Synchronization of Frequency Hopping DPSK Signals

The time synchronization problem of frequency hopping DPSK signals is considered in this paper. Before DPSK data can be properly demodulated by the receiver several dimensions of time synchronization must first be achieved. These include the acquisition and tracking of the frequency hop time epoch, symbol synchronization of the DPSK data stream, and the frame synchronization which involves the determination of the first DPSK bit within each hop period. Two symbol sync structures for DPSK signals, with and without data aiding, are first discussed. They are optimal in the Gaussian noise channel in the sense that they are both motivated by maximum a posteriori (MAP) estimation theory. Methods for acquiring the frequency hop time and its tracking for this type of signal, as well as the determination of the first DPSK symbol in each hop, are next discussed. The effect of symbol sync error on the probability of DPSK detection error is analyzed. Numerical results showing the bit error as a function of both fixed and random symbol sync error are given.