Capacity per unit energy of fading channels with a peak constraint

Vignesh Sethuraman, Bruce Hajek

Research output: Contribution to journalArticlepeer-review


A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdú for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.

Original languageEnglish (US)
Pages (from-to)3102-3120
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2005


  • Capacity per unit cost
  • Channel capacity
  • Correlated fading
  • Flat fading
  • Gauss-Markov fading

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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