IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006 659
A Simple Cooperative Diversity Method Based
on Network Path Selection
Aggelos Bletsas, Member, IEEE, Ashish Khisti, Student Member, IEEE, David P. Reed, Member, IEEE, and
Andrew Lippman, Member, IEEE
Abstract—Cooperative diversity has been recently proposed as
a way to form virtual antenna arrays that provide dramatic gains
in slow fading wireless environments. However, most of the pro-
posed solutions require distributed space–time coding algorithms,
the careful design of which is left for future investigation if there is
more than one cooperative relay. We propose a novel scheme that
alleviates these problems and provides diversity gains on the order
of the number of relays in the network. Our scheme first selects
the best relay from a set of
available relays and then uses this
“best” relay for cooperation between the source and the destina-
tion. We develop and analyze a distributed method to select the
best relay that requires no topology information and is based on
local measurements of the instantaneous channel conditions. This
method also requires no explicit communication among the relays.
The success (or failure) to select the best available path depends
on the statistics of the wireless channel, and a methodology to eval-
uate performance for any kind of wireless channel statistics, is pro-
vided. Information theoretic analysis of outage probability shows
that our scheme achieves the same diversity-multiplexing tradeoff
as achieved by more complex protocols, where coordination and
distributed space–time coding for
relay nodes is required, such
as those proposed by Laneman and Wornell (2003). The simplicity
of the technique allows for immediate implementation in existing
radio hardware and its adoption could provide for improved flexi-
bility, reliability, and efficiency in future 4G wireless systems.
Index Terms—Coherence time, fading channel, network cooper-
ative diversity, outage probability, wireless networks.
I. INTRODUCTION
I
N THIS work, we propose and analyze a practical scheme
that forms a virtual antenna array among single antenna
terminals, distributed in space. The setup includes a set of
cooperating relays which are willing to forward received infor-
mation toward the destination and the proposed method is about
a distributed algorithm that selects the most appropriate relay to
forward information toward the receiver. The decision is based
on the end-to-end instantaneous wireless channel conditions
and the algorithm is distributed among the cooperating wireless
terminals.
Manuscript received January 16, 2005; revised August 25, 2005. This work
was supported in part by the National Science Foundation under Grant CNS-
0434816, in part by the Massachusetts Institute of Technology Media Labora-
tory Digital Life Program, and in part by a Nortel Networks graduate fellowship
award.
A. Bletsas was with the Massachusetts Institute of Technology, Cambridge,
MA 02139 USA. He is now with Mitsubishi Electric Research Laboratories
(MERL), Cambridge, MA 02139 USA (e-mail: aggelos@media.mit.edu).
A. Khisti, D. P. Reed, and A. Lippman are with the Massachusetts Institute
of Technology, Cambridge, MA 02139 USA (e-mail: khisti@mit.edu).
Digital Object Identifier 10.1109/JSAC.2005.862417
The best relay selection algorithm lends itself naturally into
cooperative diversity protocols [6], [14], [15], which have been
recently proposed to improve reliability in wireless communi-
cation systems using distributed virtual antennas. The key idea
behind these protocols is to create additional paths between the
source and destination using intermediate relay nodes. In partic-
ular, Sendonaris, Erkip, and Aazhang [14], proposed a way of
beamforming where source and a cooperating relay, assuming
knowledge of the forward channel, adjust the phase of their
transmissions so that the two copies can add coherently at the
destination. Beamforming requires considerable modifications
to existing radio frequency (RF) front ends that increase com-
plexity and cost. Laneman, Tse, and Wornell [6] assumed no
channel state information (CSI) at the transmitters and, there-
fore, assumed no beamforming capabilities and proposed the
analysis of cooperative diversity protocols under the framework
of diversity-multiplexing tradeoffs. Their basic setup included
one sender, one receiver, and one intermediate relay node and
both analog as well as digital processing at the relay node were
considered. Subsequently, the diversity-multiplexing tradeoff of
cooperative diversity protocols with multiple relays was studied
in [1] and [7]. While [7] considered the case of orthogonal trans-
mission
1
between source and relays, [1] considered the case
where source and relays could transmit simultaneously. It was
shown in [1] that by relaxing the orthogonality constraint, a con-
siderable improvement in performance could be achieved, al-
beit at a higher complexity at the decoder. These approaches
were, however, information theoretic in nature and the design
of practical codes that approach these limits was left for further
investigation.
Such code design is difficult in practice and an open area of
research: while space time codes for the multiple-input mul-
tiple-output (MIMO) link do exist [17] (where the antennas be-
long to the same central terminal), more work is needed to use
such algorithms in the relay channel, where antennas belong to
different terminals distributed in space. The relay channel is fun-
damentally different than the point-to-point MIMO link since
information is not a priori known to the cooperating relays but
rather needs to be communicated over noisy links. Moreover, the
number of participating antennas is not fixed since it depends
on how many relay terminals participate and how many of them
are indeed useful in relaying the information transmitted from
1
Note that in that scheme the relays do not transmit in mutually orthogonal
time/frequency bands. Instead they use a space–time code to collaboratively
send the message to the destination. Orthogonality refers to the fact that the
source transmits in time slots orthogonal to the relays. Throughout this paper,
we will refer to Laneman’s scheme as orthogonal cooperative diversity.
0733-8716/$20.00 © 2006 IEEE
660 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
Fig. 1. Transmission is overheard by neighboring nodes. Distributed space–
time coding is needed so that all overhearing nodes could simultaneously
transmit. In this work, we analyze “opportunistic relaying” where the relay
with the strongest transmitter-relay-receiver path is selected among several
candidates in a distributed fashion using instantaneous channel measurements.
the source. For example, for relays that decode and forward, it
is necessary to decode successfully before retransmitting. For
relays that amplify and forward, it is important to have a good
received signal-to-noise ratio (SNR), otherwise they would for-
ward mostly their own noise [21]. Therefore, the number of par-
ticipating antennas in cooperative diversity schemes is in gen-
eral random and space–time coding invented for fixed number of
antennas should be appropriately modified. It can be argued that
for the case of orthogonal transmission studied in the present
work (i.e., transmission during orthogonal time or frequency
channels), codes can be found that maintain orthogonality in the
absence of a number of antennas (relays). That was pointed in
[7] where it was also emphasized that it remains to be seen how
such codes could provide residual diversity without sacrifice of
the achievable rates. In short, providing for practical space–time
codes for the cooperative relay channel is fundamentally dif-
ferent than space–time coding for the MIMO link channel and
is still an open and challenging area of research.
Apart from practical space–time coding for the cooperative
relay channel, the formation of virtual antenna arrays using
individual terminals distributed in space, requires significant
amount of coordination. Specifically, the formation of cooper-
ating groups of terminals involves distributed algorithms [7]
while synchronization at the packet level is required among
several different transmitters. Those additional requirements
for cooperative diversity demand significant modifications
to almost all layers of the communication stack (up to the
routing layer) which has been built according to “traditional,”
point-to-point (noncooperative) communication.
In Fig. 1, a transmitter transmits its information toward the
receiver while all the neighboring nodes are in listening mode.
For a practical cooperative diversity in a three-node setup, the
transmitter should know that allowing a relay at location B to
relay information would be more efficient than repetition from
the transmitter itself. This is not a trivial task and such event de-
pends on the wireless channel conditions between transmitter
and receiver as well as between transmitter-relay and relay-
receiver. What if the relay is located in position A? This problem
also manifests in the multiple relay case when one attempts to
simplify the physical layer protocol by choosing the best avail-
able relay. In [20], it was suggested that the best relay be se-
lected based on location information with respect to source and
destination based on ideas from geographical routing proposed
in [18]. Such schemes require knowledge or estimation of dis-
tances between all relays and destination and, therefore, require
either 1) infrastructure for distance estimation (for example GPS
receivers at each terminal) or 2) distance estimation using ex-
pected SNRs, which is itself a nontrivial problem and is more
appropriate for static networks and less appropriate for mobile
networks, since in the latter case, estimation should be repeated
with substantial overhead.
In contrast, we propose a novel scheme that selects the best
relay between source and destination based on
instantaneous
channel measurements. The proposed scheme requires no
knowledge of the topology or its estimation. The technique
is based on signal strength measurements rather than distance
and requires a small fraction of the channel coherence time.
Additionally, the algorithm itself provides for the necessary co-
ordination in time and group formation among the cooperating
terminals.
The three-node reduction of the multiple relay problem
we consider greatly simplifies the physical layer design. In
particular, the requirement of space–time codes is completely
eliminated if the source and relay transmit in orthogonal
time-slots. We further show that there is essentially no loss in
performance in terms of the diversity-multiplexing tradeoff as
compared to the transmission scheme in [7], which requires
space–time coding across the relays successful in decoding the
source message. We also note that our scheme can be used to
simplify the nonorthogonal multiple relay protocols studied in
[1]. Intuitively, the gains in cooperative diversity do not come
from using complex schemes, but rather from the fact that we
have enough relays in the system to provide sufficient diversity.
The simplicity of the technique allows for immediate im-
plementation in existing radio hardware. An implementation of
the scheme using custom radio hardware is reported in [3]. Its
adoption could provide for improved flexibility (since the tech-
nique addresses coordination issues), reliability, and efficiency
(since the technique inherently builds upon diversity) in future
4G wireless systems.
A. Key Contributions
One of the key contribution of this paper is to propose and
analyze a simplification of user cooperation protocols at the
physical layer by using a smart relay selection algorithm at the
network layer. Toward this end, we take the following steps.
• A new protocol for selection of the “best” relay between
the source and destination is suggested and analyzed. This
protocol has the following features.
— The protocol is distributed and each relay only makes
local channel measurements.
— Relay selection is based on instantaneous channel
conditions in slow fading wireless environments. No
BLETSAS et al.: A SIMPLE COOPERATIVE DIVERSITY METHOD 661
prior knowledge of topology or estimation of it is re-
quired.
— The amount of overhead involved in selecting the best
relay is minimal. It is shown that there is a flexible
tradeoff between the time incurred in the protocol and
the resulting error probability.
• The impactofsmartrelayingontheperformance of user co-
operation protocols is studied. In particular, it is shown that
for orthogonal cooperative diversity protocols there is no
loss in performance (in terms of the diversity-multiplexing
tradeoff) if only the best relay participates in cooperation.
Opportunistic relaying provides an alternative solution
with a very simple physical layer to conventional coop-
erative diversity protocols that rely on space–time codes.
The scheme could be further used to simplify space–time
coding in the case of nonorthogonal transmissions.
Since the communication scheme exploits the wireless
channel at its best, via distributed cooperating relays, we natu-
rally called it
opportunistic relaying. The term “opportunistic”
has been widely used in various different contexts. In [24], it
was used in the context of repetitive transmission of the same
information over several paths in 802.11b networks. In our
setup, we do not allow repetition since we are interested in
providing diversity without sacrificing the achievable rates. The
term “opportunistic” has also been used in the context of effi-
cient flooding of signals in multihop networks [25] to increase
communication range and, therefore, has no relationship with
our work. We first encountered the term “opportunistic” in the
work by Viswanath, Tse, and Laroia [26], where the base station
always selects the best user for transmission in an artificially
induced fast fading environment. In our work, a mechanism of
multiuser diversity is provided for the relay channel in single
antenna terminals. Our proposed scheme resembles selection
diversity that has been proposed for centralized multiantenna
receivers [8]–[10]. In our setup, the single antenna relays are
distributed in space and attention has been given in selecting
the “best” possible antenna, well before the channel changes
again, using minimal communication overhead.
In Section II, we describe in detail opportunistic relaying and
contrast its distributed location information-free nature to ex-
isting approaches in the field. Probabilistic analysis and close
form expressions regarding the success (or failure) and speed of
“best” path selection, for any kind of wireless channel statistics,
are provided in Section III. In Section IV, we prove that oppor-
tunistic relaying has no performance loss compared to complex
space–time coding under the same assumptions of orthogonal
channel transmissions [7] and discuss the ability of the scheme
to further simplify space–time coding for nonorthogonal chan-
nels. We also discuss in more detail why space–time codes de-
signed for the MIMO link are not directly applicable to the co-
operative relay channel. We conclude in Section V.
II. D
ESCRIPTION OF OPPORTUNISTIC RELAYING
According to opportunistic relaying, a single relay among
a set of
relay nodes is selected, depending on which relay
provides for the “best” end-to-end path between source and
destination (Figs. 1 and 2). The wireless channel
between
source and each relay
, as well as the channel between relay
Fig. 2. Source transmits to destination and neighboring nodes overhear
the communication. “Best” relay among
M
candidates is selected to relay
information, via a distributed mechanism and based on instantaneous
end-to-end channel conditions. For the diversity-multiplexing tradeoff analysis,
transmission of source and “best” relay occur in orthogonal time channels.
Scheme could be easily modified to incorporate simultaneous transmissions
from source and “best” relay.
and destination affect performance. These parameters model
the propagation environment between any communicating ter-
minals and change over time, with a rate that macroscopically
can be modeled as the Doppler shift, inversely proportional
to the channel coherence time. Opportunistic selection of
the “best” available relay involves the discovery of the most
appropriate relay, in a distributed and “quick” fashion, well
before the channel changes again. We will explicitly quantify
the speed of relay selection in Section III.
The important point to make here is that under the proposed
scheme, the relay nodes monitor the instantaneous channel
conditions toward source and destination, and decide in a
distributed fashion which one has the strongest path for infor-
mation relaying, well before the channel changes again. In that
way, topology information at the relays (specifically location
coordinates of source and destination at each relay) is not
needed. The selection process reacts to the physics of wireless
propagation, which are in general dependent on several param-
eters including mobility and distance. By having the network
select the relay with the strongest end-to-end path, macroscopic
features like “distance” are also taken into account. Moreover,
the proposed technique is advantageous over techniques that
select the best relay a priori, based on distance toward source or
destination, since distance-dependent relay selection neglects
well-understood phenomena in wireless propagation such as
shadowing or fading: communicating transmitter-receiver pairs
with similar distances might have enormous differences in
terms of received SNRs. Furthermore, average channel condi-
tions might be less appropriate for mobile terminals than static.
Selecting the best available path under such conditions (zero
topology information, “fast” relay selection well bellow the
coherence time of the channel and minimum communication
overhead) becomes nonobvious and it is one of the main con-
tributions of this work.
More specifically, the relays overhear a single transmission of
a ready-to-send (RTS) packet and a clear-to-send (CTS) packet
from the destination. From these packets, the relays assess how
appropriate each of them is for information relaying. The trans-
mission of RTS from the source allows for the estimation of
the instantaneous wireless channel
between source and relay
, at each relay (Fig. 2). Similarly, the transmission of CTS
662 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
from the destination allows for the estimation of the instanta-
neous wireless channel
between relay and destination at
each relay
according to the reciprocity theorem [27]
2
. Note
that the source does not need to listen to the CTS packet
3
from
the destination.
Since communication among all relays should be minimized
for reduced overall overhead, a method based on time was se-
lected: as soon as each relay receives the CTS packet, it starts a
timer from a parameter
based on the instantaneous channel
measurements
, . The timer of the relay with the best
end-to-end channel conditions will expire first. That relay trans-
mits a short duration
flag packet, signaling its presence. All re-
lays, while waiting for their timer to reduce to zero (i.e., to ex-
pire), are in listening mode. As soon as they hear another relay
to flag its presence or forward information (the best relay), they
back off.
For the case where all relays can listen source and destination,
but they are “hidden” from each other (i.e., they can not listen
each other), the best relay notifies the destination with a short
duration flag packet and the destination notifies all relays with
a short broadcast message.
The channel estimates
, at each relay, describe the
quality of the wireless path between source-relay-destination,
for each relay
. Since the two hops are both important for
end-to-end performance, each relay should quantify its appro-
priateness as an active relay, using a function that involves the
link quality of both hops. Two functions are used in this work:
under Policy I, the minimum of the two is selected, while under
Policy II, the harmonic mean of the two is used [28]. Policy I se-
lects the “bottleneck” of the two paths while Policy II balances
the two link strengths and it is a smoother version of the first
one.
• Under Policy I
(1)
• Under Policy II
(2)
The relay
that maximizes function is the one with the
“best” end-to-end path between initial source and final desti-
nation. After receiving the CTS packet, each relay
will start
its own timer with an initial value
, inversely proportional to
the end-to-end channel quality
, according to the following
equation:
(3)
Here,
is a constant. The units of depend on the units of .
Since
is a scalar, has the units of time. For the discussion
in this work,
has simply values of microseconds.
(4)
2
We assume that the forward and backward channels between the relay and
destination are the same due to the reciprocity theorem. Note that these trans-
missions occur on the same frequency band and same coherence interval.
3
The CTS packet name is motivated by existing MAC protocols. However, un-
like the existing MAC protocols, the source does not need to receive this packet.
(5)
Therefore, the “best” relay has its timer reduced to zero
first [since it started from a smaller initial value, according
to (3)–(5)]. This is the relay
that participates in forwarding
information from the source. The rest of the relays will overhear
the “flag” packet from the best relay (or the destination, in the
case of hidden relays) and back off.
After the best relay has been selected, then it can be used to
forward information toward the destination. Whether that “best”
relay will transmit simultaneously with the source or not is com-
pletely irrelevant to the relay selection process. However, in
the diversity-multiplexing tradeoff analysis in Section IV, we
strictly allow only one transmission at each time and, therefore,
we can view the overall scheme as a two-step transmission: one
from source and one from “best” relay, during a subsequent (or-
thogonal) time channel (Fig. 2).
A. A Note on Time Synchronization
In principle, the RTS/CTS transmissions between source and
destination, existent in many medium access control (MAC)
protocols, is only needed so that all intermediate relays can as-
sess their connectivity paths toward source and destination. The
reception of the CTS packet triggers at each relay the initia-
tion of the timing process, within an uncertainty interval that
depends on different propagation times, identified in detail in
Section III. Therefore, an explicit time synchronization protocol
among the relays is not required. Explicit time synchronization
would be needed between source and destination only if there
was no direct link between them. In that case, the destination
could not respond with a CTS to a RTS packet from the source,
and, therefore, source and destination would need to schedule
their RTS/CTS exchange by other means. In such cases, “crude”
time synchronization would be useful. Accurate synchroniza-
tion schemes, centralized [2] or decentralized [4], do exist and
have been studied elsewhere. We will assume that source and
destination are in communication range and, therefore, no syn-
chronization protocols are needed.
B. A Note on CSI
CSI at the relays, in the form of link strengths (not signal
phases), is used at the network layer for “best” relay selection.
CSI is not required at the physical layer and is not exploited ei-
ther at the source or the relays. The wireless terminals in this
work do not exploit CSI for beamforming and do not adapt their
transmission rate to the wireless channel conditions, either be-
cause they are operating in the minimum possible rate or be-
cause their hardware do not allow multiple rates. We will em-
phasize again that no CSI at the physical layer is exploited at the
source or the relays during the diversity-multiplexing tradeoff
analysis in Section IV.
C. Comparison With Geometric Approaches
As can be seen from the above equations, the scheme de-
pends on the instantaneous channel realizations or equivalently,
on received instantaneous SNRs, at each relay. An alternative
approach would be to have the source know the location of the
destination and propagate that information, alongside with its
BLETSAS et al.: A SIMPLE COOPERATIVE DIVERSITY METHOD 663
own location information to the relays, using a simple packet
that contained that location information. Then, each relay,
assuming knowledge of its own location information, could
assess its proximity toward source and destination and based
on that proximity, contend for the channel with the rest of the
relays. That is an idea proposed by Zorzi and Rao [18] in the
context of fading-free wireless networks when nodes know
their location and the location of their destination (for example,
they are equipped with GPS receivers). The objective there was
to study geographical routing and study the average number of
hops needed under such schemes. All relays are partitioned into
a specific number of geographical regions between source and
destination and each relay identifies its region using knowledge
of its location and the location of source and destination.
Relays at the region closer to the destination contend for the
channel first using a standard carrier sense multiple access
(CSMA) splitting scheme. If no relays are found, then relays at
the second closest region contend and so on, until all regions
are covered, with a typical number of regions close to 4. The
latency of the above distance-dependent contention resolution
scheme was analyzed in [19].
Zorzi and Rao’s scheme of distance-dependent relay selec-
tion was employed in the context of Hybrid-ARQ, proposed by
Zhao and Valenti [20]. In that work, the request to an automatic
repeat request (ARQ) is served by the relay closest to the des-
tination, among those that have decoded the message. In that
case, code combining is assumed that exploits the direct and
relayed transmission (that is why the term
Hybrid was used).
4
Relays are assumed to know their distances to the destination
(valid for GPS equipped terminals) or estimate their distances
by measuring the expected channel conditions using the ARQ
requests from the destination or using other means.
We note that our scheme of opportunistic relaying differs
from the above scheme in the following aspects.
•
The above scheme performs relay selection based on ge-
ographical regions while our scheme performs selection
based on instantaneous channel conditions. In wireless
environment, the latter choice could be more suitable as
relay nodes located at similar distance to the destination
could have vastly different channel gains due to effects
such as fading.
•
The above scheme requires measurements to be only per-
formed once if there is no mobility among nodes but re-
quires several rounds of packet exchanges to determine
the average SNR. On the other hand, opportunistic re-
laying requires only three packet exchanges in total to
determine the instantaneous SNR, but requires that these
measurements be repeated in each coherence interval. We
show in Section III that the overhead of relay selection is
a small fraction of the coherence interval with collision
probability less than 0.6%.
•
We also note that our protocol is a proactive protocol since
it selects the best relay before transmission. The protocol
can easily be made to be reactive (similar to [20]) by se-
lecting the relay after the first phase. However, this mod-
4
The idea of having a relay terminal respond to an ARQ instead of the original
source was also reported and analyzed in [6], albeit for repetition coding instead
of hybrid code combining.
Fig. 3. Middle row corresponds to the “best” relay. Other relays (top or bottom
row) could erroneously be selected as “best” relays if their timer expired within
intervals when they can not hear the best relay transmission. That can happen
in the interval
[
t ;t
]
for case (a) (no hidden relays) or
[
t
;t
]
for case (b)
(hidden relays).
t
,
t
are time points where reception of the CTS packet is
completed at best relay
b
and relay
j
, respectively.
ification would require all relays to listen to the source
transmission which can be energy inefficient from a net-
work sense.
III. P
ROBABILISTIC ANALYSIS OF
OPPORTUNISTIC
RELAYING
The probability of having two or more relay timers expire “at
the same time” is zero. However, the probability of having two
or more relay timers expire within the same time interval
is
nonzero and can be analytically evaluated, given knowledge of
the wireless channel statistics.
The only case where opportunistic relay selection fails is
when one relay can not detect that another relay is more appro-
priate for information forwarding. Note that we have already
assumed that all relays can listen initial source and destination,
otherwise they do not participate in the scheme. We will assume
two extreme cases: 1) all relays can listen to each other and
2) all relays are hidden from each other (but they can listen
source and destination). In that case, the flag packet sent by
the best relay is received from the destination which responds
with a short broadcast packet to all relays. Alternatively, other
schemes based on “busy tone” (secondary frequency) control
channels could be used, requiring no broadcast packet from the
destination and partly alleviating the “hidden” relays problem.
From Fig. 3, collision of two or more relays can happen if
the best relay timer
and one or more other relay timers ex-
pire within
for the case of no hidden relays [case (a)].
This interval depends on the radio switch time from receive to
transmit mode
and the propagation times needed for signals
to travel in the wireless medium. In custom low-cost transceiver
hardware, this switch time is typically on the order of a few mi-
croseconds while propagation times for a range of 100 m is on
the order of 1/3
s. For the case of “hidden” relays, the uncer-
tainty interval becomes
since now the duration of the
flag packet should be taken into account, as well as the propaga-
tion time toward the destination and back toward the relays and
the radio switch time at the destination. The duration of the flag
packet can be made small, even one bit transmission could suf-
fice. In any case, the higher this uncertainty interval, the higher
the probability of two or more relay timers to expire within that
interval. That is why we will assume maximum values of
,so
that we can assess worst case scenario performance.
