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

  • Authors:
  • Antonia M. Tulino;Giuseppe Caire;Shlomo Shamai;Sergio Verdú

  • Affiliations:
  • Department of Wireless Communications, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ;University of Southern California, Los Angeles, CA;Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel;Princeton University, Princeton, NJ

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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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.