An approximate maximum-likelihood rule (ML) is derived for joint symbol and frame synchronization with pulse-position modulation, Simulation results show that this approximate rule performs virtually as well as the optimum ML rule over a wide range of practical signal-to-noise ratios. Yet it is substantially simpler to implement.

The problem of locating a periodically inserted frame synchronization pattern in random data for aM-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 noncoherentMary 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.

The problem of locating a periodically inserted frame synchronization pattern in random data is considered for a directdetection optical communication channel. Both pulse-position modulation and on-off keying with known symbol synchronization are considered. The high signal-to-noise ratio approximation of the maximum likelihood decision rule is derived for each of these cases. Analytical bounds and simulation results on synchronization probability show that the high SNR ML rule has a performance approaching that of the optimum ML rule over a wide range of signal-to-noise ratios. This decision rule also provides a substantial performance improvement over the correlator rule with virtually no additional implementation complexity.