Wideband time delay and Doppler stretch estimation: the application of wavelet transform and the optimum signal

The application of the wavelet transform in the joint time delay and Doppler stretch estimation for a wideband signal is discussed. It was previously shown by the authors that, under a high signal to noise ratio, the joint estimation using the wavelet transform is unbiased and the estimation variance is close to the Cramer-Rao bound (CRB) for a large variety of signals. Here, it is demonstrated that the joint estimation accuracy depends on the signal structure and the optimum signal structure is strongly related to the form of its wavelet transform. Optimum signals for the joint estimation of time delay and the Doppler stretch under practical constraints are designed, and, through computer simulations, their performance is shown to be superior to that of the commonly used signals.<>