Cognitive transmit beamforming from binary CSIT

Balasubramanian Gopalakrishnan, Nicholas D. Sidiropoulos

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


Transmit beamforming is used to steer radiated power towards a receiver of interest and to limit interference to unintended receivers, thereby facilitating coexistence. Transmit beamforming requires accurate channel state information (CSI) at the transmitter, which is often difficult to acquire, particularly in cognitive underlay settings, where the primary receiver cannot be expected to cooperate with the secondary system to enable it to learn the secondary to primary crosstalk channel. This paper considers cases where it is not realistic to assume channel reciprocity, or that the receivers are capable of accurate CSI estimation and feedback - because they are legacy systems, or have limited computation/energy resources. Transmit beamforming from binary and infrequent CSI is first considered for an isolated link. An online beamforming and learning algorithm is developed using the analytic center cutting plane method and is shown to asymptotically attain optimal performance. A robust maximum-likelihood formulation is next developed to handle feedback errors and correlation drift. The setup is then generalized to a cognitive underlay setting, also exploiting the standard acknowledgement/negative-acknowledgement feedback on the reverse primary link. This is the first solution to jointly tackle secondary signal-to-noise ratio maximization and primary interference mitigation from only rudimentary CSI, without assuming channel reciprocity.

Original languageEnglish (US)
Article number6919297
Pages (from-to)895-906
Number of pages12
JournalIEEE Transactions on Wireless Communications
Issue number2
StatePublished - Feb 2015

Bibliographical note

Publisher Copyright:
© 2015 IEEE.


  • Transmit beamforming
  • cognitive radio network underlay
  • cutting plane method
  • maximum likelihood
  • online learning
  • spatial channel correlation


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