Optimization of training and feedback overhead for beamforming over block fading channels

Wiroonsak Santipach*, Michael L. Honig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We examine the capacity of beamforming over a single-user, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-inputsingle-output (MISO) and multi-inputmulti-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead (T and B) as L and the number of transmit antennas N t both become large. The optimal Nt is limited by the coherence time, and increases as L/log L. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1/log Nt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log 2Nt).

Original languageEnglish (US)
Article number5625641
Pages (from-to)6103-6115
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 1 2010


  • Block fading
  • channel capacity
  • channel estimation
  • limited feedback
  • multiple-input multiple-output (MIMO)

ASJC Scopus subject areas

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

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