Distributed optimal beamformers for cognitive radios robust to channel uncertainties

Yu Zhang, Emiliano Dallanese, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


Through spatial multiplexing and diversity, multi-input multi-output (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimizes the design of transmit-and receive-beamformers for ad hoc CR networks when CR-to-CR channels are known, but CR-to-PU channels cannot be estimated accurately. Capitalizing on a norm-bounded channel uncertainty model, the optimal beamforming design is formulated to minimize the overall mean-square error (MSE) from all data streams, while enforcing protection of the PU system when the CR-to-PU channels are uncertain. Even though the resultant optimization problem is non-convex, algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations, along with suitable convex approximation techniques. Enticingly, the novel schemes also lend themselves naturally to distributed implementations. Numerical tests are reported to corroborate the analytical findings.

Original languageEnglish (US)
Article number6298975
Pages (from-to)6495-6508
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number12
StatePublished - 2012

Bibliographical note

Funding Information:
Manuscript received January 29, 2012; revised June 01, 2012 and August 15, 2012; accepted August 24, 2012. Date of publication September 11, 2012; date of current version November 20, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Francesco Verde. This work was supported by QNRF Grant NPRP 09-341-2-128. Part of this work was presented at the Thirty-Seventh International Conference on Acoustics, Speech, and Signal Processing, Kyoto, Japan, March 25–30, 2012.


  • Beamforming
  • MIMO wireless networks
  • channel uncertainty
  • cognitive radios
  • distributed algorithms
  • robust optimization


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