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

Masahiro Yukawa, Isao Yamada

Research output: Contribution to journalConference article


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.

Original languageEnglish
JournalEuropean Signal Processing Conference
Publication statusPublished - 2006 Dec 1
Event14th European Signal Processing Conference, EUSIPCO 2006 - Florence, Italy
Duration: 2006 Sep 42006 Sep 8


ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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