684 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 21, NO. 5, JUNE 2003
Capacity Limits of MIMO Channels
Andrea Goldsmith, Senior Member, IEEE, Syed Ali Jafar, Student Member, IEEE, Nihar Jindal, Student Member, IEEE,
and Sriram Vishwanath, Student Member, IEEE
Invited Paper
Abstract—We provide an overview of the extensive recent
results on the Shannon capacity of single-user and multiuser
multiple-input multiple-output (MIMO) channels. Although
enormous capacity gains have been predicted for such channels,
these predictions are based on somewhat unrealistic assumptions
about the underlying time-varying channel model and how well
it can be tracked at the receiver, as well as at the transmitter.
More realistic assumptions can dramatically impact the potential
capacity gains of MIMO techniques. For time-varying MIMO
channels there are multiple Shannon theoretic capacity definitions
and, for each definition, different correlation models and channel
information assumptions that we consider. We first provide a
comprehensive summary of ergodic and capacity versus outage
results for single-user MIMO channels. These results indicate that
the capacity gain obtained from multiple antennas heavily depends
on the available channel information at either the receiver or
transmitter, the channel signal-to-noise ratio, and the correlation
between the channel gains on each antenna element. We then focus
attention on the capacity region of the multiple-access channels
(MACs) and the largest known achievable rate region for the
broadcast channel. In contrast to single-user MIMO channels,
capacity results for these multiuser MIMO channels are quite
difficult to obtain, even for constant channels. We summarize
results for the MIMO broadcast and MAC for channels that are
either constant or fading with perfect instantaneous knowledge
of the antenna gains at both transmitter(s) and receiver(s). We
show that the capacity region of the MIMO multiple access and
the largest known achievable rate region (called the dirty-paper
region) for the MIMO broadcast channel are intimately related
via a duality transformation. This transformation facilitates
finding the transmission strategies that achieve a point on the
boundary of the MIMO MAC capacity region in terms of the
transmission strategies of the MIMO broadcast dirty-paper region
and vice-versa. Finally, we discuss capacity results for multicell
MIMO channels with base station cooperation. The base stations
then act as a spatially diverse antenna array and transmission
strategies that exploit this structure exhibit significant capacity
gains. This section also provides a brief discussion of system level
issues associated with MIMO cellular. Open problems in this field
abound and are discussed throughout the paper.
Index Terms—Antenna correlation, beamforming, broadcast
channels (BCs), channel distribution information (CDI), channel
state information (CSI), multicell systems, multiple-access chan-
nels (MACs), multiple-input multiple-output (MIMO) channels,
multiuser systems, Shannon capacity.
Manuscript received November 8, 2002; revised January 31, 2003. This work
was supported in part by the Office of Naval Research (ONR) under Grants
N00014-99-1-0578 and N00014-02-1-0003. The work of S. Vishwanath was
supported by a Stanford Graduate Fellowship.
The authors are with the Department of Electrical Engineering, Stanford
University, Stanford, CA 94305 USA (e-mail: andrea@wsl.stanford.edu;
syed@wsl.stanford.edu; njindal@wsl.stanford.edu; sriram@wsl.stanford.edu).
Digital Object Identifier 10.1109/JSAC.2003.810294
I. INTRODUCTION
WIRELESS systems continue to strive for ever higherdata rates. This goal is particularly challenging for
systems that are power, bandwidth, and complexity limited.
However, another domain can be exploited to significantly
increase channel capacity: the use of multiple transmit and
receive antennas. Pioneering work by Winters [81], Foschini
[20], and Telatar [69] ignited much interest in this area by
predicting remarkable spectral efficiencies for wireless systems
with multiple antennas when the channel exhibits rich scat-
tering and its variations can be accurately tracked. This initial
promise of exceptional spectral efficiency almost “for free”
resulted in an explosion of research activity to characterize the
theoretical and practical issues associated with multiple-input
multiple-output (MIMO) wireless channels and to extend these
concepts to multiuser systems. This tutorial summarizes the
segment of this recent work focused on the capacity of MIMO
systems for both single-users and multiple users under different
assumptions about spatial correlation and channel information
available at the transmitter and receiver.
The large spectral efficiencies associated with MIMO chan-
nels are based on the premise that a rich scattering environment
provides independent transmission paths from each transmit an-
tenna to each receive antenna. Therefore, for single-user sys-
tems, a transmission and reception strategy that exploits this
structure achieves capacity on approximately sepa-
rate channels, where is the number of transmit antennas and
is the number of receive antennas. Thus, capacity scales lin-
early with relative to a system with just one transmit
and one receive antenna. This capacity increase requires a scat-
tering environment such that the matrix of channel gains be-
tween transmit and receive antenna pairs has full rank and in-
dependent entries and that perfect estimates of these gains are
available at the receiver. Perfect estimates of these gains at both
the transmitter and receiver provides an increase in the constant
multiplier associated with the linear scaling. Much subsequent
work has been aimed at characterizing MIMO channel capacity
under more realistic assumptions about the underlying channel
model and the channel estimates available at the transmitter and
receiver. The main question from both a theoretical and prac-
tical standpoint is whether the enormous capacity gains initially
predicted by Winters, Foschini, and Telatar can be obtained in
more realistic operating scenarios and what specific gains result
from adding more antennas and/or a feedback link to feed re-
ceiver channel information back to the transmitter.
0733-8716/03$17.00 © 2003 IEEE