Capacity of channels with frequency-selective and time-selective fading

Antonia M. Tulino, Giuseppe Caire, Shlomo Shamai, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


This paper finds the capacity of single-user discrete-time channels subject to both frequency-selective and time-selective fading, where the channel output is observed in additive Gaussian noise. A coherent model is assumed where the fading coefficients are known at the receiver. Capacity depends on the first-order distributions of the fading processes in frequency and in time, which are assumed to be independent of each other, and a simple formula is given when one of the processes is independent identically distributed (i.i.d.) and the other one is sufficiently mixing. When the frequency-selective fading coefficients are known also to the transmitter, we show that the optimum normalized power spectral density is the waterfilling power allocation for a reduced signal-to-noise ratio (SNR), where the gap to the actual SNR depends on the fading distributions. Asymptotic expressions for high/low SNR and easily computable bounds on capacity are also provided.

Original languageEnglish (US)
Article number5429107
Pages (from-to)1187-1215
Number of pages29
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2010

All Science Journal Classification (ASJC) codes

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


  • Additive Gaussian noise
  • Channel capacity
  • Coherent communications
  • Frequency-flat fading
  • Frequency-selective Fading
  • Orthogonal frequency-division multiplexing (OFDM)
  • Random matrices
  • Waterfilling


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