### Abstract

In some applications of LMS type adaptive algorithms, it is necessary to implement a variant of the algorithm with feedback delay in the weight update calculation. In this paper we consider the normed version of such an algorithm and show that the algorithm converges exponentially if the update gain parameter, μm, is sufficiently small. The result is first proved for inputs which satisfy a standard deterministic mixing condition, and then the development is extended to the case when the input may not be strictly mixing, but is instead a stationary ergodic vector sequence with positive definite autocorrelation.

Original language | English (US) |
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Title of host publication | Conference Record of the Asilomar Conference on Signals, Systems & Computers |

Editors | Avtar Singh |

Publisher | Publ by IEEE |

Pages | 179-183 |

Number of pages | 5 |

Volume | 1 |

ISBN (Print) | 0818641207 |

State | Published - 1993 |

Event | Proceedings of the 27th Asilomar Conference on Signals, Systems & Computers - Pacific Grove, CA, USA Duration: Nov 1 1993 → Nov 3 1993 |

### Other

Other | Proceedings of the 27th Asilomar Conference on Signals, Systems & Computers |
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City | Pacific Grove, CA, USA |

Period | 11/1/93 → 11/3/93 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture
- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*Conference Record of the Asilomar Conference on Signals, Systems & Computers*(Vol. 1, pp. 179-183). Publ by IEEE.

**Almost sure convergence of the normed LMS algorithm with error feedback delay.** / Voltz, Peter.

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

*Conference Record of the Asilomar Conference on Signals, Systems & Computers.*vol. 1, Publ by IEEE, pp. 179-183, Proceedings of the 27th Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA, 11/1/93.

}

TY - GEN

T1 - Almost sure convergence of the normed LMS algorithm with error feedback delay

AU - Voltz, Peter

PY - 1993

Y1 - 1993

N2 - In some applications of LMS type adaptive algorithms, it is necessary to implement a variant of the algorithm with feedback delay in the weight update calculation. In this paper we consider the normed version of such an algorithm and show that the algorithm converges exponentially if the update gain parameter, μm, is sufficiently small. The result is first proved for inputs which satisfy a standard deterministic mixing condition, and then the development is extended to the case when the input may not be strictly mixing, but is instead a stationary ergodic vector sequence with positive definite autocorrelation.

AB - In some applications of LMS type adaptive algorithms, it is necessary to implement a variant of the algorithm with feedback delay in the weight update calculation. In this paper we consider the normed version of such an algorithm and show that the algorithm converges exponentially if the update gain parameter, μm, is sufficiently small. The result is first proved for inputs which satisfy a standard deterministic mixing condition, and then the development is extended to the case when the input may not be strictly mixing, but is instead a stationary ergodic vector sequence with positive definite autocorrelation.

UR - http://www.scopus.com/inward/record.url?scp=0027814135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027814135&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027814135

SN - 0818641207

VL - 1

SP - 179

EP - 183

BT - Conference Record of the Asilomar Conference on Signals, Systems & Computers

A2 - Singh, Avtar

PB - Publ by IEEE

ER -