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This article is part of the series Nonlinear Signal and Image Processing—Part I.

Open Access Open Badges Research Article

The Cramer-Rao Bound and DMT Signal Optimisation for the Identification of a Wiener-Type Model

H Koeppl1*, AS Josan2, G Paoli3 and G Kubin1

Author Affiliations

1 Christian Doppler Laboratory for Nonlinear Signal Processing, Graz University of Technology, Graz 8010, Austria

2 Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India

3 System Engineering Group, Infineon Technologies, Villach 9500, Austria

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EURASIP Journal on Advances in Signal Processing 2004, 2004:642938  doi:10.1155/S1110865704404168

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2004/12/642938

Received:2 September 2003
Revisions received:8 January 2004
Published:29 September 2004

© 2004 Koeppl et al.

In linear system identification, optimal excitation signals can be determined using the Cramer-Rao bound. This problem has not been thoroughly studied for the nonlinear case. In this work, the Cramer-Rao bound for a factorisable Volterra model is derived. The analytical result is supported with simulation examples. The bound is then used to find the optimal excitation signal out of the class of discrete multitone signals. As the model is nonlinear in the parameters, the bound depends on the model parameters themselves. On this basis, a three-step identification procedure is proposed. To illustrate the procedure, signal optimisation is explicitly performed for a third-order nonlinear model. Methods of nonlinear optimisation are applied for the parameter estimation of the model. As a baseline, the problem of optimal discrete multitone signals for linear FIR filter estimation is reviewed.

Wiener model; Cramer-Rao bound; signal design; nonlinear system identification

Research Article