Optimal training for MIMO frequency-selective fading channels

Xiaoli Ma, Liuqing Yang, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

155 Scopus citations


High data rates give rise to frequency-selective propagation effects. Space - time multiplexing and/or coding offer attractive means of combating fading and boosting capacity of multi-antenna communications. As the number of antennas increases, channel estimation becomes challenging because the number of unknowns increases, and the power is split at the transmitter. Optimal training sequences have been designed for flat-fading multi-antenna systems or for frequency-selective single transmit antenna systems. We design a low-complexity optimal training scheme for block transmissions over frequency-selective channels with multiple antennas. The optimality in designing our training schemes consists of maximizing a lower bound on the ergodic (average) capacity that is shown to be equivalent to minimizing the mean square error of the linear channel estimator. Simulation results confirm our theoretical analysis that applies to both single- and multicarrier transmissions.

Original languageEnglish (US)
Pages (from-to)453-466
Number of pages14
JournalIEEE Transactions on Wireless Communications
Issue number2
StatePublished - Mar 2005
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received November 29, 2002; accepted September 18, 2003. The editor coordinating the review of this paper and approving it for publication is H. Boelcskei. The work in this paper was prepared through collaborative participation in the Communications and Networks Consortium supported by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011.


  • Channel estimation
  • Ergodic capacity
  • Frequency-selective channels
  • Multi-input multi-output MIM
  • Pilot symbol-aided modulation


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