Interference alignment and the degrees of freedom of wireless X networks

Viveck R. Cadambe, Syed A. Jafar

Research output: Contribution to journalArticlepeer-review

337 Scopus citations


We explore the degrees of freedom of M, × N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to MN/M + N - 1 per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M = 2 or N = 2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1). For these cases the degrees of freedom outer bound is exactly achievable.

Original languageEnglish (US)
Pages (from-to)3893-3908
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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