### 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.

Original language | English |
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Title of host publication | European Signal Processing Conference |

Publication status | Published - 2006 |

Externally published | Yes |

Event | 14th European Signal Processing Conference, EUSIPCO 2006 - Florence, Italy Duration: 2006 Sep 4 → 2006 Sep 8 |

### Other

Other | 14th European Signal Processing Conference, EUSIPCO 2006 |
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Country | Italy |

City | Florence |

Period | 06/9/4 → 06/9/8 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*European Signal Processing Conference*

**Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation.** / Yukawa, Masahiro; Yamada, Isao.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*European Signal Processing Conference.*14th European Signal Processing Conference, EUSIPCO 2006, Florence, Italy, 06/9/4.

}

TY - GEN

T1 - Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation

AU - Yukawa, Masahiro

AU - Yamada, Isao

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84862604150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862604150&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84862604150

BT - European Signal Processing Conference

ER -