Degrees of freedom of two-hop wireless networks: Everyone gets the entire cake

Ilan Shomorony, Amir Salman Avestimehr

Research output: Contribution to journalArticlepeer-review


We show that fully connected two-hop wireless networks with K sources, K relays, and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new achievability scheme which we call Aligned Network Diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. In addition, we extend our scheme to multihop networks with fully connected hops, and multihop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.

Original languageEnglish (US)
Article number6766765
Pages (from-to)2417-2431
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2014
Externally publishedYes


  • Two-hop communications
  • degrees of freedom
  • relays
  • wireless networks

ASJC Scopus subject areas

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


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