Simultaneous Symbol Timing and Frame Synchronization for Phase Shift Keying

We develop an estimator of time offset (or time-of-arrival) of a transmitted communications signal that contains both pilot symbols, known to the receiver, and data symbols, unknown to the receiver. We focus on signalling constellations that have symbols lying on the complex unit circle, such as M-ary phase shift keying (M-PSK). We describe an algorithm for computing the estimator that requires O(L log L) operations in the worst case, where L is the number of transmitted symbols. Our estimator integrates information from the pilot symbols more effectively than popular estimators from the literature that usually split estimation into two subproblems called symbol timing and frame synchronisation. Our estimator combines these subproblems into a single operation, that of estimating time offset. We hypothesise that our estimator will be statistically more accurate. Monte-Carlo simulations support this hypothesis.