The Cramer-Rao Bound and DMT Signal Optimisation for the Identification of a Wiener-Type Model
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
EURASIP Journal on Advances in Signal Processing 2004, 2004:642938 doi:10.1155/S1110865704404168Published: 29 September 2004
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.