Design and analysis of transmit-beamforming based on limited-rate feedback

Research output: Contribution to journalArticlepeer-review

212 Scopus citations


This paper deals with design and performance analysis of transmit beamformers for multiple-input multiple-output (MIMO) systems based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limited-rate feedback as an equivalent sphere vector quantization (SVQ) problem, multiantenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels are first considered. The rate-distortion function of the vector source is upper-bounded, and the operational rate-distortion performance achieved by the generalized Lloyd's algorithm is lower-bounded. Although different in nature, the two bounds yield asymptotically equivalent performance analysis results. The average signal-to-noise ratio (SNR) performance is also quantified. Finally, beamformer codebook designs are studied for correlated Rayleigh fading channels, and a low-complexity codebook design that achieves near-optimal performance is derived.

Original languageEnglish (US)
Pages (from-to)1853-1863
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 2006

Bibliographical note

Funding Information:
Manuscript received July 18, 2004; revised March 16, 2005. Prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. This work was also supported by the NSF Grant no. 01-0516. Part of this work appeared in IEEE Vehicular Technology Conference 2004-Fall, Los Angeles, CA, September 26–29, 2004. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U. S. Government. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Steven L. Grant.


  • Beamforming
  • Generalized Lloyd algorithm
  • Grassmannian line packing
  • Limited rate feedback
  • Multiple-input multiple-output (MIMO)
  • Partial channel state information
  • Rate-distortion function
  • Vector quantization
  • Welch bound


Dive into the research topics of 'Design and analysis of transmit-beamforming based on limited-rate feedback'. Together they form a unique fingerprint.

Cite this