Optimum metric for frame synchronization with gaussian noise and unequally distributed data symbols

The problem of frame synchronization with equiprobable data symbols is widely analyzed in the literature and the optimum metric for AWGN channels has been derived both in the case of periodically and aperiodically embedded data symbols. On the contrary, the case of non-equiprobable data symbols has not been studied, although it can occur in many practical situations. An optimum metric for frame synchronization in data streams with non-uniformly distributed data symbols is derived in this paper and its performance is investigated through simulation. A performance comparison with the metric which is optimal for equiprobable data symbols is also provided. Results show that the derived optimum metric results in an evident gain, at the expense of a small additional complexity.