  In this paper, we investigate the uplink transmissions in low-power wide-area
networks (LPWAN) where the users are self-powered by the energy harvested from
the ambient environment. Demonstrating their potential in supporting diverse
Internet-of-Things (IoT) applications, we focus on long range (LoRa) networks
where the LoRa users are using the harvested energy to transmit data to a
gateway via different spreading codes. Precisely, we study the throughput
fairness optimization problem for LoRa users by jointly optimizing the
spreading factor (SF) assignment, energy harvesting (EH) time duration, and the
transmit power of LoRa users. First, through examination of the various
permutations of collisions among users, we derive a general expression of the
packet collision time between LoRa users, which depends on the SFs and EH
duration requirements. Then, after reviewing prior SF allocation work, we
develop two types of algorithms that either assure fair SF assignment indeed
purposefully 'unfair' allocation schemes for the LoRa users. Our results
unearth three new findings. Firstly, we demonstrate that, to maximize the
minimum rate, the unfair SF allocation algorithm outperforms the other
approaches. Secondly, considering the derived expression of packet collision
between simultaneous users, we are now able to improve the performance of the
minimum rate of LoRa users and show that it is protected from inter-SF
interference which occurs between users with different SFs. That is, imperfect
SF orthogonality has no impact on minimum rate performance. Finally, we have
observed that co-SF interference is the main limitation in the throughput
performance, and not the energy scarcity.
