Capacity of Wireless Ad-hoc Networks under Ultra Wide Band with Power Constraint

In this paper, we study how the achievable throughput scales in a wireless network with randomly located nodes as the number of nodes increases, under a communication model where (i) each node has a maximum transmission power W_0 and is capable of utilizing B Hz of bandwidth and (ii) each link can obtain a channel throughput according to the Shannon capacity. Under the limiting case that B tends to infinity, we show that each node can obtain a throughput of \Theta(n^{(\alpha-1)/2}) where n is the density of the nodes and \alpha is the path loss exponent. Both the upper bound and lower bound are derived through percolation theory. In order to derive the capacity bounds, we have also derived an important result on random geometric graphs: if the distance between two points in a Poisson point process with density n is non-diminishing, the minimum power route requires power rate at least \Omega(n^{(1-\alpha)/2}). Our results show that the most promising approach to improving the capacity bound in wireless ad hoc networks is to employ unlimited bandwidth resources, such as UWB