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Abstract
The problem of locating a periodically inserted frame synchronization pattern in random data is considered where the decision rule is based on a multiple number of channel output frames. Optimum multiple frame maximum likelihood (ML) rules, high signal-to-noise-ratio (SNR) approximate ML rules and correlation rules were derived for the coherent-phase and noncoherent-phase additive white Gaussian noise (AWGN) channel, the direct detection optical Poisson channel, and the Rayleigh fading channel. General modulation schemes were considered for the AWGN channel. This work was restricted to pulse position modulation (PPM) and on-off keying (OOK) signalling over the optical channel. Orthogonal signalling was considered primarily in the Rayleigh fading case. A general upper bound on correct synchronization probability was derived along with some lower bounds valid for the correlation decision rule used over the coherent AWGN and optical channels. Computer simulations and analytical bounds on performance show that the high SNR approximate ML rule has performance approaching that of the ML rule over a wide range of SNRs. These high SNR approximate ML decision rules also provide substantial performance improvements over the correlation rules with virtually no additional implementation complexity. The performance improvements gained by using a multiple number of frames were also substantial. In many of the cases considered the two-frame correlation rule was better than the one-frame ML rule.
Spatial and time diversity techniques were investigated for the Rayleigh channel case. It was found that time diversity yielded no performance advantage. Spatial diversity was advantageous in cases where the length of the fixed synchronization pattern was substantial compared to the frame length. In other cases, multiple frame observations was better than spatial diversity.
The joint symbol and frame synchronization problem was investigated for PPM signalling over the direct detection optical channel. The optimum ML decision rule for the problem previously derived by other work was shown to be incorrect. The correct optimum ML was derived and was shown to have a substantial performance improvement over the previous incorrect ML rule. A computationally efficient implementation for the optimum ML rule was also derived.
