On the scalability and capacity of wireless networks with omnidirectional antennas

We consider a wireless network of N nodes equipped with omnidirectional antennas, and we extend the capacity results of some previous works by finding bounds on the maximum achievable per-node end-to-end throughput, λ_e, while using a general network model and a bounded propagation model. Specifically, we show that when the network domain has a fixed area, λ_e is Θ(1/N) even when the mobility pattern of the nodes, the temporal variation of transmission powers, the source-destination pairs, and the possibly multi-path routes between them are optimally chosen. This result continues to hold even when the nodes are capable of maintaining multiple transmissions and/or receptions simultaneously, or when the communication bandwidth is partitioned into sub-channels of smaller bandwidth. We also address how λ_e depends on the other network parameters such as the area of the network domain, the path loss exponent, or the average number of hops between a source and a destination. Finally, we determine some required conditions to achieve a non-vanishing per-node end-to-end throughput as the number of nodes in the network grows large.