Optimal training for block transmissions over doubly selective wireless fading channels

Xiaoli Ma, Georgios B. Giannakis, Shuichi Ohno

Research output: Contribution to journalArticlepeer-review

391 Scopus citations


High data rates give rise to frequency-selective propagation, whereas carrier frequency-offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. To mitigate the resulting time- and frequency-selective (or doubly selective) channels, optimal training sequences have been designed only for special cases: pilot symbol assisted modulation (PSAM) for time-selective channels and pilot tone-assisted orthogonal frequency division multiplexing (OFDM) for frequency-selective channels. Relying on a basis expansion channel model, in this paper, we design low-complexity optimal PSAM for block transmissions over doubly selective channels. The optimality in designing our PSAM parameters consists of maximizing a tight lower bound on the average channel capacity that is shown to be equivalent to the minimization of the minimum mean-square channel estimation error. Numerical results corroborate our theoretical designs.

Original languageEnglish (US)
Pages (from-to)1351-1366
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 2003

Bibliographical note

Funding Information:
Manuscript received November 11, 2001; revised November 19, 2002. The work in this paper was supported by the National Science Foundation under Grant 0122431 and the Army Research Laboratory/CTA under Grant DAAD19-01-2-011. The associate editor coordinating the review of this paper and approving it for publication was Prof. Xiaodong Wang.


  • Doubly selective channels
  • Frequency selective
  • Mutual information
  • Optimal training
  • Pilot symbol assisted modulation
  • Time-selective
  • Wireless fading channels


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