A Capacity Upper Bound for Large Wireless Networks with Generally Distributed Nodes

Since the seminal work of Gupta and Kumar, extensive research has been done on studying the capacity of large wireless networks under various scenarios. Most of the existing work focuses on studying the capacity of networks with uniformly or Poissonly distributed nodes. While uniform and Poisson distribution form an important class of spatial distributions, their capability in capturing the spatial distribution of users in various scenarios and application settings is limited. Therefore it is critical to investigate to what extent, the aforementioned results on capacity of networks with uniformly or Poissonly distributed nodes depend on the underlying node distribution being uniform or Poisson. In this paper, we study the capacity of networks under a general node distribution. A capacity upper bound on networks with generally distributed nodes is obtained, which is valid for both finite networks and asymptotically infinite networks. By imposing some mild conditions on the transmission range, we further simplify the result and show that the asymptotic capacity upper bound can be expressed as a product of four factors, which represents respectively the impact of node distribution, link capacity, number of source destination pairs and the transmission range. The upper bound is shown to be tight in the sense that for the special case of networks with uniformly distributed nodes, the bound is in the same order as known results in the literature.