Collaboration Improves the Connectivity of Wireless Networks

In the standard approach to studying connectivity, a physical layer is assumed that allows direct transmission between neighbors within some fixed distance. The graph resulting from connecting all such pairs of neighbors reveals clusters of nodes within which communication is possible. However, future wireless networks will provide a physical layer where nodes that are connected can collaboratively search for more connections via simultaneous RF transmission and reception, thus adding connections that are not possible in the traditional non-collaborative model. The purpose of this paper is to introduce this collaborative network model and to characterize its asymptotic connectivity properties for one characterization (noncoherent power summing) of the physical layer collaboration. In the case of sparse ad hoc networks, simulations show that an infinite cluster will emerge in the infinite two-dimensional plane at a node density roughly 20% of that required in non-collaborative ad hoc networks. In the case of dense ad hoc networks, the probability for the event that the network is connected goes to one asymptotically if the transmission area of each node is [4pi(4 log N)
^{alpha/alpha+2}
(log log N+log 2)
^2/alpha+2
]/N no less than , where N is the number of nodes in the network of unit area and a is the pathless exponent. Hence, significant gains in the asymptotic connectivity properties of the ad hoc network are obtained through collaboration.