Cooperative transmission for relay networks based on second-order statistics of channel state information

Jiangyuan Li, Athina P. Petropulu, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


Cooperative transmission in relay networks is considered, in which a source transmits to its destination with the help of a set of cooperating nodes. The source first transmits locally. The cooperating nodes that receive the source signal retransmit a weighted version of it in an amplify-and-forward (AF) fashion. Assuming knowledge of the second-order statistics of the channel state information, beamforming weights are determined so that the signal-to-noise ratio (SNR) at the destination is maximized subject to two different power constraints, i.e., a total (source and relay) power constraint, and individual relay power constraints. For the former constraint, the original problem is transformed into a problem of one variable, which can be solved via Newton's method. For the latter constraint, this problem is solved completely. It is shown that the semidefinite programming (SDP) relaxation of the original problem always has a rank one solution, and hence the original problem is equivalent to finding the rank one solution of the SDP problem. An explicit construction of such a rank one solution is also provided. Numerical results are presented to illustrate the proposed theoretical findings.

Original languageEnglish (US)
Article number5643179
Pages (from-to)1280-1291
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2011

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Channel uncertainty
  • Semidefinite programming
  • cooperative communications
  • relay networks


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