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Optimum synchronization of frames with unknown, variable lengths on Gaussian channels

In this paper, we study frame synchronization based on the sync word in the general case when the frame size is unknown and possibly variable on a frame by frame basis. We assume a Gaussian channel with binary symbols and coherent decoding, where soft values are provided to the frame synchronizer. According to the hypothesis testing theory, the optimum likelihood ratio test (LRT) is derived using the Neyman-Pearson lemma. Then, the performance of the test is analytically assessed. The obtained closed form expressions allow also the derivation of the receiver operating characteristic (ROC) curves for the LRT synchronizer, showing that a remarkable gain is obtained with respect to synchronization based on a correlation metric.