Properties of power control algorithms in wireless networks with delays: A Positive Systems Approach

This paper investigates power control algorithms for wireless networks. In particular, it is shown how the most frequently used algorithm for distributed on-line power control (the Foschini-Miljanic algorithm) can be studied using tools from Positive Systems theory. Thus, the stability of the algorithm in the presence of the inherent time-varying delays is proved, and the derivation of bounds on the minimum power requirements needed to fulfill its objectives are discussed. This bounds are derived also for the situation where the link parameters are not perfectly known. An illustrative example shows the applicability of the proposed results.