To code or not to code across time: Space-time coding with feedback

Che Lin, Vasanthan Raghavan, Venugopal V. Veeravalli

Research output: Contribution to journalArticlepeer-review


Space-time codes leverage the availability of multiple antennas to enhance the reliability of communication over wireless channels. While space-time codes have initially been designed with a focus on open-loop systems, recent technological advances have enabled the possibility of low-rate feedback from the receiver to the transmitter. The focus of this paper is on the implications of this feedback in a single-user multi-antenna system with a general model for spatial correlation. We assume a limited feedback model, that is, a coherent receiver and statistical knowledge at both the ends, along with B bits of error-free quantized channel information at the transmitter. We study space-time coding with a family of linear dispersion (LD) codes that meet an additional orthogonality constraint so as to ensure low-complexity decoding. Our results show that, when the number of bits of feedback (B) is small, a space-time coding scheme that is equivalent to beamforming and does not code across time is optimal in a weak sense in that it maximizes the average received SNR. As B increases, this weak optimality transitions to optimality in a strong sense that is characterized by the maximization of average mutual information. Thus, from a system designer's perspective, our work suggests that beamforming may not only be attractive from a low-complexity viewpoint, but also from an information-theoretic viewpoint.

Original languageEnglish (US)
Article number4641968
Pages (from-to)1588-1598
Number of pages11
JournalIEEE Journal on Selected Areas in Communications
Issue number8
StatePublished - Oct 2008


  • Adaptive coding
  • Diversity methods
  • Fading channels
  • Feedback communications
  • MIMO systems
  • Multiplexing
  • Quantization

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


Dive into the research topics of 'To code or not to code across time: Space-time coding with feedback'. Together they form a unique fingerprint.

Cite this