Superimposed frame synchronization optimization for Finite block-length regime.

Considering a short frame length, which is typical in Ultra-Reliable Low-Latency and massive Machine Type Communications, a trade-off exists between improving the performance of frame synchronization (FS) and 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. Then we optimize the fraction of power allocated to the superimposed synchronization sequence in order to maximize the probability of receiving a frame without synchronization errors nor decoding errors. Comparison of the theoretical model predictions to a practical setup show very close optimal power allocation policies.