On beamforming with finite rate feedback in multiple-antenna systems

Krishna Kiran Mukkavilli, Ashutosh Sabharwal, Elza Erkip, Behnaam Aazhang

Research output: Contribution to journalArticlepeer-review


In this paper, we study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t - 1)2-B/t-1, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.

Original languageEnglish (US)
Pages (from-to)2562-2579
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2003


  • Beamforming
  • Feedback
  • Multiple antennas
  • Outage probability
  • Transmit diversity
  • Unitary codes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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