Large wireless networks under fading, mobility, and delay constraints

We study wireless ad hoc networks with a large number of nodes, following the line of investigation initiated in [1] and continued in [2]. 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 λ ₁(n) = K ₁(n log n) ^-1/2. This result was first shown in [1] 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 λ ₂(n) = K ₂n ^-1/2(log n) ^-3/2. Next, we extend our formulation to study the effects of node mobility. We first develop a simple scheme under which each of the n mobile nodes can send data to a randomly chosen destination node with a rate λ ₃(n) = K ₃n ^-1/2 (log n) ^-3/2, 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 λ ₄(n) = K ₄n ^d-1/2 (log n) ^-5/2, provided that nodes are willing to tolerate packet delays smaller than d _max(n) < K ₅n ^d, where 0 < d < 1. With both schemes, a general model of fading is assumed. In addition, nodes require no global topology or routing information, and only need to coordinate locally. The above results hold for an appropriate choice of values for the constants K _i, and with probability approaching 1 as the number of nodes n approaches infinity.