Time delay estimation with nonstationary signals

This paper presents two new techniques with time-modulated (i.e., time expansion or compression) discrete sequences. One for generating such sequences and the other for estimating the time delay between these sequences. The Time-Varying Discrete Fourier Transform (TVDFT) is introduced to generate time-modulated discrete signals. For time delay estimation, two time-modulated received signals are cross-correlated in the frequency domain, via TVDFT. Compensation of their time-modulation effect is realized by searching for perfect matching between them. A new optimization technique is specifically developed for maximizing the cross-correlation function. The optimization vector has as elements the time delay and a preassinged number of time-modulation coefficients. This optimization technique is a modification of the N-STEP Newton method and guarantees convergence to the local maximum. At high Signal-to-Noise Ratio (SNR), the scheme attains the Cramer-Rao Lower Bound (CRLB) in variance. Simulation results are given to demonstrate the effectiveness of the scheme and to confirm the validity of the development.