### 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 |

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 |

### Publication series

Name | Conference Record of the Asilomar Conference on Signals, Systems & Computers |
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Volume | 1 |

ISSN (Print) | 1058-6393 |

### 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 |

### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

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## Cite this

Voltz, P. J. (1993). Almost sure convergence of the normed LMS algorithm with error feedback delay. In A. Singh (Ed.),

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