A calculus for log-convex interference functions

Holger Boche, Martin Schubert

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish
Pages (from-to)5469-5490
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - 2008
Externally publishedYes


  • Achievable region
  • Interference function
  • Log-convex
  • Max-min fairness
  • Multiuser wireless communication
  • Quality-of-service (QoS)


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