In this paper, we develop a comprehensive statistical framework to characterize and model large-scale unmanned aerial vehicle-enabled post-disaster recovery cellular networks. In the case of natural or man-made disasters, the cellular network is vulnerable to destruction resulting in coverage voids or coverage holes. Drone-based small cellular networks (DSCNs) can be rapidly deployed to fill such coverage voids. Due to capacity and back-hauling limitations on drone small cells (DSCs), each coverage hole requires a multitude of DSCs to meet the shortfall coverage at a desired quality-of-service. Moreover, ground users also tend to cluster in hot-spots in a post-disaster scenario. Motivated by this fact, we consider the clustered deployment of DSCs around the site of a destroyed BS. Joint consideration partially operating BSs and deployed DSCs yields a unique topology for such public safety networks. Borrowing tools from stochastic geometry, we develop a statistical framework to quantify the down-link performance of a DSCN. Our proposed clustering mechanism extends the traditional Matern and Thomas cluster processes to a more general case, where cluster size is dependent upon the size of the coverage hole. We then employ the newly developed framework to find closed-form expressions (later verified by Monte-Carlo simulations) to quantify the coverage probability, area spectral efficiency, and the energy efficiency for the down-link mobile user. Finally, we explore several design parameters (for both of the adopted cluster processes) that address optimal deployment of the network (i.e., number of drones per cluster, drone altitudes, and transmit power ratio between the traditional surviving base stations and the drone base stations).
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