Analysis of BER and Coverage Performance of LoRa Modulation under Same Spreading Factor Interference

In the patented LoRa modulation, linearly increasing cyclic chirp signals span the LoRa bandwidth. The rate of increase of these chirp signals is dependent on the applied spreading factor that could vary between 7 and 12. Typically, LoRa signals with different spreading factors are quasi-orthogonal such that LoRa supports multiple simultaneous logical networks. Nevertheless, coverage of LoRa signals may still be maintained under same spreading factor interference provided that the signal of interest satisfies some SNR as well as SIR thresholds. In this paper, numerical approximation of BER performance of LoRa modulation as a function of both SNR and SIR is provided. The advantage of the proposed analysis is that it incorporates the joint impact of SNR and SIR on the coverage probability of LoRa signals exposed to same spreading factor interference. This is contrary to the prevailing approaches in the literature that set independent SNR and SIR thresholds to signify coverage. Comparison between numerical and simulation results shows the high accuracy of the presented approximation. Moreover, simulation of LoRa networks with uniformly distributed end-devices reveals that the approaches adopted in the literature of using a constant SIR threshold of 6 dB to declare coverage may significantly underestimate the coverage probability of LoRa signals under same spreading factor interference.