Robust modeling and analysis for wireless data resource management

Recent publications recognize that decentralized algorithms useful in wireless data applications can be obtained via microeconomics and game theory. In these studies, each agent maximizes, under appropriate rules and constraints, a quality-of-service (QoS) index. A key solution is a "Nash equilibrium"; i.e., an allocation from which no agent is better off by unilaterally "deviating". The actual maximization may be made by software which may not be directly "controllable" by a human user. The model and, especially, the chosen QoS index should be as general as possible, so that the derived results be applicable to a wide variety of channel conditions, modulation schemes, and other physical-layer characteristics. Likewise, the chosen index should exhibit predictable and reliable technical behavior, without exacting a high complexity cost. This note describes a model, and particularly, a QoS index which can accommodate a wide variety of physical layer situations. The proposed index is shown to exhibit solid technical behavior, be physically significant, intuitively appealing, and applicable to a wide variety of physical layer situations. A game in which terminals carrying multi-rate traffic seek to maximize this index is analyzed, and closed-form equilibrium conditions and power levels are derived "from first principles". All terminals want the same signal-to-interference ratio (SIR), but some cannot reach the necessary power level. At equilibrium, a number of terminals transmit full power, and others achieve the same optimal SIR. A basic rationale to search for these equilibria is provided.