IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 2619
Fading Channels: Information-Theoretic
and Communications Aspects
Ezio Biglieri, Fellow, IEEE, John Proakis, Life Fellow, IEEE, and Shlomo Shamai (Shitz), Fellow, IEEE
(Invited Paper)
Abstract— In this paper we review the most peculiar and
interesting information-theoretic and communications features of
fading channels. We first describe the statistical models of fading
channels which are frequently used in the analysis and design
of communication systems. Next, we focus on the information
theory of fading channels, by emphasizing capacity as the most
important performance measure. Both single-user and multiuser
transmission are examined. Further, we describe how the struc-
ture of fading channels impacts code design, and finally overview
equalization of fading multipath channels.
Index Terms—Capacity, coding, equalization, fading channels,
information theory, multiuser communications, wireless systems.
I. INTRODUCTION
THE theory for Gaussian dispersive channels, whethertime-invariant or variant, has been well established for
decades with new touches motivated by practical technological
achievements, reported systematically over the years (see
[2], [62], [64], [94], [114], [122], [223], [225], [267] for
some recent developments). Neither the treatment of statistical
time-varying channels is new in information theory, and in
fact by now this topic is considered as classic [64], with
Shannon himself contributing to some of its aspects [261] (see
[164] for a recent tutorial exposition, and references therein).
Fading phenomena were also carefully studied by information-
theoretic tools for a long time. However, it is only relatively
recently that information-theoretic study of increasingly com-
plicated fading channel models, under a variety of interesting
and strongly practically related constraints has accelerated to a
degree where its impact of the whole issue of communications
in a fading regime is notable also by nonspecialists of infor-
mation theory. Harnessing information-theoretic tools to the
investigation of fading channels, in the widest sense of this
notion, has not only resulted in an enhanced understanding
of the potential and limitations of those channels, but in fact
Information Theory provided in numerous occasions the right
guidance to the specific design of efficient communications
systems. Doubtless, the rapid advance in technology on the
one hand and the exploding demand for efficient high-quality
Manuscript received December 5, 1997; revised May 3, 1998.
E. Biglieri is with the Dipartimento di Elettronica, Politecnico di Torino,
I-10129 Torino, Italy.
J. Proakis is with the Department of Electrical and Computer Engineering,
Northeastern University, Boston, MA 02115 USA.
S. Shamai (Shitz) is with the Department of Electrical Engineering, Tech-
nion–Israel Institute of Technology, 32000 Haifa, Israel.
Publisher Item Identifier S 0018-9448(98)06815-1.
and volume of digital wireless communications over almost
every possible media and for a variety of purposes (be it
cellular, personal, data networks, including the ambitious
wireless high rate ATM networks, point-to-point microwave
systems, underwater communications, satellite communica-
tions, etc.) plays a dramatic role in this trend. Evidently
these technological developments and the digital wireless
communications demand motivate and encourage vigorous
information-theoretical studies of the most relevant issues in an
effort to identify and assess the potential of optimal or close-to-
optimal communications methods. This renaissance of studies
bore fruits and has already led to interesting and very relevant
results which matured to a large degree the understanding
of communications through fading media, under a variety of
constraints and models. The footprints of information-theoretic
considerations are evidenced in many state-of-the-art coding
systems. Typical examples are the space–time codes, which
attempt to benefit from the dramatic increase in capacity of
spatial diversity in transmission and reception, i.e., multiple
transmit and receive antennas [92], [226], [280], [281], [283].
The recently introduced efficient turbo-coded multilevel modu-
lation schemes [133] and the bit interleaved coded modulation
(BICM) [42], as a special case, were motivated by information-
theoretic arguments demonstrating remarkable close to the
ultimate capacity limit performance in the Gaussian and fading
channels. Equalization whether explicit or implicit is an inher-
ent part of communications over time-varying fading channels,
and information theory has a role here as well. This is
mainly reflected by the sensitivity of the information-theoretic
predictions to errors in the estimated channel parameters on
one hand, and the extra effort (if any) ratewise, needed to
track accurately the time-varying channel. Clearly, information
theory provides also a yardstick by which the efficiency
of equalization methods is to be measured, and that is by
determining the ultimate limit of communications on the given
channel model, under prescribed assumptions (say channel
state parameters not available to either transmitter or receiver),
without an explicit partition to equalization and decoding. In
fact, the intimate relation among pure information-theoretic
arguments, specific coding and equalization methods motivates
the tripartite structure of this paper.
This intensive study, documented by our reference list,
not only affected the understanding of ultimate limits and
preferred communication techniques over these channels em-
bracing a wide variety of communication media and models,
0018–9448/98$10.00  1998 IEEE