This paper addresses the problem of resource allocation in an interference-coupled wireless network. The Nash bargaining theory is an established framework for analyzing resource allocation problems. But in a wireless context, interference between users can result in a complicated structure of the quality-of-service region, depending on many aspects, like power allocation, signal processing etc. For this model, there also exists an established framework of network utility optimization, motivated by fairness and efficiency issues. In this paper, we show that for a certain class of log-convex interference functions, the symmetric Nash bargaining game is equivalent to proportional fairness, as introduced by Kelly et.al. This provides a link between the axiomatic framework of interference functions and the bargaining theory (which is also based on axioms). In particular, it turns out that under certain conditions, proportional fair resource allocation can be interpreted as a symmetric Nash bargaining game, with equal user priorities. So besides the classical motivation for proportional fairness (as an alternative to max-min fairness), an additional motivation in terms of bargaining is obtained. This is a step towards a general better understanding of fairness issues in wireless networks.
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