Dynamic Spectrum Sharing Among Repeatedly Interacting Selfish Users With   Imperfect Monitoring
  We develop a novel design framework for dynamic distributed spectrum sharing among secondary users (SUs) who adjust their power levels to compete for spectrum opportunities while satisfying the interference temperature (IT) constraints imposed by primary users. The considered interaction among the SUs is characterized by the following three features. First, since the SUs are decentralized, they are selfish and aim to maximize their own long-term payoffs from utilizing the network rather than obeying the prescribed allocation of a centralized controller. Second, the SUs interact with each other repeatedly and they can coexist in the system for a long time. Third, the SUs have limited and imperfect monitoring ability: they only observe whether the IT constraints are violated, and their observation is imperfect due to the erroneous measurements. To capture these features, we model the interaction of the SUs as a repeated game with imperfect monitoring. We first characterize the set of Pareto optimal payoffs that can be achieved by deviation-proof spectrum sharing policies, which are policies that the selfish users find it in their interest to comply with. Next, for any given payoff in this set, we show how to construct a deviation-proof policy to achieve it. The constructed deviation-proof policy is amenable to distributed implementation, and allows users to transmit in a time-division multiple-access (TDMA) fashion. In the presence of strong multi-user interference, our policy outperforms existing spectrum sharing policies that dictate users to transmit at constant power levels simultaneously. Moreover, our policy can achieve Pareto optimality even when the SUs have limited and imperfect monitoring ability, as opposed to existing solutions based on repeated games, which require perfect monitoring abilities. 
Yuanzhang Xiao and Mihaela van der Schaar
cs.IT math.IT