This paper focuses on the error probability performance of LoRa, a long-range low-power wireless communication technology suited for the Internet of Things (IoT). We propose accurate approximations for the bit error probability of the uncoded LoRa chirp modulation in additive white Gaussian noise (AWGN) channel. Our approach, which is based on a smart modification of a union bound on the error probability, is applied to both coherent and noncoherent detection. Simulation results show that the proposed theoretical bit error rate (BER) expressions are more accurate than the existing BER approximations that use similar complexity. We show that the proposed BER expressions are valid for both orthogonal and quasi-orthogonal LoRa, and are easier to compute than the exact BER for orthogonal signaling. Moreover, we extend the theoretical performance analysis to coded LoRa systems and we propose analytical BER expressions for Hamming-coded LoRa signals with hard-decision decoding. In addition, we analyze by simulation the error probability of coded LoRa systems with soft-decision decoding in multipath channels. The obtained results (both theoretical and simulated) quantify the performance gains of channel coding with respect to uncoded transmissions, in both AWGN and multipath channels, for coded LoRa systems that use the same bandwidth (with lower bit rate) of the uncoded LoRa system.

本文重点介绍LoRa的错误概率性能，LoRa是一种适用于物联网（IoT）的远程低功耗无线通信技术。我们为加性高斯白噪声（AWGN）信道中未编码LoRa线性调频调制的误码率提出了精确的近似值。我们的方法基于对错误概率的并集进行智能修改的方法，适用于相干检测和非相干检测。仿真结果表明，所提出的理论误码率（BER）表达式比使用相似复杂度的现有BER近似更为准确。我们表明，所提出的BER表达式对于正交和准正交LoRa均有效，并且比用于正交信令的确切BER更容易计算。此外，我们将理论性能分析扩展到已编码的LoRa系统，并针对具有硬决策解码的汉明编码的LoRa信号提出了解析BER表达式。此外，我们通过仿真分析了在多径信道中采用软判决解码的LoRa编码系统的错误概率。对于使用与未编码LoRa系统相同带宽（比特率较低）的已编码LoRa系统，所获得的结果（理论和仿真结果）均量化了AWGN和多径信道中信道编码相对于未编码传输的性能增益。