The relentless expansion of communications services and applications in 5G networks and their further projected growth bring the challenge of necessary spectrum scarcity, a challenge which might be overcome using the concept of cognitive radio. Furthermore, an extremely high number of low-power devices are introduced by the concept of the Internet of Things (IoT), which also requires efficient energy usage and practically applicable device powering. Motivated by these facts, in this paper, we analyze a wirelessly powered underlay cognitive system based on a realistic case in which statistical channel state information (CSI) is available. In the system considered, the primary and the cognitive networks share the same spectrum band under the constraint of an interference threshold and a maximal tolerable outage permitted by the primary user. To adopt the system model in realistic IoT application scenarios in which network nodes are mobile, we consider the randomly moving cognitive user receiver. For the analyzed system, we derive the closed-form expressions for the outage probability, the outage capacity, and the ergodic capacity. The obtained analytical results are corroborated by an independent simulation method.