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.