The noncoherent Rician fading channel - Part I: Structure of the capacity-achieving input

Mustafa Cenk Gursoy, H. Vincent Poor, Sergio Verdu

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


Transmission of information over a discrete-time memoryless Rician fading channel is considered, where neither the receiver nor the transmitter knows the fading coefficients. First, the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire signal-to-noise ratio (SNR) range when there is only a peak-power constraint. The Rician fading with the phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model, it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average-power-limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.

Original languageEnglish (US)
Pages (from-to)2193-2206
Number of pages14
JournalIEEE Transactions on Wireless Communications
Issue number5
StatePublished - Sep 2005

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


  • Capacity-achieving input
  • Channel capacity
  • Fading channels
  • Memoryless fading
  • Peak constraints
  • Phase noise
  • Rician fading


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