Adaptive parallel quadratic-metric projection algorithms

Masahiro Yukawa, Konstantinos Slavakis, Isao Yamada

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


This paper indicates that an appropriate design of metric leads to significant improvements in the adaptive projected subgradient method (APSM), which unifies a wide range of projection-based algorithms [including normalized least mean square (NLMS) and affine projection algorithm (APA)]. The key is to incorporate a priori (or a posteriori) information on characteristics of an estimandum, a system to be estimated, into the metric design. We propose a family of efficient adaptive filtering algorithms based on a parallel use of quadratic-metric projection, which assigns every point to the nearest point in a closed convex set in a quadratic-metric sense. We present two versions: (1) constant-metric and (2) variable-metric, i.e., the metric function employed is (1) constant and (2) variable among iterations. As a constant-metric version, adaptive parallel quadratic-metric projection (APQP) and adaptive parallel min-max quadratic-metric projection (APMQP) algorithms are naturally derived by APSM, being endowed with desirable properties such as convergence to a point optimal in asymptotic sense. As a variable-metric version, adaptive parallel variable-metric projection (APVP) algorithm is derived by a generalized APSM, enjoying an extended monotone property at each iteration. By employing a simple quadratic-metric, the computational complexity of the proposed algorithms is kept linear with respect to the filter length. Numerical examples demonstrate the remarkable advantages of the proposed algorithms in an application to acoustic echo cancellation.

Original languageEnglish
Article number4244541
Pages (from-to)1665-1680
Number of pages16
JournalIEEE Transactions on Audio, Speech and Language Processing
Issue number5
Publication statusPublished - 2007 Jul
Externally publishedYes


  • Acoustic echo cancellation
  • Adaptive filtering
  • Adaptive projected subgradient method (APSM)
  • Quadratic- metric

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


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