Mathematical Characterization and Simulation of LoRa

LoRa is a recently developed physical layer modulation technique characterized by low power consumption and long range communication capabilities. Due to the organic relevance of these features in the Internet of Things, LoRa has gained significant traction in the contemporary telecom industry. LoRa has been rigorously analyzed with regard to its functionalities and applications. However, due to its proprietary nature, precise descriptions of the underlying modulation waveforms are not publicly available. In this paper, we first derive a mathematical characterization of LoRa with regard to its chirp frequency and phase. Our analysis shows that asinglematched filter is sufficient to decodeallLoRa data symbols. Further, when the output of the matched filter is sampled at a rate equal to the transmission bandwidth, aconstantfrequency output is produced, which directly corresponds to the transmitted symbol value. For a visual understanding of LoRa, we present detailed simulations of its waveforms at different stages of the communication pipeline. In particular, the error performance simulation clearly demonstrates that LoRa can receive and decode data packets even when the SNR is below 0 dB.