Performance of Unslotted ALOHA With Capture and Multiple Collisions in LoRaWAN

This article explores the capacity limits and the tradeoff between the antagonistic means of enabling reliable data delivery in a loaded LoRaWAN cell. In fact, channel attenuation and variability call for robust transmission settings but the associated load increase causes more collisions between frames. In addition to the physical-layer parameters of the LoRa modulation, this article considers the benefits and tuning of interpacket error correction codes (ECCs), which also trade transmission redundancy for reliability. We thus start by proposing a refined packet delivery ratio (PDR) model that improves the ones found in the literature in that, first, it takes into account the dependency between overcoming ambient noise and dominating colliding frames, and second, it considers the sum of interference powers when multiple colliding frames are present, even if the interference preexists. Moreover, the model extends to the case of a gateway with receiver diversity. In a second step, the model allows to set out the level of redundancy at which ECC is the most effective without hindering capacity: a coding rate of one third. When this is fixed, it allows to define the transmission parameters allocation within a cell and thus the size of the cell. We finally develop an ad-hoc Python discrete-event simulator, freely accessible, to complement the model for assessing the effect of inter-SF and near-far interference and to show the benefits of power control in this respect.