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

Abstract

This paper deals with time and frequency synchronization in 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 a LoRa receiver. <br>

A Maximum-Likelihood-Based Two-User Receiver for LoRa Chirp Spread-Spectrum Modulation

“…Contrary to the algorithms of [38], [39], and [46], the synchronization algorithm of our two-user receiver has to detect and estimate the parameters of a new user even in the presence of a colliding user. For a single-user receiver, demodulating the upchirps and downchirps in the preamble (see Fig.…”