Maximum-diversity transmissions over doubly selective wireless channels

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207 Scopus citations


High data rates and multipath propagation give rise to frequency-selectivity of wireless channels, while carrier frequency offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. The resulting time- and frequency-selective (or doubly selective) channels offer joint multipath-Doppler diversity gains. Relying on a basis expansion model of the doubly selective channel, we prove that the maximum achievable multipath-Doppler diversity order is determined by the rank of the correlation matrix of the channel's expansion coefficients, and is multiplicative in the effective degrees of freedom that the channel exhibits in the time and frequency dimensions. Interestingly, it turns out that time-frequency reception alone does not guarantee maximum diversity, unless the transmission is also designed judiciously. We design such block precoded transmissions. The corresponding designs for frequency-selective or time-selective channels follow as special cases, and thorough simulations are provided to corroborate our theoretical findings.

Original languageEnglish (US)
Pages (from-to)1832-1840
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2003

Bibliographical note

Funding Information:
Manuscript received September 7, 2001; revised September 22, 2002. This work was supported by the ARL/CTA under Grant DAAD19-01-2-011. The material in this correspondence was presented in part at the 39th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2001 and the IEEE Wireless Communications and Networking Conference, Orlando, FL, March 2002.


  • Diversity
  • Doppler
  • Doubly selective channels
  • Fading
  • Multipath
  • Precoding
  • Time-selective channels


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