## Abstract

This letter presents a novel approach for evaluating the mean behavior of the well known normalized least mean squares (NLMS) adaptive algorithm for a circularly correlated Gaussian input. The mean analysis of the NLMS algorithm requires the calculation of some normalized moments of the input. This is done by first expressing these moments in terms of ratios of quadratic forms of spherically symmetric random variables and finding the cumulative density function (CDF) of these variables. The CDF is then used to calculate the required moments. As a result, we obtain explicit expressions for the mean behavior of the NLMS algorithm.

Original language | English (US) |
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Article number | 5613147 |

Pages (from-to) | 7-10 |

Number of pages | 4 |

Journal | IEEE Signal Processing Letters |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

## Keywords

- Adaptive algorithms
- indefinite quadratic forms
- mean behavior
- spherically symmetric random variables

## ASJC Scopus subject areas

- Signal Processing
- Applied Mathematics
- Electrical and Electronic Engineering