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Dynamic variable step size LMS adaptation algorithms -- Application to adaptive feedforward noise attenuation

Tudor-Bogdan Airimitoaie, Bernard Vau, Dariusz Bismor, Gabriel Buche, Ioan Doré Landau

Abstract

The paper explores in detail the use of dynamic adaptation gain/step size (DAG) for improving the adaptation transient performance of variable step-size LMS (VS-LMS) adaptation algorithms. A generic form for the implementation of the DAG within the VS-LMS algorithms is provided. Criteria for the selection of the coefficients of the DAG filter which is required to be a strictly positive real transfer operator are given. The potential of the VS-LMS adaptation algorithms using a DAG is then illustrated by experimental results obtained on a relevant adaptive active noise attenuation system.

Dynamic variable step size LMS adaptation algorithms -- Application to adaptive feedforward noise attenuation

Abstract

The paper explores in detail the use of dynamic adaptation gain/step size (DAG) for improving the adaptation transient performance of variable step-size LMS (VS-LMS) adaptation algorithms. A generic form for the implementation of the DAG within the VS-LMS algorithms is provided. Criteria for the selection of the coefficients of the DAG filter which is required to be a strictly positive real transfer operator are given. The potential of the VS-LMS adaptation algorithms using a DAG is then illustrated by experimental results obtained on a relevant adaptive active noise attenuation system.
Paper Structure (9 sections, 3 theorems, 36 equations, 9 figures, 1 table)

This paper contains 9 sections, 3 theorems, 36 equations, 9 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Introducing the DAG-VS-LMS algorithms
  3. Relations with other algorithms
  4. Design of the dynamic adaptation gain/learning rate
  5. Performance issues
  6. Stability issues
  7. Experimental results
  8. Conclusion
  9. Derivation of the PLMS algorithm

Key Result

Lemma III.1

Assume that the polynomials $C(z^{-1})$ and $D'(z^{-1})$ have all their zeros inside the unit circle, then:

Figures (9)

  • Figure 1: Least mean squares (LMS) adaptive filtering problem.
  • Figure 2: Frequency characteristics of DAGs used in the experimental section (see also Table \ref{['perf1']}).
  • Figure 3: Intersection in the plane $c_1 - c_2$ of the contour $H_{PAA}=PR$ with the contour $H_{DAG}=SPR$ for $d'_1=0.5$.
  • Figure 4: Duct active noise control test-bench .
  • Figure 5: Feedforward AVC with FIR-YK adaptive feedforward compensator.
  • ...and 4 more figures

Theorems & Definitions (3)

  • Lemma III.1
  • Lemma III.2
  • Theorem III.3