence speed. We then propose an efficient adaptive algorithm named adaptive quadratic-metric parallel subgradient projection (AQ-PSP). Numerical examples demonstrate that AQ-PSP with a very simple metric achieves even better echo canceling ability than ESP, proportionate NLMS, and Euclidean-metric version of AQ-PSP, while keeping low computational complexity.
Author Yukawa, Masahiro
Yamada, Isao
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  givenname: Isao
  surname: Yamada
  fullname: Yamada, Isao
  email: isao@comm.ss.titech.ac.jp
  organization: Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol., Tokyo, Japan
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Snippet Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA....
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SubjectTerms Abstracts
Adaptation models
Hilbert space
Indexes
Signal processing algorithms
Vectors
Title Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation
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