On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

This article deals with time and frequency synchronization in the Long Range (LoRa) system based on the preamble symbols. A thorough analysis of the maximum-likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the
a priori
solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of an LoRa receiver.