Nash Bargaining and Proportional Fairness for Wireless Systems
Boche, H.
Schubert, M.
Fraunhofer Inst. for Telecommun., Heinrich-Hertz-Inst., Berlin, Germany;
This paper appears in: Networking, IEEE/ACM Transactions on
Publication Date: Oct. 2009
Volume: 17,
Issue: 5
On page(s): 1453-1466
ISSN: 1063-6692
INSPEC Accession Number: 10918115
Digital Object Identifier: 10.1109/TNET.2009.2026645
First Published: 2009-08-21
Current Version Published: 2009-10-13
Abstract
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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