  Low-power long-range (LoRa) modulation has been used to satisfy the low power
and large coverage requirements of Internet of Things (IoT) networks. In this
paper, we investigate performance improvements of 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. 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
coherent detection. Simulation and analytical results show very large power
gains provided by the use of multiple antennas for all the detection schemes
considered.
