1804 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 11, NOVEMBER 2005
Cooperative Space–Time Coding for Wireless Networks
Andrej Stefanov, Member, IEEE, and Elza Erkip, Senior Member, IEEE
Abstract—We consider a cooperative transmission scheme in
which the collaborating nodes may have multiple antennas. We
present the performance analysis and design of space–time codes
that are capable of achieving the full diversity provided by user
cooperation. Our codes use the principle of overlays in time and
space, and ensure that cooperation takes place as often as possible.
We show how cooperation among nodes with different numbers
of antennas can be accomplished, and how the quality of the
interuser link affects the cooperative performance. We illustrate
that space–time cooperation can greatly reduce the error rates of
all the nodes involved, even for poor interuser channel quality.
Index Terms—Cooperative diversity, diversity methods, error-
correction coding, fading channels, multiple-input multiple-output
(MIMO) systems.
I. INTRODUCTION
C
OOPERATIVE communication provides a new way of in-
troducing spatial diversity in wireless networks [1]–[4]. In
a cooperative system, each user is assigned one or more partners.
The partners overhear each other’s transmitted signals, process
these signals, and retransmit toward the destination to provide
extra observations of the source signal at the destination. Even
though the interpartner channel is noisy, the virtual transmit-an-
tenna array consisting of these partners provides additional di-
versity, and results in improvements in terms of error rates and
throughput for all the nodes involved.
In this letter, we consider a model which allows for the part-
nering nodes and their destinations to have multiple antennas.
This leads us to consider cooperative space–time channel codes.
We argue that cooperative space–time codes (STCs) should be
based on the principle of overlays [5] in time, where we start
from a good STC to be used in the quasi-static interuser channel,
and then add additional coded bits to ensure that when coopera-
tion takes place, the code provides diversity and coding benefits
in the cooperative block fading channel. We also provide a per-
formance analysis that shows the potential coding and diversity
gains of cooperation as a function of the number of antennas
in each node and the destination, for various interuser channel
qualities. Our simulation results confirm the observations made
in our performance analysis, and illustrate that cooperation is
beneficial for all the nodes involved.
Paper approved by A. Anastasopoulos, the Editor for Wireless Communica-
tions of the IEEE Communications Society. Manuscript received May 10, 2004;
revised December 6, 2004. The work of E. Erkip was supported by the National
Science Foundation under Grant 0093163. This paper was presented in part at
the IEEE Information Theory Workshop, Paris, France, April 2003, and in part
at the IEEE Wireless Communications and Networking Conference, New Or-
leans, LA, March 2003.
The authors are with the Department of Electrical and Computer Engineering,
Polytechnic University, Brooklyn, NY 11201 USA (e-mail: stefanov@poly.edu;
elza@poly.edu).
Digital Object Identifier 10.1109/TCOMM.2005.858641
II. COOPERATIVE
SPACE–TIME SYSTEM
MODEL AND
PROTOCOL
We consider a wireless communication system, and focus on
the cooperation between two users,
and , where user
has antennas, . These nodes may have a common
destination, or may wish to communicate with separate destina-
tions. The results of this letter are applicable to both scenarios.
The information bits at each node are encoded by a channel en-
coder. The coded bits are multiplexed to be used for the coopera-
tive system. The coded and multiplexed bits are passed through a
serial-to-parallel converter, and are mapped to a particular signal
constellation. At each time slot
, the output of the modulator for
node
is a signal that is transmitted using transmit antenna
, for . All signals for node are transmitted simul-
taneously, each from a different transmit antenna, and all signals
have the same transmission period
. When node transmits,
the received signal by antenna
at the destination at time , de-
noted by
is given by , where
the noise samples
are modeled as independent, zero-mean
complex Gaussian random variables with variance
per di-
mension. The coefficient
is the path gain from transmit an-
tenna
of node , , to receive antenna of the
destination,
. We assume frequency-nonselective
quasi-static Rayleigh fading, i.e., the path gains are constant
during the transmission of any given user (for
symbols), and
are samples of a zero-mean complex Gaussian random variable
with variance 0.5 per dimension. The path gains for different an-
tennas of the same user, and the path gains of different users, are
assumed to be independent. Throughout, we will assume perfect
channel state information at all the respective receivers.
As in [2] and [4], we focus on time division among the nodes.
We assume that when the nodes do not cooperate, they transmit
for
time slots, which we will call a frame. When coopera-
tion is employed,
channel uses for node are divided into
two segments. This leads to
channel uses, in which user
transmits to its partner and the destination, and channel
uses, which are used for cooperation. For cooperation, we as-
sume that along with a STC used for error correction, we have
cyclic redundancy check (CRC) for error detection. In the co-
operative segment, based on the channel conditions and as indi-
cated by the CRC, either the partner
relays the information
of
to the destination, or continues transmission.
III. A
NALYSIS AND DESIGN OF COOPERATIVE STCS
A. Performance Analysis
Without loss of generality, we study performance gains for
through cooperative time coding for various interuser channel
qualities. Similar analysis can also be performed for user
.
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