Superimposed frame synchronization optimization for Finite block-length regime
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Considering a fixed frame length, a trade-off exists between improving the performance of frame synchronization (FS) versus improving the performance of information throughput. In this paper, we consider the case of continuous transmission over AWGN channels where the synchronization sequence is superimposed to the data symbols, as opposed to being added as a frame header. The advantage of this superposition is that the synchronization length is as long as the frame length. On the other hand, its power has to be traded-off not to degrade the code performance. We first provide the analysis of FS error probability using an approximation of the probability distribution of the overall received signal. Numerical evaluations show the tightness of our analytic results. We illustrate the optimization of the power allocation granted to the superimposed synchronization sequence in order to maximize the probability of receiving a frame without synchronization errors nor decoding errors. Finally, this theoretical model is compared to a practical setup to show that their optimal power allocations are very close.
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