Power control in wireless ad hoc networks: Stability and convergence under uncertainties

A successful distributed power control algorithm requires only local measurements for updating the power level of a transmitting node, so that eventually all transmittersmeet their QoS requirements, i.e. the solution converges to the global optimum. There are numerous algorithmwhich claim to work under ideal conditions in which there exist no uncertainties and the model is identical to the real-world implementation. Nevertheless, the problem arises when real-world phenomena are introduced into the problem, such as uncertainties (such as changing environment and time delays) or the QoS requirements cannot be achieved for all the users in the network. In this chapter, we study some distributed power control algorithms for wireless ad hoc networks and discuss their robustness to real-world phenomena. Simulations illustrate the validity of the existing results and suggest directions for future research.