LoRaWAN : Single gateway capacity for a reasonable traffic

We model a LoRaWAN cell and estimate the number of nodes that it can accommodate. We consider a Rayleigh channel and physical capture when two frame transmissions overlap. If all nodes have the same traffic generation pattern, regardless of the spreading factor used, the SF allocation between the nodes has a dramatic impact on the cell capacity. In effect, the modulation choice needs to strike a balance between packet losses due to a weak signal reaching the gateway and more robust modulations which cause longer channel occupation by the transmission and thus more collisions.