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A Calculus for Log-Convex Interference Functions

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

The behavior of certain interference-coupled multiuser systems can be modeled by means of logarithmically convex (log-convex) interference functions. In this paper, we show fundamental properties of this framework. A key observation is that any log-convex interference function can be expressed as an optimum over elementary log-convex interference functions. The results also contribute to a better understanding of certain quality-of-service (QoS) tradeoff regions, which can be expressed as sublevel sets of log-convex interference functions. We analyze the structure of the QoS region and provide conditions for the achievability of boundary points. The proposed framework of log-convex interference functions generalizes the classical linear interference model, which is closely connected with the theory of irreducible nonnegative matrices (Perron-Frobenius theory). We discuss some possible applications in robust communication, cooperative game theory, and max-min fairness.

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Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 12 )