Capacity of ad hoc wireless networks with infrastructure support

We determine the asymptotic scaling for the per user throughput in a large hybrid ad hoc network, i.e., a network with both ad hoc nodes, which communicate with each other via shared wireless links of capacity W bits/s, and infrastructure nodes which in addition are interconnected with each other via high capacity links. Specifically, we consider a network model where ad hoc nodes are randomly spatially distributed and choose to communicate with a random destination. We identify three scaling regimes, depending on the growth of the number of infrastructure nodes, m relative to the number of ad hoc nodes n, and show the asymptotic scaling for the per user throughput as n becomes large. We show that when m ≲ √n/logn the per user throughput is of order W/√n log n and could be realized by allowing only ad hoc communications, i.e., not deploying the infrastructure nodes at all. Whenever √n/log n ≲ m ≲ n/log n, the order for the per user throughput is Wm/n and, thus, the total additional bandwidth provided by m infrastructure nodes is effectively shared among ad hoc nodes. Finally, whenever m ≳ n/log n, the order of the per user throughput is only W/log n, suggesting that further investments in infrastructure nodes will not lead to improvement in throughput. The results are shown through an upper bound which is independent of the routing strategy, and by constructing scenarios showing that the upper bound is asymptotically tight.