We investigate the uplink transmission performance of low-power wide-area networks (LPWANs) with regards to coexisting radio modules using LoRa as an example. In doing so we adopt a new topology to model the network where the node locations of the network of focus (LoRa) follow a Poisson cluster process (PCP) while other coexisting interfering radio modules follow a Poisson point process (PPP). To characterize the performance of the proposed model as well as obtain insights, both analytical and closed-form approximated expressions for coverage probability are derived. Based on this, area spectrum efficiency, and energy efficiency are further characterized. These results demonstrate the degree to which the performance, with regard to the aforementioned metrics, is capable of being enhanced through varying the density of the deployment of LoRa nodes around each LoRa receiver. Moreover, simulation results unveil that an optimal value of active LoRa nodes in each cluster exists that maximizes area spectrum efficiency.