PROBABILISTIC RETRANSMISSION STRATEGY FOR
SINGLE-RELAY COOPERATIVE ARQ
Juan J. Alcaraz, Joan Garc´ıa-Haro and Fernando Cerd´an
Department of Information Technologies and Communication, Technical University of Cartagena
Plaza Hospital 1, Cartagena, Spain
Keywords:
Automatic repeat request (ARQ), cooperative diversity, multi-objective optimization.
Abstract:
In wireless networks with cooperative automatic repeat request (C-ARQ) protocols, a relay node, placed within
the range of the sender node and the destination node, assists the sender in the process of frame retransmis-
sion. In a collision-free scenario, the sender and the relay use different physical channels for retransmissions.
This paper highlights the tradeoff between throughput increment and efficiency in the use of radio resources.
By using a probabilistic retransmission strategy, the sender only retransmits in some time-slots after a frame
error notification. At the other time-slots, the source can assign the radio resources to other communication
processes, resulting in more efficient use of the bandwidth. The retransmission probability must be carefully
adjusted according to the network parameters. In this paper we propose a Markov model to compute the
throughput performance and a complementary reward model to compute the retransmission rate of the source.
In order to keep the throughput at a high value and to reduce the retransmission rate at the same time, we
present a multi-objective optimization method that is capable of balancing both objectives in any scenario. It
is shown that the increment in bandwidth efficiency can be very high, especially for degraded links, compen-
sating the small throughput reduction associated with a probabilistic retransmission at the source.
1 INTRODUCTION
Cooperative automatic repeat request protocols, C-
ARQ, are attracting increasing research attention.
These type of protocols apply the concept of cooper-
ative communication to improve the performance of
link-layer protocols in wireless networks. In cooper-
ative communications, each node not only transmits
and receives data for its own application, but can also
act as a relay node providing an alternative path for
other pairs of communicating nodes (A. Nosratinia,
2004). This idea is known as cooperative diversity
and is commonly presented as an extension of the
spatial diversity concept of multiple-input multiple-
output (MIMO), where each one of the multiple an-
tennas are located at each cooperative node instead of
in a single node. Future evolutions of mobile access
networks are expected to make use of cooperative di-
versity using relay nodes to improve the connectivity
of the terminal nodes, see (R. Pabst, 2004), (F. Fitzek,
2006) or (K. Doppler, 2007).
Classical (non-cooperative) ARQ protocols are
widely used in wireless links to increase the relia-
bility of the data frame delivery process between a
sender node and a destination node. Several factors
of the wireless channel, e.g. path loss, fading and
noise, can degrade the quality of the received sig-
nal so that received frames can not be correctly de-
coded at the destination node. ARQ protocols spec-
ify how to retransmit data frames when frame losses
are detected. C-ARQ exploits the broadcast nature
of the wireless channel, involving additional nodes
(relay nodes) in the retransmission process. A re-
lay node is located within the transmission ranges of
both the sender node and the destination node. If
the relay node overhears a frame that the destination
is unable to decode, it can assist the sender by re-
transmitting the same copy of the lost frame. Pre-
vious works (M. Dianati, 2006), (L. Xiong, 2008),
(I. Cerutti, 2007) have shown that C-ARQ increases
the probability of successful retransmission, resulting
in higher throughput between the sender and the re-
ceiver nodes.
In general, C-ARQ protocols are evaluated in a
slotted radio channel, where the destination node can
receive simultaneously from the sender and the re-
lay nodes. These nodes use different physical chan-
nels to communicate with the destination node, and
21
J. Alcaraz J., Gar
´
cıa-Haro J. and Cerdán F. (2008).
PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ.
In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 21-28
DOI: 10.5220/0002024600210028
Copyright
c
SciTePress
therefore signals do not collide. In CDMA-based net-
works, this requires the use of different scrambling
codes; in OFDM networks, different orthogonal fre-
quencies and, in TDMA, different time-slots. C-ARQ
applied to these types of networks provides higher re-
liability at the cost of a more extensive use of wireless
resources, assuming that both the sender and the relay
node retransmit the lost frame.
The idea proposed in this paper is that, in certain
circumstances, it may be beneficial that the sender
does not retransmit in every time-slot after a frame
loss notification. This way, in a time-slot not assigned
to retransmission, the radio resources assigned to the
link between the sender node and the receiver node
are released. Therefore, the sender node can re-assign
this resources temporarily to other links, introduc-
ing new data in the network and making a more ef-
ficient use of radio resources. In many existing and
future radio access networks this is possible because
resource allocation is done slot by slot. Two examples
of this are the high speed downlink data access (HS-
DPA) (H. Holma, 2006) and the WINNER 4G concept
(K. Doppler, 2007).
There exists a clear tradeoff between retransmis-
sion probability and efficiency in bandwidth use.
Our approach consists of adjusting the retransmission
probability of the sender node in order to reduce its
retransmission rate, while trying to keep the through-
put close to its maximum. The amount of resources
that this strategy is able to release compensates the
slight reduction of the throughput compared to the de-
terministic strategy, especially when the link between
the sender and the destination is highly degraded.
This paper shows how to find an optimal working
point that balances throughputand resource efficiency
according to the parameters that characterize the net-
work. The proposed strategy provides a new view of
cooperativediversity, in which the relay node not only
assists the sender node in the retransmission process,
but it also allows the sender to release radio resources
increasing the overall utilization of the bandwidth.
Probabilistic retransmission has been previously
considered in a very recent work (L. Xiong, 2008) as
a strategy to balance cooperation and collision prob-
ability in order to achieve smaller latencies. In con-
trast, our work is focused in collision-free networks,
and therefore its results are applicable to mobile ac-
cess networks. Other works like (M. Dianati, 2006),
(I. Cerutti, 2007) and (I. Cerutti, 2006) consider a de-
terministic retransmission scheme at the source node.
The contributions of this paper are:
We develop an analytical model based on a dis-
crete time Markov chain (DTMC), useful to com-
pute the throughput. The simplicity of this model
allows a closed-form solution, which is of great
utility for the optimization analysis.
The Markov model is complemented with a re-
ward model for the derivation of the retransmis-
sion rate of the sender node.
We propose a multi-objective optimization ap-
proach to adjust the retransmission probability
balancing bandwidth efficiency and throughput.
It is shown that it is possible to achieve a notable
reduction of the retransmission rate of the sender
node while keeping the throughput very close to
the deterministic scheme.
The rest of the paper is organized as follows. In
Section 2 we describe the system under study and its
model as a DTMC. This model is used in Section 3
to analyze the performance of the system in terms
of throughput and retransmission rate. The multi-
objective optimization approach is presented in Sec-
tion 4, and numerical results are discussed in Sec-
tion 5. Finally, the implications and future research
lines derived from this work are outlined in Section 6.
2 SYSTEM MODEL
The system under study, illustrated in Figure 1, con-
sists of a sender node (S) that transmits data frames
to a destination node (D), and a relay node (N) that
receives the data frames directed to D, so it can as-
sist S in retransmissions of lost frames. The physical
layer consists of slotted radio interface. A time-slot is
defined as the time from a frame transmission to the
completion of its ACK/NACK. Slots are of fixed du-
ration and synchronized at all the nodes. This kind of
radio interface is characteristic of mobile access net-
works.
S
N
D
p
S
p
B
p
C
p
A
p
N
Figure 1: C-ARQ system.
We assume a simple channel model, similar to
(L. Xiong, 2008), where the channel can be in one of
two states: either “on”, in which transmitted signals
arrive with sufficient power to be decoded without er-
ror, or “off”, in which a transmitted signal can not be
decoded. The probability of the channel being “on”
WINSYS 2008 - International Conference on Wireless Information Networks and Systems
22
or “off” in a given time-slot is independent of its state
in previous time-slots, and independent of the chan-
nel states of different node pairs. The probability of
being in the “off” state is denoted by p
A
for the chan-
nel between S and D (direct link), p
B
for the channel
between S and N, and p
C
for the channel between N
and D (relay channel).
It is assumed that ACK/NACKs are not lost in any
channel, therefore both S and N are informed of the
reception status of the frame in D. This assumption
is common in performance evaluation of wireless net-
works, because the shorter length of control messages
make it feasible to protect them with longer error cor-
rection codes. In the subsequent time-slots after the
original transmission, if the relay node possesses a
copy of the packet, it may decide to make a coop-
erative retransmission over its relay channel.
The probability that the relay node performs a re-
transmission in a time-slot is denoted by p
N
. This
probability depends on the amount of resources that
N can assign to the communication between S and
D given its traffic load, its scheduling policy and its
processing limitations. In the numerical examples of
section 5, we set p
N
= 1, assuming a relay node fully
devoted to cooperation, in line with recent proposals
for mobile access networks where relay nodes are de-
ployed as part of the radio cell infrastructure. How-
ever, the analysis is valid for p
N
< 1, and the con-
clusions can be generalized to this case as well. The
model includes a probability of retransmission in the
sender node, denoted by p
S
. The analysis of the in-
fluence of this parameter in the overall performance
and its optimization is one of the main goals of this
paper. Note that this implies that the node computing
the optimum p
S
(in general, the sender node) must be
informed of the link qualities and the retransmission
probability of the relay node.
For successful reception, the destination node
must decode without errors at least one frame sent by
either S or N. The radio interface is collision-free, as
explained in the introduction. We assume a stop-and-
wait operation of the protocol, similarly to (M. Di-
anati, 2006). However, due to the probabilistic re-
transmission scheme at the sender, it may transmit
new frames to the receiver in time slots not assigned
to retransmissions. Each frame transmission is then
handled by independent parallel processes in a way
similar to HSDPA, (H. Holma, 2006).
The states of the Markov chain describing the op-
eration of the system are combinations of the indi-
vidual states of N and D. Let N
f
represent the state
of the relay node. N
f
= true (or simply N
f
) if the
relay node has successfully decoded the frame, and
N
f
= false (or simply
N
f
) otherwise. Because the re-
lay node is assumed not to discard frames, N
f
= true
in every time-slot between the successful reception of
a frame at N and the reception of this frame at D. The
states of the destination node are: D
f
, if the frame is
correctly decoded, and
D
f
otherwise.
The DTMC comprises the following three states:
State 0: N
f
, D
f
State 1: N
f
,
D
f
State 2: D
f
The transition diagram of the DTMC is depicted in
Figure 2. In order to describe analytically the transi-
tion probabilities let us define the following events:
S: S retransmits a frame.
N: N retransmits a frame.
N
S
: N successfully decodes a frame sent by S.
D
N
: D successfully decodes a frame sent by N.
D
S
: D successfully decodes a frame sent by S.
S, N, N
S
, D
N
, D
S
: are the complementary of the
events above.
Making use of the description of the C-ARQ protocol
and the definition of the events, the transition proba-
bilities from state 0 are given by:
p
00
= P{(S D
S
N
S
) S}
p
01
= P{S D
S
N
S
}
p
02
= P{S D
S
}
Applying the channel state and retransmission proba-
bilities of the model we obtain the following values:
p
00
= p
S
p
A
p
B
+ (1 p
S
)
p
01
= p
S
p
A
(1 p
B
)
p
02
= p
S
(1 p
A
)
(1)
When the system is in state 1, it can not enter into state
0, because the relay node does not discard frames
(p
10
= 0). The system remains in the same state with
the following probability:
p
11
= P{((N
D
N
) N) ((S D
S
) S)} =
= (p
N
p
C
+ (1 p
N
))(p
S
p
A
+ (1 p
S
))
(2)
0
1
2
p
01
p
00
p
11
p
12
p
02
p
21
p
20
p
22
Figure 2: Discrete Time Markov Chain model of the C-
ARQ protocol.
PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ
23
The system makes a transition from state 1 to state 2
with probability p
12
= 1 p
11
. Finally, if the system
is in state 2, i.e. the destination has successfully de-
coded the frame, the source transmits a new frame,
resulting in a new transition to any of the three states.
The transition probabilities from state 2 are
p
20
= P{
N
S
D
S
} = p
A
p
B
p
21
= P{N
S
D
S
} = p
A
p
B
p
22
= P{N
S
} = 1 p
A
(3)
The transition matrix of the DTMC is given by
P =
p
00
p
01
p
02
0 p
11
p
12
p
20
p
21
p
22
(4)
3 PERFORMANCE ANALYSIS
In this section we use the proposed model to obtain
two important performance metrics of the C-ARQ
scheme: the throughput and the retransmission rate of
the source. The throughput is defined as the average
number of frames successfully received in the destina-
tion node per time-slot. According to the model, the
throughput is the average number of time-slots that
the DTMC spends in state 2. The retransmission rate
is defined as the number of retransmissions from the
source, normalized by the total number of time-slots.
This measurement reflects the amount of resources al-
located to retransmissions. Therefore, for an efficient
use of the bandwidth, the goal is to reduce this rate.
For the computation of the retransmission rate, a re-
ward model is constructed.
3.1 Throughput Performance
Let
π = {π
0
, π
1
, π
2
} be the steady-state distribution of
the DTMC, where π
i
is the steady-state probability of
state i {0, 1, 2}.
π is obtained by solving the follow-
ing system of linear equations:
π = πP
i
π
i
= 1
(5)
where = {0, 1, 2}, and P is given by (4). Solving
(5) for
π we obtain the following solution:
π
2
=
h
1+
p
20
1 p
00
+
p
01
p
21
(1 p
00
)(1 p
11
)
+
p
21
1 p
11
i
1
π
1
=
h
p
01
p
21
(1 p
00
)(1 p
11
)
+
p
21
1 p
11
i
π
2
π
0
=
p
20
1 p
00
π
2
(6)
From the transition probabilities obtained in Sec-
tion 2 we can compute
π as π(p
A
, p
B
, p
C
, p
S
, p
N
). Be-
cause we focus on finding the optimal p
S
, we use,
for convenience, a simpler notation:
π(p
S
). The
throughput of the system is denoted by T(p
S
) =
π
2
(p
S
). It is obvious that, for any given set of val-
ues {p
A
, p
B
, p
C
, p
N
}, the maximum throughput is ob-
tained when the source retransmits in every time-slot
after a frame loss notification (p
S
= 1). Therefore we
define the maximum throughput as T
M
= T(1). T
M
is
taken as a reference to evaluate different values of p
S
.
3.2 Retransmission Rate of the Source
In this subsection we develop a reward model to com-
pute the average retransmission rate in the source
node. This approach has been previously applied to
the analysis of ARQ protocols. See (M. Zorzi, 1996)
for a description of this technique.
In the DTMC considered, let X
i
X
j
represent a
transition from state i to state j. Let R
ij
be the reward
associated to this transition. In our context, R
ij
rep-
resents the average number of retransmissions from
S, in the time-slots where X
i
X
j
. Analytically, it
is expressed as R
ij
= rP{S|X
i
X
j
}, where r is the
number of frames in a retransmission time-slot. In the
system under study, r = 1 because only one frame can
be transmitted per time-slot.
The reward associated to a transition is 1 if the
transition can only take place when the source retrans-
mits the frame. Therefore, any transition from state 0
to a different state involves a single reward:
R
01
= R
02
= 1
(7)
The first transmission of a frame is not considered a
retransmission, therefore the transitions from state 2
involve a null reward:
R
20
= R
21
= R
22
= 0
(8)
The reward associated to X
0
X
0
is given by
R
00
= P{S|X
0
X
0
}
which, making use of the definition of conditional
probability can be expressed as
P{S|(X
0
X
0
)} =
P{S
D
N
D
S
}
P{X
0
X
0
}
Applying the probabilities of each event, we obtain
the following value:
R
00
=
p
S
p
A
p
B
p
00
(9)
Similarly, R
11
equals the following conditional prob-
ability:
P{S|(X
1
X
1
)} =
P{(S
D
N
) ((N D
N
) N
S
)}
P{X
1
X
1
}
WINSYS 2008 - International Conference on Wireless Information Networks and Systems
24
which, according to the model results in
R
11
=
p
S
p
A
(p
N
p
C
+ 1 p
N
)
p
11
(10)
Finally, R
12
is given by
P{S|(X
1
X
2
)} =
P{(S
D
S
) ((S D
S
) (N D
N
))}
P{X
1
X
2
}
which results in
R
12
=
p
S
(1 p
A
) + p
S
p
A
p
N
(1 p
C
)
p
12
(11)
The retransmission rate associated to a reference
state, i, is computed with the following expression:
R
i
=
j
p
ij
R
ij
(12)
The average retransmission rate from S is given by a
weighted sum of the rates obtained in (12), where the
weighting factors are the steady state probabilities of
the Markov chain:
R =
i
π
i
R
i
(13)
Applying the rewards (7), (8), (9), (10) and (11) in
(12), it can be easily checked that R
0
= R
1
= p
S
and
R
2
= 0. For convenience, we can write R in terms
of p
S
as R(p
S
) = p
S
(1 π
2
(p
S
)). At the maximum
throughput, obtained with p
S
= 1, the retransmission
rate is R
M
= R(1).
4 MULTI-OBJECTIVE
OPTIMIZATION STRATEGY
There exists a clear tradeoff between the two per-
formance measurements derived in previous section.
The maximum throughput, T
M
, is achieved setting
p
S
= 1. However, this can lead to a high retrans-
mission rate, especially if the direct link is highly de-
graded. On the other hand, if p
S
= 0, then the retrans-
mission rate reduces to 0. In order to find an optimum
balance between both objectives, we propose an ap-
proach based on a multi-objective optimization tech-
nique, known as global criterion method (Rao, 1996).
This method consists of minimizing a global criterion
function, defined as:
G(p
S
) =
n
k=1
α
k
O
k
f
k
(p
S
)
O
k
2
(14)
where n is the number of objective functions, f
k
(p
S
)
are the objective functions, O
k
are the optimum val-
ues for each objective function and α
k
are the factors
weighting the relative importance assigned to each
objective. In the system analyzed, we are balancing
two objectives. First, it is desirable that the through-
put approaches its maximum, T
M
, as much as possi-
ble, i.e. f
1
(p
s
) = T(p
s
) and O
1
= T
M
. Second, it is
also desirable to reduce the retransmission rate of S,
therefore f
2
(p
s
) = R(p
s
) + C, and O
2
= C, where C
is an auxiliary non-zero real number required to avoid
a division by 0 in the global objective. In our model
we choose C = 1 because the relative importance of
R(p
S
) approaching to 0 is already controlled by α
2
.
Making use of these definitions in (14) we obtain:
G(p
S
) = α
1
T
M
T(p
S
)
T
M
2
+ α
2
R(p
S
)
2
(15)
Let p
S
denote the solution to the multi-objective op-
timization problem. Because p
S
is a probability,
the problem is subject to the constraint 0 p
S
1.
Therefore we have:
p
S
= argmin
0p
S
1
{G(p
S
)}
(16)
Let T
O
= T(p
S
) be the optimum throughput in terms
of the multi-objective optimization problem. Simi-
larly, let R
O
= R(p
S
) denote the optimum retransmis-
sion rate. In the following section we compare T
O
and
R
O
with T
M
and R
M
in several scenarios. The weight-
ing factors chosen are α
1
= 1 and α
2
= 0.2. Addition-
ally, the effect of α
2
is also discussed in the following
section.
5 RESULTS
In this section we investigate the performance of the
probabilistic retransmission approach numerically. It
is shown that, with the computed probability, the sys-
tem achievesa notable reduction in the retransmission
rate of the source with a relatively small reduction of
the throughput. Moreover, we show that the two ob-
jectives are well-balanced in many different combina-
tions of link quality conditions.
In the framework of cooperative mobile access
networks, relay nodes are considered to be part of the
cell infrastructure, specifically deployed to enhance
the connectivity of mobile users. In this scenario, a
relay node is always willing to cooperate. Assuming
that there are enough resources available, p
N
= 1. The
frame error probability in the source-relay link can be
a network design parameter, and therefore its value
can be relatively small. In the numerical evaluations
of this section we set p
B
= 0.2.
First, we study the effect of p
A
in the performance
of the proposed strategy, and compare it with the max-
imum throughput configuration (p
S
= 1). For this
PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ
25
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T
M
T
O
R
M
R
O
Performance vs p
A
p
A
Figure 3: C-ARQ performance vs. p
A
.
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Optimum p
S
p
S
p
A
Figure 4: Optimum p
S
vs. p
A
.
evaluation, the typical situation of a good relay chan-
nel is assumed: p
C
= 0.1.
The results are shown in Figure 3. It is clear that,
as the quality of the source-destination channel wors-
ens, the retransmission rate of the source with the
proposed strategy, R
O
, is notably reduced compared
to the maximum throughput scheme, R
M
. The most
interesting result is that the cost of this reduction in
terms of throughput is very small. Figure 4 shows the
corresponding values of p
S
in this scenario.
In order to evaluate the effect of the weighting fac-
tors, we can set α
1
= 1 and compute the performance
for a range of values of α
2
. Let consider the previous
configuration of the system, with p
A
= 0.4. Figure 5
plots the performance metrics obtained with α
2
in the
range 10
2
α
2
10. While it was expectable that
both T
O
and R
O
decrease as α
2
is set to higher val-
ues, it is surprising to check that the throughput does
not decay dramatically when α
2
= 1 or even at higher
values. From the values of p
S
shown in Figure 6, we
observe that a reduction of p
S
from 0.9 to 0.4 (more
than 50%), causes a reduction of about 10% in the
throughput. This fact suggests that, in practice, the
system tolerates certain inaccuracy in the computa-
10
−2
10
−1
10
0
10
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
T
M
T
O
R
M
R
O
Influence of α
2
α
2
Figure 5: C-ARQ performance vs. α
2
.
10
−2
10
−1
10
0
10
1
0
0.2
0.4
0.6
0.8
1
Optimum p
S
p
S
α
2
Figure 6: Optimum p
S
vs. α
2
.
tion of p
S
, without much impact on the throughput.
Because of the mobility of the user terminals,
many different combinations of p
A
and p
C
are pos-
sible. Figure 7 shows the computed p
S
for differ-
ent settings of both parameters. In order to focus on
the performance improvement obtained with p
S
com-
pared to p
S
= 1, Figure 8 plots the difference between
R
M
and R
O
, and Figure 9 depicts the difference be-
tween T
M
and T
O
. These figures show that, while
the retransmission rate is highly reduced, especially
in poor channel conditions, the throughput never de-
cays noticeable below the maximum. We can observe
that the proposed algorithm provides a good balance
between the two objectives pursued, even under dif-
ferent combinations of link qualities.
6 CONCLUSIONS
The analysis done in this paper shows that, in wire-
less networks with cooperative ARQ, a probabilistic
retransmission policy in the source node provides no-
table benefits in terms of efficiency in the use of radio
resources, especially in situations of poor propagation
WINSYS 2008 - International Conference on Wireless Information Networks and Systems
26
0
0.2
0.4
0.6
0.8
1
0
0.5
1
0
0.2
0.4
0.6
0.8
1
p
C
Optimum p
S
p
A
Figure 7: Optimum p
S
vs. p
A
and p
C
.
0
0.2
0.4
0.6
0.8
1
0
0.5
1
0
0.2
0.4
0.6
0.8
p
C
R
M
− R
O
p
A
Figure 8: R
M.
R
O
vs. p
A
and p
C
.
0
0.2
0.4
0.6
0.8
1
0
0.5
1
0
0.2
0.4
0.6
0.8
1
p
C
T
M
− T
O
p
A
Figure 9: T
M.
T
O
vs. p
A
and p
C
.
conditions in the direct link. The optimal retrans-
mission probability for the source node is obtained
by means of a multi-objective optimization technique,
known as global criterion method. It is shown that this
strategy reduces the retransmission rate of the source
node with a negligible reduction of the throughput.
This new concept breaks with the classical and
widely adopted policy of giving maximum priority
to retransmissions in wireless links. Consider, as an
example, the Radio Link Protocol of 3G access net-
works (H. Holma, 2004). As a consequence, the
results of this paper can be useful in the design of
scheduling mechanisms for cooperative wireless net-
works. The idea is to consider the computed re-
transmission probability, p
S
, as a lower bound for the
amount of time-slots (i.e. bandwidth) reserved for
retransmissions at the base station. The rest of the
bandwidth can be assigned to other communication
processes whenever they have available data.
The model described can be extended to include
the concept of cooperation group defined in (M. Dia-
nati, 2006). With this enhancement, the cooperation
involves an undefined number of relays. Another fu-
ture line of research consists in the addition of Hybrid
ARQ features e.g. incremental redundancy and chase
combining, in the model.
ACKNOWLEDGEMENTS
This research has been supported by project grant
TEC2007-67966-01/TCM (CON-PARTE-1) and it
was also developed in the framework of Programa de
Ayudas a Grupos de Excelencia de la Regi´on de Mur-
cia, Fundaci´on Seneca, Agencia de Ciencia y Tec-
nolog´ıa de la RM (Plan Regional de Ciencia y Tec-
nolog´ıa 2007/2010)”.
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