Figure 1.

Two received Long Range (LoRa) signals constitute eight preamble upchirp symbols at $2.4$ GHz with a bandwidth equal to 812 kHz. The spreading factor (SF) of the short signal, which ended after approximately 5 ms, is equal to 9, while the SF of the long-duration signal is equal to 10. Figures (a) and (b) represent the combined received signals in the time domain and in the spectrogram (i.e., time and frequency) domain, respectively. Figures (c) and (d) are the cross-correlation functions (6) when the received signals have been cross-correlated with base chirps of the SF equal to 10 and 9, respectively.