Large wireless networks under fading, mobility, and delay constraints

We study wireless ad hoc networks with a large number of nodes. We first focus on a network of n immobile nodes, each with a destination node chosen in random. We develop a scheme under which, in the absence of fading, the network can provide each node with a traffic rate λ₁(n)=K₁(nlog n)^-1 2/. This result was first shown in J. Hightower and G. Borriello (2001) under a similar setting, however the proof presented here is shorter and uses only basic probability tools. We then proceed to show that, under a general model of fading, each node can send data to its destination with a rate λ₂(n)=K₂n^-1/ ²(log n)^-32/. Next, we extend our formulation to study the effects of node mobility. We first develop a simple scheme under which each of the a mobile nodes can send data to a randomly chosen destination node with a rate λ₃(n)=K₃n^-12/(log n)^-32/, and with a fixed upper bound on the packet delay d_max that does not depend on n. We subsequently develop a scheme under which each of the nodes can send data to its destination with a rate λ₄(n)=K₄n^(d-1) 2/(log n)^-5 2 /provided that nodes are willing to tolerate packet delays smaller than d_max(n)5n^d, where 0i, and with probability approaching 1 as the number of nodes n approaches infinity.