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Considering a short frame length, which is typical in Ultra-ReliableLow-Latency and massive Machine Type Communications, a trade-off exists betweenimproving the performance of frame synchronization (FS) and improving theperformance of information throughput. In this paper, we consider the case ofcontinuous transmission over AWGN channels where the synchronization sequenceis superimposed to the data symbols, as opposed to being added as a frameheader. The advantage of this superposition is that the synchronization lengthis as long as the frame length. On the other hand, its power has to betraded-off not to degrade the code performance. We first provide the analysisof FS error probability using an approximation of the probability distributionof the overall received signal. Numerical evaluations show the tightness of ouranalytic results. Then we optimize the fraction of power allocated to thesuperimposed synchronization sequence in order to maximize the probability ofreceiving a frame without synchronization errors nor decoding errors.Comparison of the theoretical model predictions to a practical setup show veryclose optimal power allocation policies.

Superimposed Frame Synchronization Optimization for Finite Blocklength Regime