Spread spectrum-based cooperative and individual time-frequency synchronization

We have recently given a time-frequency synchronization method, called a Phase Updating Loop (PUL), in which a delay and a Doppler can be acquired separately and cooperatively by using a strategy to determine a phase term satisfying Time Frequency Symmetry (TFS) in time and frequency domains. In active and passive PULs, phase distortions caused by the delay and the Doppler are compensated for by the transmitter and the receiver, respectively. Phase correction terms for the PULs are shown to be effective for synchronization.