QAM and PSK codebooks for limited feedback MIMO beamforming

Daniel J. Ryan*, I. Vaughan L. Clarkson, Iain B. Collings, Dongning Guo, Michael L. Honig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

Original languageEnglish
Pages (from-to)1184-1196
Number of pages13
JournalIEEE Transactions on Communications
Issue number4
Publication statusPublished - Apr 2009
Externally publishedYes


  • multiple-input multiple-output (MIMO)
  • beamforming
  • limited feedback
  • vector quantization
  • wireless communications


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