Optimal receiver design with wavelet bases

A generalized orthogonal series expansion should reflect the natural modes of a signal. In doing so, the transform becomes precise and useful. The most precise transform is the Karhunen-Loeve (KL) transform. The covariance function of a signal expanded in its KL basis has uncorrelated coefficients. This property can be used to derive optimal detection structures. Erdol and Bao (see Proceedings of the Asilomar Conf. on Signals, Systems and Computers, 1993) addressed the classical problem of detection of a message signal in white noise by considering a variable coefficient wavelet series expansion of the input signal. It is shown that, given the hypothesis that there exists a wavelet eigen basis of the message signal, then the optimization problem of searching for the eigen wavelet may be transformed into a search over an array of variables. These variables are shown to be the coefficients that arise in the representation of one wavelet basis in terms of another. In this paper, the structure of this array of coefficients is explored for simplifying the search space