Resource Allocation for Robust Stabilization of Foschini-Miljanic Algorithm

In this paper, we study stabilization problems for a distributed power control algorithm (Foschini-Miljanic Algorithm) for wireless communication networks. Due to the practical importance of the algorithm, several methodologies for the stability analysis of the algorithm have been developed in the literature. However, the problem of stabilizing the dynamics of the algorithm by tuning its parameters has been left as an open problem. In this context, we consider the problem of adjusting transmission and interference gains of the channels in the communication network for ensuring the stability of the algorithm. The main results of this paper show that the following two stabilization problems, namely, the problems of input-output stabilization and stabilization subject to structural uncertainties, can be efficiently solved by geometric programming. We present numerical simulations for illustrating the effectiveness of the theoretical results obtained in the paper.