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

  • H. Koeppl1Email author,

    Affiliated with

    • A.S. Josan2,

      Affiliated with

      • G. Paoli3 and

        Affiliated with

        • G. Kubin1

          Affiliated with

          EURASIP Journal on Advances in Signal Processing20042004:642938

          DOI: 10.1155/S1110865704404168

          Received: 2 September 2003

          Published: 29 September 2004

          Abstract

          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.

          Keywords and phrases

          Wiener model Cramer-Rao bound signal design nonlinear system identification

          Authors’ Affiliations

          (1)
          Christian Doppler Laboratory for Nonlinear Signal Processing, Graz University of Technology
          (2)
          Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati
          (3)
          System Engineering Group, Infineon Technologies

          Copyright

          © Koeppl et al. 2004