In this letter, we investigate performance improvements of low-power long-range (LoRa) modulation when a gateway is equipped with multiple antennas. We derive the optimal decision rules for both coherent and non-coherent detections when combining signals received from multiple antennas. To provide insights on how signal combining can benefit LoRa systems, we present expressions of the symbol/bit error probabilities of both the coherent and non-coherent detections in AWGN and Rayleigh fading channels, respectively. Moreover, we also propose an iterative semi-coherent detection that does not require any overhead to estimate the channel-state-information (CSI) while its performance can approach that of the ideal coherent detection. Simulation and analytical results show very large power gains, or coverage extension, provided by the use of multiple antennas for all the detection schemes considered.

中文翻译：

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LoRa 调制与信号组合和半相干检测的性能改进

在这封信中，我们研究了网关配备多个天线时低功耗远程 (LoRa) 调制的性能改进。当组合从多个天线接收的信号时，我们推导出相干和非相干检测的最佳决策规则。为了深入了解信号组合如何使 LoRa 系统受益，我们分别给出了 AWGN 和瑞利衰落信道中相干和非相干检测的符号/比特错误概率的表达式。此外，我们还提出了一种迭代半相干检测，它不需要任何开销来估计信道状态信息（CSI），而其性能可以接近理想相干检测的性能。仿真和分析结果显示非常大的功率增益或覆盖范围扩展，