A Novel Approach to Power Allocation in Wireless Ad Hoc Networks

In this paper, we investigate the role of power allocation in wireless ad hoc networks. First, by modeling the network with a random geometric graph, we propose a two-level power allocation scheme with the total power constraint which expands the ruin-cut of the underlying random geometric graph. Then, based on available information theoretic upper bounds on transport capacity of wireless networks, we find a new power allocation which improves such bound. As will be shown, the new bound is computed based on the largest eigenvalue of a structural matrix which depends on the random location of the nodes. Finally, it will be shown that both approaches (random geometric graph min-cut analysis and the information theoretic upper bound framework) reveal that it is a fundamental network design guideline that more power should be allocated to central nodes of the network.