Capacity of Channels With Frequency-Selective and Time-Selective Fading

• Published in: IEEE transactions on information theory Vol. 56; no. 3; pp. 1187 - 1215
• Main Authors: Tulino, A.M., Caire, G., Shamai, S., Verdu, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive Gaussian noise; Additive noise; Allocations; Applied sciences; Asymptotic properties; Channel capacity; Channels; coherent communications; Decoding; Density; Electric noise; Exact sciences and technology; Fading; Frequencies; Frequency; frequency-flat fading; frequency-selective fading; Gaussian; Gaussian noise; Information theory; Information, signal and communications theory; Mathematical models; Multiplexing; orthogonal frequency-division multiplexing (OFDM); Radio spectrum management; Radiocommunications; random matrices; Signal and communications theory; Signal to noise ratio; Spectra; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; waterfilling; Additive noise; Fading channels; Channel capacity; Discrete channel; random matrices; Power spectral density; Transmitter; Power allocation; Additive Gaussian noise; Selective fading; Frequency selection; Gaussian noise; frequency-selective fading; First order; Discrete time; Orthogonal frequency division multiplexing; coherent communications; waterfilling; frequency-flat fading; orthogonal frequency-division multiplexing (OFDM); Signal to noise ratio
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2039041

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.