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