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Nash Bargaining and Proportional Fairness for Wireless Systems

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2 Author(s)
Boche, H. ; Fraunhofer Inst. for Telecommun., Heinrich-Hertz-Inst., Berlin, Germany ; Schubert, M.

Nash bargaining and proportional fairness are popular strategies for distributing resources among competing users. Under the conventional assumption of a convex compact utility set, both techniques yield the same unique solution. In this paper, we show that uniqueness is preserved for a broader class of logarithmically convex sets. Then, we study a scenario where the performance of each user is measured by its signal-to-interference ratio (SIR). The SIR is modeled by an axiomatic framework of log-convex interference functions. No power constraints are assumed. It is shown how existence and uniqueness of a proportionally fair optimizer depends on the interference coupling among the users. Finally, we analyze the feasible SIR set. Conditions are derived under which the Nash bargaining strategy has a single-valued solution.

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Networking, IEEE/ACM Transactions on  (Volume:17 ,  Issue: 5 )