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

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186 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 1 2006


  • 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

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