A power control game with smooth reduction of SINR objectives

When rate expectations of users in a wireless network cannot all be satisfied, one choice is to discard some users from the system, in a mechanism called admission control. However, in a data network, users have a certain tolerance to occasional rate outages. In this paper we argue that it may be preferable for users to reduce their rate objectives smoothly, by considering an outage probability tolerance, rather than not be provided any service at all. We propose a distributed utility based algorithm for doing this. The smoothness of reactions is obtained by making transmit power reaction curves absolutely subhomogeneous functions of interference. This is done using an ¿objective reduction factor¿, in addition to a linear price. We first provide conditions for a unique Nash equilibrium. Assuming that distributed nodes use gradient based optimization, convergence and error sensitivity of gradient based iterative algorithms are analyzed. Lastly, the continuous-time counterpart of the problem is considered and a stability condition is established for the system.