Jointly Optimal Power Allocation and Constrained Node Placement in Wireless Networks of Agents

In this paper, we investigate the optimal design of wireless networks. We consider wireless networks that have fixed and movable nodes, and we assume that all nodes feature adjustable transmission power. Hence, we aim at maximizing network centric objectives, by optimizing over admissible choices of the positions of the movable nodes as well as the transmission power at all the nodes. We adopt exponential path loss, which is a realistic assumption in urban and sub sea environments, and we propose ways of using this assumption to obtain a tractable optimization problem. Our formulation allows for the optimization of typical network centric objectives, such as power and throughput. It also allows signal-to-interference based constraints, such as rate-regions and outage probabilities, under the high signal to interference regime. We show that our optimization paradigm is convex and that it can be solved up to an arbitrary degree of accuracy via geometric programming techniques. By using a primal-dual decomposition, we also provide a case-study that illustrates how certain instances of our optimization paradigm can be solved via distributed iterative algorithms. We show that such a solution method also leads to a convenient layering in the primal step, whereby the power allocation and the node placement become two independent sub-problems.