OPTIMUM DISCRETE WAVELET SCALING AND ITS APPLICATION TO DELAY AND DOPPLER ESTIMATION

This paper studies the scaling of an arbitrary waveform from its sampl es. The scaling problem is formulated as a mean-square minimization, a nd the resulting estimator consists of two parts: noise filtering and sine function scaling. Sine function scaling is a time-dependent proce ss and requires O(N-2) operations, where N is the data length. A fast algorithm based on the FFT is proposed to reduce the complexity to O(N log(2) N). This new algorithm is applied to wideband time delay and D oppler estimation, where the optimum wavelet is one of the received si gnal 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).