### Abstract

equation. In the limiting case of a linear system, the estimator has the form of a Wiener filter in discrete-time polynomial matrix system form. A non-linear channel equalisation problem is considered for the design example.

Language | English |
---|---|

Pages | 618-629 |

Number of pages | 12 |

Journal | IET Signal Processing |

Volume | 4 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2010 |

### Fingerprint

### Keywords

- channel estimation
- equalisers
- polynomial matrices
- stochastic processes

### Cite this

*IET Signal Processing*,

*4*(6), 618-629. https://doi.org/10.1049/iet-spr.2009.0001

}

*IET Signal Processing*, vol. 4, no. 6, pp. 618-629. https://doi.org/10.1049/iet-spr.2009.0001

**Optimal minimum variance estimation for nonlinear discrete-time multichannel systems.** / Grimble, M.J.; Ali Naz, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal minimum variance estimation for nonlinear discrete-time multichannel systems

AU - Grimble, M.J.

AU - Ali Naz, S.

PY - 2010/12

Y1 - 2010/12

N2 - A non-linear operator approach to estimation in discrete-time multivariable systems is described. It involves inferential estimation of a signal which enters a communication channel that contains non-linearities and transport delays. The measurements are assumed to be corrupted by a coloured noise signal correlated with the signal to be estimated. The solution of the non-linear estimation problem is obtained using nonlinear operators. The signal and noise channels may be grossly non-linear and are represented in a very general non-linear operator form. The resulting so-called Wiener non-linear minimum variance estimation algorithm is relatively simple to implement. The optimal non-linear estimator is derived in terms of the nonlinear operators and can be implemented as a recursive algorithm using a discrete-time non-linear difference equation. In the limiting case of a linear system, the estimator has the form of a Wiener filter in discrete-time polynomial matrix system form. A non-linear channel equalisation problem is considered for the design example.

AB - A non-linear operator approach to estimation in discrete-time multivariable systems is described. It involves inferential estimation of a signal which enters a communication channel that contains non-linearities and transport delays. The measurements are assumed to be corrupted by a coloured noise signal correlated with the signal to be estimated. The solution of the non-linear estimation problem is obtained using nonlinear operators. The signal and noise channels may be grossly non-linear and are represented in a very general non-linear operator form. The resulting so-called Wiener non-linear minimum variance estimation algorithm is relatively simple to implement. The optimal non-linear estimator is derived in terms of the nonlinear operators and can be implemented as a recursive algorithm using a discrete-time non-linear difference equation. In the limiting case of a linear system, the estimator has the form of a Wiener filter in discrete-time polynomial matrix system form. A non-linear channel equalisation problem is considered for the design example.

KW - channel estimation

KW - equalisers

KW - polynomial matrices

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=78649920740&partnerID=8YFLogxK

U2 - 10.1049/iet-spr.2009.0001

DO - 10.1049/iet-spr.2009.0001

M3 - Article

VL - 4

SP - 618

EP - 629

JO - IET Signal Processing

T2 - IET Signal Processing

JF - IET Signal Processing

SN - 1751-9675

IS - 6

ER -