Distributed topology control of wireless networks

We propose and analyze a distributed control law that will maintain prescribed local properties of a wireless ad hoc network in the presence of node mobility, MAC layer power control and link fades. The control law uses a simple and intuitive power adaptation mechanism. We consider as an example the topology requirement of maintaining the out degrees of each node at prescribed values and keeping the in degree close to the out degree. The topology objective is achieved by adapting the transmission power based only on local information. This power adaptation algorithm is analyzed using the o.d.e. approach to stochastic approximation. Simulation results verify the analysis and demonstrate its effectiveness. We also study the ability of the proposed objective to maintain connectivity. Although many heuristics are described in the literature to maintain local topological properties, the algorithm proposed in this paper is the first one that has proven convergence properties.