It has been well recognized that channel state information (CSI) feedback isof great importance for dowlink transmissions of closed-loop wireless networks.However, the existing work typically researched the CSI feedback problem foreach individual mobile station (MS), and thus, cannot efficiently model theinteractions among self-interested mobile users in the network level. To thisend, in this paper, we propose an alternative approach to investigate the CSIfeedback rate control problem in the analytical setting of a game theoreticframework, in which a multiple-antenna base station (BS) communicates with anumber of co-channel MSs through linear precoder. Specifically, we firstpresent a non-cooperative feedback-rate control game (NFC), in which each MSselects the feedback rate to maximize its performance in a distributed way. Toimprove efficiency from a social optimum point of view, we then introducepricing, called the non-cooperative feedback-rate control game with price(NFCP). The game utility is defined as the performance gain by CSI feedbackminus the price as a linear function of the CSI feedback rate. The existence ofthe Nash equilibrium of such games is investigated, and two types of feedbackprotocols (FDMA and CSMA) are studied. Simulation results show that byadjusting the pricing factor, the distributed NFCP game results in closeoptimal performance compared with that of the centralized scheme.
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