Power control for 3G networks based on probabilistic constrained programming

This paper deals with the power control problem for wireless cellular networks. The problem is modelled by a stochastic optimization problem with probabilistic constraints considering the link gains as random vectors whose probability distribution satisfies uncertain mean and covariance constraints. Specifically, we consider that the mean vector and covariance matrix are not perfectly known, however they belong to convex hull of a fixed set. The solution is established in terms of an optimization problem over linear matrix inequalities (LMIs) and it is robust in the sense that from the set of probability distributions matching the given bounds on the mean vector and covariance matrix, we take the one that produces the lowest tail probability.