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 a single matched filter is sufficient to decode all LoRa data symbols. Further, when the output of the matched filter is sampled at a rate equal to the transmission bandwidth, a constant frequency 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.

LoRa是最近开发的物理层调制技术，其特征在于低功耗和远程通信能力。由于这些功能在物联网中的有机关联，LoRa在当代电信行业中获得了巨大的吸引力。对LoRa的功能和应用进行了严格的分析。但是，由于其专有的性质，潜在的调制波形的精确描述尚未公开。在本文中，我们首先针对LoRa的chi频率和相位推导了数学特征。我们的分析表明，单个匹配滤波器足以解码所有LoRa数据符号。此外，当以等于传输带宽的速率对匹配滤波器的输出进行采样时，会产生一个恒定频率输出，该频率直接对应于所传输的符号值。为了直观了解LoRa，我们在通信管道的不同阶段提供了其波形的详细仿真。特别地，错误性能仿真清楚地表明，即使SNR低于0 dB，LoRa仍可以接收和解码数据包 。