Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback

Shengli Zhou, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

360 Scopus citations


Optimal transmitter designs obeying the water-filling principle are well-documented; they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter. Because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems, we design, in this paper, an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels. Our optimal transmitter design turns out to be an eigen-beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams. The optimality pertains to minimizing an upper bound on the symbol error rate, which leads to better performance than maximizing the expected signal-to-noise ratio (SNR) at the receiver. Coupled with orthogonal space-time block codes, two-directional eigen-beamforming emerges as a more attractive choice than conventional one-directional beamforming with uniformly improved performance, without rate reduction, and without essential increase in complexity. With multiple receive antennas and reasonably good feedback quality, the two-directional eigen-beamformer is also capable of achieving the best possible performance in a large range of transmit-power-to-noise ratios, without a rate penalty.

Original languageEnglish (US)
Pages (from-to)2599-2613
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - Oct 2002

Bibliographical note

Funding Information:
Manuscript received November 1, 2001; revised May 13, 2002. This work was supported by the the National Science Foundation (NSF) under Grant 0105612, the NSF under Wireless Initiative Grant 99-79443, and by the ARL/CTA under Grant DAAD19-01-2-011. This work was presented in part at the International Conference on Acoustics Speech and Signal Processing, Orlando, FL, USA, May 13–17, 2002. The associate editor coordinating the review of this paper and approving it for publication was Prof. Brian L. Hughes.


  • Beamforming
  • Mean feedback
  • Space-time block codes
  • Transmit diversity


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