On the scalability and capacity of planar wireless networks with omnidirectional antennas

Abstract

An Erratum has been published for this article in Wireless Communications and Mobile Computing 2004; 4(4): 473. We extend the previously well-known results on the capacity of wireless networks and present the implications of our results on network scalability. In particular, we find bounds on the maximum achievable per-node end-to-end throughput, λe, and the maximum number of simultaneously successful wireless transmissions, Ntmax, under a more general network scenario than previously considered. Furthermore, in the derivation of our results, we make no restrictions on the mobility pattern of the nodes or on the number simultaneous transmissions and/or receptions that nodes are capable of maintaining. In our derivation, we analyze the effect of parameters such as the area of the network domain, A, the path loss exponent, γ, the processing gain, G, and the SINR threshold, β. Specifically, we prove the following results for a wireless network of N nodes that are equipped with omnidirectional antennas: (1) λe is Θ(1/N) under very general conditions. This result continues to hold even when the communication bandwidth is divided into sub-channels of smaller bandwidth. (2) Ntmax has an upper bound that does not depend on N, which is the simultaneous transmission capacity of the network domain, NtQ. For a circular network domain, NtQ is O(Amin{γ/2,1}) if γ≠2 and O(A/log(A)) if γ = 2. In addition, NtQ is O(γ2) and O(G/β). Moreover, lack of attenuation and lack of space are equivalent, where NtQ cannot exceed 1 + G/β. (3) As N ∞ a desired per-node end-to-end throughput is not achievable, unless the average number of hops between a source and a destination does not grow indefinitely with N, A grows with N and N is O(Amin{γ/2,1}) if γ≠2 and O(A/log(A)) if γ = 2. Copyright © 2004 John Wiley & Sons, Ltd.