Optimum discrete wavelet scaling and its application to delay and Doppler estimation

This paper studies the scaling of an arbitrary waveform from its samples. The scaling problem is formulated as a mean-square minimization, and the resulting estimator consists of two parts: noise filtering and sinc function scaling. Sinc function scaling is a time-dependent process and requires O(N²) operations, where N is the data length. A fast algorithm based on the FFT is proposed to reduce the complexity to O(Nlog₂N). This new algorithm is applied to wideband time delay and Doppler estimation, where the optimum wavelet is one of the received signal samples that has no analytic form. The scaling method is found to be very effective in that the estimation accuracy achieves the Cramer-Rao lower bound (CRLB)