Topological entropy in wireless networks subject to composite fading

We analyze topological entropy in wireless networks that are subject to local scattering and macroscopic shadowing effects. To this end, we model a network as a random geometric graph with probabilistic pair connections (due to channel randomness) and define uncertainty as the Shannon entropy of the underlying graph ensemble.We present new bounds on topological entropy that are functionals of the underlying composite fading distributions and use these to show that different fading models lead to very different network entropies under certain conditions, a result that has significant implications for self-organization and storage of the network state. We also study the behavior of the entropy bounds as the number of nodes n in the network grows large while the typical connection range r0 varies monotonically with n. This analysis leads to two key results that quantify the rate of growth or decay of r0, as a function of the number of nodes n, that must be obeyed in order for the entropy bounds to converge to a positive limit. Although the contributions of this paper are theoretical, they have applications in systems such as ad hoc networks employing opportunistic routing and device-to-device (D2D) networks for future cellular communication