On the Achievable Throughput in Two-Scale Wireless Networks

We propose a new model of wireless networks which we refer to as "two-scale networks". At a local scale, characterized by nodes being within a distance r, channel strengths are drawn independently and identically from a distance-independent distribution. At a global scale, characterized by nodes being further apart from each other than a distance r, channel connections are governed by a Rayleigh distribution, with the power satisfying a distance-based decay law. Thus, at a local scale, channel strengths are determined primarily by random effects such as obstacles and scatterers whereas at the global scale channel strengths depend on distance. For such networks, we propose a hybrid communications scheme, combining elements of P. Gupta et al. (2000) (for distance-dependent networks) and R. Gowaikar et al. (2006) (for random networks). For a particular class of two-scale networks with N nodes, we show that an aggregate throughput of the form N[1divide(t-1)] /log2N is achievable, where t > 2 is a parameter that depends on the distribution of the connection at the local scale and is independent of the decay law that operates at a global scale. For t < 3, this offers a significant improvement over the O(radicN) results of P. Gupta et al. (2000)