  In this paper, 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.
