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Variable-Rate Two-Phase Collaborative Communication
Protocols for Wireless Networks
Hideki Ochiai
Department of Electrical and Computer Engineering, Yokohama National University
79-5 Tokiwadai, Hodogaya-ku, Yokohama, Japan 240-8501
Patrick Mitran and Vahid Tarokh
Division of Engineering and Applied Sciences, Harvard University
33 Oxford Street, Cambridge, MA 02138
Abstract
The performance of two-phase collaborative communication protocols is studied for wireless
networks. All the communication nodes in the cluster are assumed to share the same channel and transmit
or receive collaboratively in a quasi-static Rayleigh flat-fading environment. In addition to small-scale
fading, the effect of large-scale path loss is also considered. Based on a decode-and-forward approach, we
consider various variable-rate two-phase protocols that can achieve full diversity order and analyze the
effect of node geometry on their performance in terms of the outage probability of mutual information.
For the single relay node case, it is shown that if the collaborator node is close to the source node, a
protocol based on space-time coding (STC) can achieve good diversity gain. Otherwise, a protocol based
on receiver diversity performs better. These protocols are also compared with one based on fixed-rate
repetition coding and their performance trade-offs with node geometry are studied. The second part deals
with multiple relays. It is known that with N relays an asymptotic diversity order of N +1 is achievable
with STC-based protocols in the two-phase framework. However, in the framework of collaborative STC,
those relay nodes which fail to decode remain silent (this event is referred to as a node erasure). We
show that this node erasure has the potential to considerably reduce the diversity order and point out the
importance of designing the STC to be robust against such node erasure.
Index Terms
Collaborative (cooperative) communication, relay channel, space-time coding, spatial diversity,
wireless networks.
The material of this paper was in part presented at IEEE Fall Vehicular Technology Conference, Los
Angels, CA, September 2004. This work was in part supported by the Telecommunications Advancement
Foundation (TAF).
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I. INTRODUCTION
In many wireless networks, the power consumption of communication nodes is a critical issue. In
addition, typical wireless channels suffer from signal fading which, for a given average transmit power,
significantly reduces communication capacity and range. If the channel is slow and flat fading, channel
coding does not help [1,2] and spatial diversity may be the only effective option that can either reduce
the average transmit power or increase communication range. Results on space-time coding (STC) [3,
4] have shown that the use of antenna arrays at the transmitter and receiver can significantly reduce
transmit energy. However, for many applications with low-cost devices such as wireless sensor networks,
deployment of multiple antennas at each node is too costly to implement due to severe constraints on
both the size and power consumption of analog devices.
The recently proposed collaborative (or cooperative) diversity approaches [5–14] demonstrate the
potential to achieve diversity or enhance the capacity of wireless systems without deploying multiple
antennas at the transmitter. Using nearby collaborators as virtual antennas, significant diversity gains can
be achieved. These schemes basically require that the relay nodes share the information data of the source
node, and this data sharing process is generally achieved at the cost of additional orthogonal channels (in
frequency or in time). In a companion paper [15], we have shown that for a given fixed rate and under
suitable node geometry conditions, there are collaborative coding schemes that can nearly achieve the
same diversity as if all the relay node antennas were connected to the source node, without any additional
orthogonal channels or bandwidth. The construction of such codes, however, appears to be challenging.
Among many approaches in the literature, Laneman [5,6] analyzes several low-complexity relaying
protocols that can achieve full diversity, under realistic assumptions such as half-duplex constraint and
no channel state information (CSI) at the transmitting nodes. It has been shown that in the low-spectral-
efficiency regime, the SNR loss relative to ideal transmit diversity system with the same information
rate is 1.5dB[5]. Multiple-relay cases are also considered in [6] and bandwidth-efficient STC-based
collaborative protocols are proposed.
Collaborative diversity protocols are largely classified into amplify-and-forward and decode-and-
forward schemes [5]. In the following, we will restrict our attention to decode-and-forward schemes
since these may provide some salient advantages. First, there is no error propagation if the relay transmits
information only when it decodes correctly. Otherwise, the relay remains silent and thus an unnecessary
energy transmission can be saved1. Second, the information rate per symbol does not need to be the same
for each phase. In other words, the relative duration of each phase can be changed according to node
geometry.
1Even though perfect detection of the codeword is not feasible in practice, one can design a cyclic redundancy-check (CRC)
or error detectable low-density parity-check (LDPC) code such that for a given system outage probability, the effect of error
propagation is negligible. Many existing communication networks have this structure.
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2
R∗
T
T1
T2
R1
R2
(a)
(b)
phase-I phase-II
Fig. 1. Two-phase communication. (a) baseline system. (b) two-phase protocol.
It is the latter property that we shall focus on in this work. Suppose that we wish to transmit data with
information rate R∗bits per second and T is the frame period, also in seconds. Then the total information
transmitted during this period is R∗T bits (per frame). The baseline frame design that achieves this is
shown in Fig.1 (a). Alternatively, we may split the time interval into two phases of duration T1 and
T2where T = T1+ T2and each phase is operated with information rate R1and R2, respectively, as
depicted in Fig.1 (b). We assume that for both phases, the same information (but with different coding
rate) is transmitted. If R1and R2are chosen such that R1T1= R2T2= R∗T, then in principle there
is no loss of total transmission rate compared to the baseline system. Let the fraction of the relative
time period for each phase be denoted by δ1? T1/T = T1/(T1+ T2), and δ2? T2/T = 1 − δ1. Then,
the information rate during each phase is R1= R∗/δ1and R2= R∗/δ2. Therefore, during each phase,
information should be transmitted employing larger constellation sizes than the baseline system2.
For ideal AWGN and interleaved fading channels under an average signal-to-noise power ratio (SNR)
constraint over the entire communication process, two-phase protocols do not necessarily achieve a gain
and may even result in performance loss compared to the baseline system. However, for quasi-static or
block Rayleigh fading channels, it is not the constellation size but diversity that is the dominant factor
for the outage behavior. Thus, if additional diversity can be achieved by two-phase methods, the resulting
outage probability of the mutual information may more than offset any loss due to constellation size and
yield a reduction in required SNR. (This is somewhat analogous to coded modulation which increases the
signal constellation size in order to achieve coding gain. In our case, however, we shall achieve diversity
gain.)
In practical collaborative wireless communication networks, node geometry is an important factor.
Intuitively, if the collaborative relay node is close to the source node, it may be efficient for the relay
2The fraction δ1 and δ2, or equivalently, the coding rate R1 and R2 are determined based on the node location, not on each
realization of fading channel coefficient as done in [15,16].
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3
to act as a transmit antenna. In this case, STC based protocols such as [6] may be efficient. On the
other hand, if the relay is close to the destination, it should operate as a receive antenna. To capture
this geometrical effect, we model the wireless network channel as an aggregate of large-scale path-loss
and small-scale fading [17]. The large-scale path-loss is the decay of signal power due to the transmitter
receiver separation, and is a function of the distance between the two terminals. On the other hand, the
small-scale fading is a consequence of multipath which may vary randomly according to any physical
change of surroundings. The overall system model is detailed in Section II.
In this paper, motivated by the rate-flexible nature of decode-and-forward protocols and the importance
of node geometry, we extend the work of Laneman [5,6] to a variable-rate framework with particular em-
phasis on path-loss gain effect of relay nodes, achieved due to the relay’s proximity to source/destination
nodes. Several low-complexity protocols are considered, including a simple multi-hopping protocol, the
bandwidth-efficient STC-based protocol of [6], as well as its receiver diversity counterpart (SectionIII).
Their performances with a single relay node are theoretically analyzed in terms of achievable diversity
gain for a given information rate based on outage probability of mutual information. For this purpose,
convenient simple analytical tools are developed in Section IV.
The main objective of the paper is, for a given relative location of the relay node, to determine a suitable
protocol and minimize the total required power of the transmitting nodes. To that end, optimal power
control factors and relative phase durations for the relay node are derived for each protocol considered.
Associated with these protocols, closed-form expressions for diversity gain are derived in SectionV, where
it is shown that by suitably choosing the protocol and controlling the transmission rate, as a function
of node geometry, the achievable diversity gain can be significantly improved. Also, it will be shown
that under severe path-loss, even a simple multi-hop protocol benefits relative to direct transmission. For
example, a significant gain is attained if the relay is located midway between the two communicating
nodes.
In the analysis of STC-based collaborative protocols, we presume two types of STC which we denote
as perfect and imperfect STC. A perfect STC refers to an STC with partial decodability, i.e., the (full)
information can be retrieved from a subset of the transmitting nodes, whereas an imperfect STC refers to
a system in which the receiving nodes fail to decode if any one of the transmitting nodes that constitute
the STC fails to transmit. This partial erasure of an STC antenna branch may happen if the relay nodes
fail to decode correctly. (This event will be referred to as a node erasure.) In SectionVI, we show that
the diversity order of an imperfect STC with N collaborative relays is at most 2, whereas that of a perfect
STC can achieve diversity order of N + 1 as in [6].
Throughout this paper, our main focus is on the achievable diversity gain for a given information rate.
The diversity-multiplexing trade-off [18] of the relay channels is also of practical importance, but this is
beyond the scope of this paper. Some results in this direction are explored in [5,6,16]. As related work,
the effect of node geometry is also considered in [12,19,20], but in a fixed-rate framework. Also, we do
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4
S
D
R
θ
HS,R
HR,D
HS,D
dS,R
dR,D
dS,D
GS
GD
Fig. 2. Two-phase communication.
not address specific design issue of coding as many existing channel/STC techniques in the literature are
applicable to our framework without major modification. Note that some practical design of collaborative
codes (with implicit variable-rate coding) is proposed in [21] and its outage behavior is evaluated in [13].
The use of incremental redundancy such as [22] may be of further potential in this framework. Finally,
we note that variable-rate coding for multiple-access channels has been recently studied in [23].
II. SYSTEM AND CHANNEL MODEL
Fig.2 illustrates the basic model which is considered throughout the paper. It is assumed that the three
nodes source(S), relay(R), and destination(D) are located in the two dimensional plane as in Fig.2 where
θ is the angle of the line S − R − D and dA,Bdenotes the Euclidean distance between nodes A and B.
We suppose that S wishes to transmit the message to D and that R has agreed to collaborate with S a
priori.
For simplicity, we assume that all the channel links are composed of large-scale path loss and
statistically independent small-scale quasi-static frequency non-selective Rayleigh fading. Consequently,
the complex channel coefficients HS,D, HS,R, and HR,D in Fig.2 are uncorrelated and circularly
symmetric complex Gaussian random variables with zero mean and unit variance. They are assumed
to be known perfectly to the receiver sides and unknown at the transmitter sides. Perfect timing and
frequency synchronization are also assumed, even though accurate acquisition of synchronization among
distributed nodes may be challenging in practice.
The path loss between two nodes, say A and B, is modeled by
PL(A,B) = K/dα
A,B,
(1)
where K is a constant that depends on the environment and α is the path-loss exponent. For free-space
path loss, we have α = 2 and K = GtGrλ2/(4π)2, where Gtand Grare antenna gains at transmitter
and receiver, respectively, and λ is the wavelength [17]. Although the path-loss exponent and the constant
factor K may vary for each channel link, throughout the paper it is assumed that α and K are identical
for all channel links.
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25
In the following discussion, the STC having this property will be referred to as an imperfect STC. The
outage performance based on this assumption may serve as an upper bound for the TD and STD protocols.
In this case we have the following theorem:
Theorem 2: For the N relay node TD and STD protocols with imperfect constituent STCs, i.e., (73)
holds, the asymptotic diversity orders are 2 and 1, respectively.
Proof: Considering the outage probability expression in (72), it is easy to see that the worst-case
terms are those with n = N − 1. Then, we have for the TD protocol
N−1
?
N−1
?
where the last equality is from Pr
E1∩ E2|F(0)
1. Therefore, by Corollary1 we obtain d∗(Pout) = d∗?B(0)N−1(1)1
For the STD protocol, we have
B(0)N−1(1)1=
i=1
e
−
A1
GS,iSNRS
1
?
?
1 − e
−
A1
GS,NSNRS
1
?
??
Pr
?
E1∩ E2|F(0)
1,...,F(0)
N−1,F(1)
N
?
=
i=1
e
−
A1
GS,iSNRS
1
1 − e
−
A1
GS,NSNRS
1
1 − e
−
A1
SNRS
1
?
,
(74)
?
1,...,F(0)
N−1,F(1)
N
?
= Pr
?= 2.
?
E2|E1,F(0)
1,...,F(0)
N−1,F(1)
N
?
=
B(0)N−1(1)1=
N−1
?
i=1
e
−
A1
GS,iSNRS
1
?
1 − e
−
A1
GS,NSNRS
1
?
,
(75)
and thus d∗(Pout) = d∗?B(0)N−1(1)1
Therefore, in the high SNR regime, the asymptotic diversity orders of the TD and STD protocols with
imperfect STC are d∗= 2 and d∗= 1, respectively. This suggests that in the high SNR regime, it is
important that collaborative STCs for distributed nodes be designed such that the information can be
decoded with only a partial subset of the code (i.e., robustness against transmit antenna erasures in the
traditional multiple-antenna STC scenario). Practical design issues in this direction are addressed in [33].
?= 1.
C. Outage Probabilities and Diversity Offset Gains for Single Relay Node Case
In the case of a single relay with imperfect STC, it is straightforward to obtain the outage probabilities
and their associated diversity offset gain expression based on the approach outlined in SectionV.
1) TD Protocol: From Theorem 2, it follows that the diversity order is 2. The corresponding outage
probability is given by
Pout= Pr[ER]Pr[E1] + Pr[¯ER]Pr[E1∩ E2|¯ER].
(76)
The closed-form expression can be found by using (38), (24), and (53). It follows that a0,a1= 0 and
a2=A2
GS
∆R
2
1
?
1 +
r
?
1 −1
Amin
A2
?Amin
A1
?
(1 + δ2∆R)2.
(77)
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26
It is observed that a2is similar to (55). In fact, if δ1> 1/2 and thus Amin= A1, the offset gain of the
TD protocol with imperfect STC, denoted by ΛIM-TD(2), is equivalent to ΛTD(2). On the other hand, if
Amin= A2, the gap becomes (assuming the same ∆optis applied)
?
ΛTD(2)/ΛIM-TD(2) =
A1
?
1 +A2
A1
r
2∆opt
?
/A2
?
1 +
r
2∆opt
?
,
(78)
which is significantly large if A1≫ A2(and thus δ1≪1
2) STD Protocol: In this case, we have
2).
Pout= 1 − Pr[¯ER∩¯E2] = 1 − Pr?C(GSSNRS
1,HS,R) > R1
?Pr?C(SNRS+R
2
,P,h) > R2
?,
(79)
fout(X) = 1 − e−
A1
GSlTD(X)X
?
∆RGDe−
A2
∆RGDlTD(X)X− e−A2lTD(X)X
∆RGD− 1
?
.
(80)
Consequently, we obtain a0= 0,
a1=A1
GS
(1 + δ2∆R)
and
a2=A1A2
2GS
?
r
∆R
−A1
A2
1
GS
?
(1 + δ2∆R)2.
(81)
Therefore, the asymptotic diversity order is 1, which agrees with Theorem 2. However, it should be noted
that the offset gain with respect to the SISO system is given by
ΛIM-STD(1) =
A0GS
A1(1 + δ2∆R)
(82)
and this indicates that if GSis large, one may still achieve significant gain over the baseline system. In
particular, for the SNR region where SNRt≪ ΛIM-STD(1) (X ≫ 1/ΛIM-STD(1)), the outage probability
has a local slope of order 2 since the term a1X in fout(X) is dominated by a2X2. The following section
elucidates this effect numerically.
3) Numerical Results: We numerically compare the performance of the two protocols with imperfect
and perfect STC in terms of outage probability. Fig.8 (a) and (b) show the outage probabilities of these
protocols with relay node locations ζ = 20 and -20dB, respectively. The performance of the RD protocols
is also shown as a reference. In these results, it is assumed that the relay performs the optimal power
control algorithm.
From Fig.8 (a), it is observed that the two protocols with imperfect STC are almost identical in the
low SNR region with a local slope of (diversity) order 2, but for high SNR, the bound for the STD
protocol shows a slope of order 1, whereas that of the TD protocol maintains a slope of diversity order
2. The gap between the two bounds becomes noticeable in Fig.8 (b), where the outage probability of
the TD protocol with an imperfect STC is identical to that of the ideal TD, whereas the STD protocol
with an imperfect STC is much worse than the ideal SISO bound. Therefore, if the STC is designed
imperfectly, then the use of the TD protocol can offer stable performance and is thus preferable.
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27
1020
SNRt[dB]
3040
10-5
10-4
10-3
10-2
10-1
100
MISO Bound
RD
TD
STD
SISO
TD/STD
IM-TD/IM-STD
2x1 MISO
RD
Outage Probability
(a)
1020
SNRt[dB]
3040
10-5
10-4
10-3
10-2
10-1
100
MIMO Bound
RD
TD
STD
IM-STD
SISO
2x1 MISO
STD
RD
1x2 SIMO
TD/IM-TD
Outage Probability
(b)
Fig. 8.Outage probability of the TD and STD protocols with perfect or imperfect STC. The result of the RD protocol and
associated MISO/SIMO bounds are also shown. Parameters: R∗= 2, α = 2, θ = π. (a) ζ = 20 dB. (b) ζ = −20 dB.
VII. CONCLUSION
We have analyzed the performance of various variable-rate two-phase collaborative diversity protocols
for wireless networks. These protocols can be implemented in a straightforward manner using standard
variable-rate channel coding and STC. Theoretical analysis of the outage probability has shown that
these protocols, if properly designed based on the node geometry, can achieve full diversity order and
considerable offset gains. Our conclusion is that if the relay is close to the source and destination, the
STD and RD protocols, respectively, achieve good performance. If the relay is midway between the
source and the destination, fixed-rate repetition coding with signal combining at the destination [6] is a
good candidate considering its simplicity of implementation.
It is also shown that for a system with N relays, a diversity order of N + 1 is achievable for the TD
based protocol using STC as in [6]. However, if the STC fails to be decoded whenever node erasure
occurs, their diversity order is considerably reduced and for the STD protocol with an imperfect STC, no
diversity offset gain can be achieved. Therefore, the design of STCs that are robust against node erasures
is an important area of future research.
Finally, even though perfect synchronizations are assumed throughout the paper, accurate timing and
frequency acquisitions among distributed nodes are difficult to achieve in practice. Further research in
this direction is of critical importance for implementation of these protocols.
ACKNOWLEDGMENT
The authors wish to thank the reviewers for their detailed comments and suggestions.
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