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Low power wide area networks (LPWAN) are emerging as a new paradigm, especially in the field of Internet of Things (IoT) connectivity. LoRa is one of the LPWAN and it is gaining quite a lot of commercial traction. The modulation underlying LoRa is patented and has never been described theoretically. The aim of this letter is to give the first rigorous mathematical signal processing description of the modulation and demodulation processes. We provide as well a theoretical derivation of the optimum receiver entailing a low-complexity demodulation process, resorting to the Fast Fourier Transform. We compare then the performance of the LoRa modulation and the frequency-shift keying modulation both in an additive white gaussian noise channel and a frequency selective channel, showing the superiority of the LoRa modulation in the frequency selective channel. The results of this letter will enable a further assessment of the LoRa based networks, much more rigorous than what has been done until now.
Lorenzo Vangelista (Tue,) studied this question.