  LoRaWAN enables massive connectivity for Internet-of-Things applications.
Many published works employ stochastic geometry to derive outage models of
LoRaWAN over fading channels assuming fixed transmit power and distance-based
spreading factor (SF) allocation. However, in practice, LoRaWAN employs the
Adaptive Data Rate (ADR) mechanism, which dynamically adjusts SF and transmit
power of nodes based on channel state. The community addressed the performance
of ADR using simulations, but analytical models have not been introduced. In
this letter, we seek to close this gap. We build over an analytical LoRaWAN
model to consider the performance of steady-state ADR-enabled LoRaWAN. We
derive outage expressions and an optimization procedure to maximize the number
of users under reliability constraints. Results show that power allocation
reduces interference and improves network capacity while reducing average
power.
