As the Internet of Things (IoT) is largely supported by wireless communication networks in unlicensed bands, there has been a proliferation of technologies that use a large variety of protocols. An ongoing challenge is how these networks can coexist given that they have different power levels, symbol periods, and access protocols. In this paper, we study the statistics of interference due to IoT networks that transmit small amounts of data. A key observation is that sets of active devices change rapidly, which leads to impulsive noise channels. Moreover, these devices operate on multiple partially overlapping resource blocks. As such, we characterize the joint distribution and propose a tractable model based on copulas. Using our copula model, we derive closed-form achievable rates. This provides a basis for resource allocation and network design for coexisting IoT networks. I. INTRODUCTION With the increasing scale of wireless network deployments for the Internet of Things (IoT), an ongoing challenge is to ensure that these networks can coexist. A key issue is that interference from a large number of devices, even if they operate at low power levels, can degrade the performance of other communication networks. This means that the interference statistics are difficult to characterize and has lead to a number of experimental studies on the interference in various contexts [1]-[4]. One feature observed in IoT networks is the presence of impulsive interference, where high amplitude interference is significantly more likely than in Gaussian models. This behavior has been observed both in experimental studies [4] and also in theoretical analysis [5], [6]. As a consequence, Gaussian models are often not appropriate and the interference statistics lie in a more general class of models. Introducing non-Gaussian interference models implies that the interference statistics are not simply characterized by their mean and variance. This issue is amplified in settings where a number of frequency bands are used for transmissions. In these cases, the covariance matrix is not sufficient in order to characterize the joint interference statistics over multiple frequency bands. This is particularly evident when the frequency bands used by different users only partially overlap [7], such as in non-orthogonal multiple access (NOMA) schemes [8] including sparse code multiple access (SCMA) [9]. Due to the rich dependence structure possible for the joint distribution of non-Gaussian random vectors, a key question is how it should be modeled. For the purposes of analysis,