Frame Synchronization for Gaussian Channels

The problem of locating a periodically inserted frame synchronization pattern in random data for a
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-ary digital communication system operating over the additive white Gaussian noise channel is considered. The optimum maximum-likelihood decision rule, high signal-to-noise approximate maximum likelihood decision rule, and ordinary correlation decision rule for frame synchronization are derived for both coherent and noncoherent phase demodulation. A general lower bound on synchronization probability is derived for the coherent correlation rule. Monte Carlo computer simulations of all three decision rules, along with evaluations of the lower bound for the coherent correlation rule, were performed for the coherent MPSK, coherent, and noncoherent
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ary orthogonal, and 16 QAM signaling schemes. These results show that in each case the high signal-to-noise maximum-likelihood rules have a performance nearly equal to that of the maximum-likelihood rules over a wide range of practically interesting signal-to-noise ratios (SNR's). These high SNR decision rules also provide significant performance improvement over the simple correlation rules. Moreover, they are much simpler to implement than the maximum-likelihood decision rules and, in fact, are no more complex than the correlation rules.