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Throughput and Delay Analysis of Truncated

Cooperative ARQ Protocols using DSTC

Marwen Bouanen

Department of Computer Science

Université du Québec à Montréal

Montréal, Québec, Canada

[email protected]

Wessam Ajib

Department of Computer Science

Université du Québec à Montréal

Montréal, Québec, Canada

[email protected]

Hatem Boujemaa

TECHTRA, SUPCOM

University of Carthage

Tunis, Tunisia

[email protected]

Abstract—In this paper, we evaluate the throughput and the

packet total transmission delay for cooperative truncated

Automatic Repeat Request (ARQ) using distributed space-

time codes, where relays use either Decode-And-Forward

(DF) or Amplify-and-Forward (AF) relaying. In this scheme,

relays are involved in the retransmission only when the

destination receives erroneously the packet. Both source and

relays make use of an orthogonal space time block code. For

the DF mode, relays are selected after a verification by the

cyclic redundancy check (CRC) sequence. However, for the

AF mode, all relays are involved in the retransmission. We

show that the proposed design can significantly improve

performances in terms of throughput and total transmission

delay.

Keywords-Cooperative communications, HARQ, Delay analysis.

I. INTRODUCTION

The employment of MIMO technology may bring spatial

diversity and therefore a significant improvement of the

channel capacity. However, in practice, nodes are constrained

by their limited size so that the implementation of multiple

antennas is difficult. As a solution, a novel approach called

"Cooperative Communications" has been introduced to

overcome such limitations. The solution consists in using relay

nodes as a virtual antenna array to help the source node in

transmitting the information. Such an approach allows to

realize cooperative diversity.

Trying to benefit from cooperative communications,

researchers have introduced many cooperative protocols such

as Amplify-and-forward (AF), Decode-and-forward (DF), and

selective relaying [1]. Other important works include

distributed space-time coding (DSTC) which are shown to

improve the bandwidth efficiency of cooperative

communications [2].1

On the other hand, many works have proposed ARQ

protocol at the link layer to overcome the fading nature of

wireless channels where CRC is a common tool to decide

whether the packet has been correctly received by the

destination node or not. Moreover, the maximum number of

This work was supported by Qatar National Research Fund under Grant

NPRP 08-577-2-241 and NSERC-DG

retransmissions is often limited. Such a variant of ARQ is

called “truncated ARQ”.

As a combination of the previous techniques, cooperative

ARQ protocol has been proposed by combining cooperative

diversity and truncated ARQ. In such protocol, relay nodes

cooperation can be implemented via a DSTC. In fact, studies

have shown that cooperative ARQ can achieve significant

throughput gains [3]. It has been shown that combination of

cooperative diversity and truncated ARQ can greatly improve

the system throughput compared to the conventional truncated

ARQ scheme. Authors of [3] aimed to maximize the

throughput by optimizing the packet length and modulation

level.

Other studies have treated cooperative ARQ from a

transmission delay point of view [4]. The author has evaluated

the delay experienced by Poisson arriving packets for a

specific variant of cooperative truncated ARQ called

cooperative hybrid ARQ with opportunistic relaying. The

results of this work indicate a significant improvement of the

packet waiting time and sojourn time when compared with

pure truncated ARQ protocol. Delays and throughput have

been studied in these mentioned works since they are

considered as important performance parameters [5].

The novelty compared to the mentioned works is that we

optimize the performance with respect to a variable which has

never been treated before : The number of available relays.

Moreover, to the best of our knowledge, studies have not yet

treated the case where the system has to handle the two

following performance metrics: throughput and total

transmission delay. In this paper, we propose a cross-layer

design between the physical layer where we use a cooperative

diversity, and the link layer where we exploit truncated ARQ.

In this scheme, we assume Q idle nodes around the source.

The source transmits a packet to the destination node. After

verifying its CRC bits, the destination decides whether the

received packet is correct or not. If the packet is erroneously

received, a retransmission process is launched, and the source

and relays use an orthogonal space-time code. Moreover,

relays can operate according to two relaying modes: DF and

AF. In DF relaying, only the relays having correctly decoded

the CRC are selected among Q nodes. Whereas, for AF mode,

all the Q relays participate in the retransmission process.

978-1-4577-9538-2/11/$26.00 ©2011 IEEE 731

In the present paper we concentrate on the performance

parameters at the link layer. The throughput and total

transmission delay are given for both DF and AF relying

modes. It will be shown that, for good source-relay channels,

using DF at relays outperforms the AF relaying.

This paper is organized as follows. Section II describes the

system model. Sections III and IV are dedicated to derive the

expressions of throughput and delay. Numerical and

simulation results are given in section V. Finally, section VI

summarizes and concludes this paper.

Notations: The subscripts , and stand for

transposition, Hermitian conjugation and element-wise

conjugation, respectively. The expectation operation is

denoted by .

Fig.1. Wireless relay network including one source, Q idle relays, and

one destination.

II. SYSTEM MODEL

We consider a network composed of a source node S, a

destination node D and K relays. It is assumed that each node

is equipped with a single antenna. Among these relays, we

assume Q idle relays to be available for the source when

transmitting a packet (see Fig.1). In a nutshell, our proposed

scheme is divided into two phases. In the first phase, the

source node transmits a packet to which a C-bit CRC is added.

Once the packet is detected at the destination, a CRC

verification is accomplished so that an acknowledgment is sent

back to the source node. In the case where the destination

detects correctly the packet, the acknowledgment is said to be

positive (ACK) and the source transmits the next packet.

Otherwise, a negative acknowledgment (NACK) is sent back

asking the source for retransmitting the packet. At that time,

the second phase starts and the Q candidate relays participate

in a retransmission process according to one of the two

relaying modes:

Decode and Forward (DF): the source node and the

concerned relays will cooperate in order to retransmit the

packet by implementing a suitable distributed orthogonal

space-time block code OSTBC. In fact, among Q relays,

the ν selected relays which are involved in the

retransmission process are those that have successfully

decoded the transmitted packet. This adaptability in the

cooperation process allows us to avoid error propagation.

Moreover, this scheme provides cooperative diversity.

That is why, an important improvement of the link layer

performance from its both sides –throughput and

transmission delay- is expected.

Amplify and Forward (AF): here, the relay nodes do not

verify the CRC so that all of the Q candidate relays are

selected to participate in the phase of retransmission,

i.e. ν = Q. The cooperation is realized by utilizing a

(Q+1)-transmit-1-receive OSTBC.

Retransmission is stopped only when the packet is correctly

detected at the destination or when the number of

retransmissions reaches its maximum . It is assumed in

the rest of the paper, that the source-to-destination, source-to-

relay and relay-to-destination links are characterized by quasi-

static Rayleigh distributed flat fading channels. The source

transmits a packet s = , consisting of L M-QAM

modulated symbols to the destination, where L is the packet

length. It is assumed that = 1. This means that

from time to , the transmitted signals are , …,

where is the average transmitted energy per symbol.

The L 1 received signals at the destination and the r-th relay

are given respectively by

(1)

and (2)

where , …, are L 1 independent identically distributed

(i.i.d.), zero-mean complex Gaussian random variables with

variance N0. Under the assumption that each source-relay link

undergoes independent Rayleigh process, , …, and are

i.i.d. complex Gaussian random variables with zero mean and

variance and

, respectively.

In the case where the destination detects erroneously the

packet, the ν relays cooperate with the source node by

transmitting linear transformations of and where

If DF is the relaying mode

If AF is the relaying mode

The implementation of the DSTC is presented at the

destination as follows

(3)

where the L 1 additive noise w and fading coefficients

, …, are i.i.d. complex zero-mean Gaussian random

variables with variance N0 and , respectively. and ,

i = 0,..., , are the result of the representation of the

i-th column of the L (ν+1) space time code matrix S

as . On the other hand, is the amplification

factor at the relay which is given by

1 If DF is the relaying mode

If AF is the relaying mode

where is the transmitted energy per symbol by the relay.

In this paper, it is assumed that the Q relays are nearby

Source Destination

Rν

R1

D

1

𝑄

⋮ ⋮

𝑣

𝑣1 1

0 𝑣0

Q

𝑤1

𝑤Q

RQ

𝑣Q

⋮ ⋮

S

𝑤

D

Destination

732

the source node so that the large scale fading of the

relay-destination channels and the source-destination channels

are almost the same, i.e. =

. Let and be the

average SNR per symbol of the transmission phase and

retransmission, respectively. Furthermore, we denote by

and the block error probability of the

transmission and retransmission, respectively. The symbol

error probabilities (SEP) of transmission and retransmission

are denoted and , respectively.

III. THROUGHPUT ANALYSIS

In this section, we derive the throughput realized by the

proposed scheme according to the DF and AF modes.

Let C be the number of CRC redundancy bits added

to the packet and L its length. The adopted modulation is

M-QAM with b = log2(M). Here, the retransmission is only

done when the destination erroneously detects the packet. The

retransmission is stopped when the packet is correctly received

at the destination or the number of retransmission reaches

its maximum .

A. Throughput of the AF relaying mode

The throughput of the AF relaying mode is given by

(4)

where is the packet successful rate which is given by

(5)

while is a random variable representing the total number

of transmissions of a given packet and is the average

number of retransmissions per packet given by

(6)

𝑄

𝑥

𝑄

where (7)

and (8)

In (6), 𝑄 is the rate of a (Q+1)-symbol STBC

where . By assuming a Rayleigh flat fading channel

over the source-destination link and a M-QAM modulation, the

expression of can be deduced from [6] as follows

(9)

where . For the retransmission phase, the

system can be considered as a (Q+1)-transmit-1-receive

distributed OSTBC with M-QAM modulation over Rayleigh-

fading channels. As a result, from [7], the symbol error

probability according to the moment generating

function (MGF) approach can be approximated as follows

(10)

where

(11)

(12)

𝑄

(13)

and

𝑄

(14)

is the exponential integral function,

and

.

B. Throughput of the DF relaying mode

For this relaying mode, the nodes that are involved in the

retransmission phase are those which have correctly detected

the CRC. Therefore, the number of relay nodes is not fixed.

The throughput expression of the DF relaying mode is given

by

(15)

where and are the packet successful probability

and the average number of retransmissions per packet,

respectively. Their explicit expressions are given by

(16)

and

𝑄

(17)

where given by

(18)

for j=0,…,Q.

In (17), is the block error probability when

j relays are involved in the retransmission. is the

probability that j relays detect correctly CRC and it is given by

𝑄

(19)

733

where j = 0,…, Q. is the block error probability

of the S-R channel which is given by

, where, is the symbol error

probability of the S-R channel.

For the DF relaying mode, the retransmission can be

considered as a (ν+1)-transmit-1-receive STBC with M-QAM

modulation over Rayleigh fading channels. A communication

in such conditions is characterized by an average symbol error

probability that is derived in [8] as follows

. 2

(20)

where is the

average SNR per symbol at relay node, 2 𝑥 and

𝑥 𝑦 are the Gauss hypergeometric function and

the Appell hypergeometric function, respectively [8]. By

substituting m = ν+1, p = 1 and in (20), then

is easily calculated.

Fig. 2. Delay model.

IV. DELAY ANALYSIS

In this section, we provide the delay model and derive the

total transmission delay presented of both DF and AF relaying

modes.

A. Delay model

We assume that relays transmit during their allocated time

slot of duration , where the frame duration and P is is

the number of slots per frame. Because of constraints on the

size of queues and the transmission delay, the number of ARQ

retransmissions is set at a maximum number of .

If a packet is not correctly received after a number

of retransmission , it will be deleted from the queue.

At the end of each service time which corresponds to

a transmission attempt, a packet has two options: either it

remains in the queue with probability or leaves the

queue with probability . We study below the total

transmission delay of proposed scheme. The arrival of packets

at the source is assumed to follow a Poisson law characterized

by an arrival rate of λ. The waiting time in the queue is defined

as the time elapsed between the arrival of the first packet and

packet transmission. It can be found using the Pollackzek-

Khinchin formula for M/G/1 queues with vacation [9], as

follows

(21)

with a stability condition

where is a random variable representing the total number of

transmission of a given packet and ε is a processing time for

amplification in the case of AF or demodulation in the case of

DF. The total delay of transmission of a packet that leads to

the destination successfully is therefore given by

(22)

To evaluate the expressions (22) and (23), all what is needed

is to calculate for both AF and DF relaying modes since

all other parameters are available.

A. Delay of the DF relaying mode

For the DF mode, the number of active relays is not fixed.

Therefore the second order-moment of is derived by

averaging over the number of selected relays , as follows

𝑄

(23)

where is calculated in (18). After injecting (23) into (22),

the total transmission delay for the DF relaying mode is easily

obtained.

B. Delay of the AF relaying mode

In AF, the number of participating relays is 𝑄, then the

second order-moment of is computed similarly to DF

relaying.

V. NUMERICAL AND SIMULATION RESULTS

A. Throughput Comparison

We assume that the CRC bits length is C=16. It is assumed

that the length of the packet is L=120. We adopt a quadrature

phase shift keying (QPSK) modulation. The maximum number

of retransmissions is and . Moreover, the

packet arrival rate was set to . We consider also the

same energy per symbol for the transmission and

retransmission processes so that . The source-relay

channels are assumed to be good by setting dB.

TABLE. 1 shows the rates of the OSTBC for different

number of relays. TABLE. 1 STBC rates

Selected relays (ν) Rate

0, 1 1

2, 3 ¾

4, 5, 6, 7 ½

Fig.3 and Fig.4 show the evolution of the throughput of the

proposed cooperative ARQ scheme with respect to the average

SNR per symbol when DF and AF are the relaying modes,

respectively. The number of available candidate relays Q

varies from 0 (which refers to the simple truncated ARQ

protocol) to 7. A good match can be observed between the

simulation and theoretical curves. It can be seen also that our

proposed scheme performs much better than the pure truncated

ARQ scheme.

Moreover, we notice that for both relaying modes,

cooperative diversity shows a considerable improvement in

pN . . . p2 p1

𝝀

1 Active

Idle

734

terms of throughput. Here, the source-relays channels are

good. That’s why, cooperative diversity gain can be fully

exploited to improve the SEP of the retransmission process so

additional throughput gains can be expected to be achieved

over the pure truncated ARQ scheme. It should be noticed that

starting from specific high values of SNR, a decrease of the

throughput is noticed for curves corresponding to Q = 5 and

Q = 7 when compared with curves Q {0, 1, 2, 3}. This

behavior is due to the fact that the STBC does not have a full

rate.

We provide Fig. 5 to conclude about the throughput

performance for the DF and AF modes. This figure draws the

throughput efficiency versus the number of available relays Q.

It can be easily seen that combining ARQ protocol at link

layer and cooperative diversity, increases the throughput. For

DF relaying, we notice an increase of the throughput

efficiency from 0.02 bit/s/Hz for pure truncated ARQ (Q = 0),

to 0.55 bit/s/Hz for the Q = 7, when . From a

throughput point of view, it can be seen that DF relaying mode

outperforms AF. This is due to the adaptability of the source-

relay channels and the reduced number of used relays.

However, this improvement is at the price of more

functionalities to be implemented at the relay nodes.

Fig .5 shows that a convenient choice of Q (for instance :

Q = 5 for the curve SNR = 12 dB), allows us to optimize the

performance in terms of throughput.

B. Delay Comparison

Fig. 6 shows the total transmission delay with respect to the

number of available relays Q. We notice that DF relaying

offers better performance than AF relaying. Indeed, for the AF

relaying, both noise and useful signal are amplified. However,

the DF relaying presents larger computational complexity and

selection time than AF relaying. Thanks to the proposed cross-

layer design, it can be seen that by optimizing Q, the total

transmission delay can be minimized. Concerning the curve

where SNR = 12 dB in Fig .6, Q = 4 is the optimal number of

available relays that should be used to minimize the total

transmission delay. Moreover, we show that a good choice of

Q, helps to avoid an overuse of relays and thus a smaller

amount of signaling between relays is needed. The SNR in

Fig. 5 and 6 denotes the average SNR of the direct link which

is the same as that of the R-D link since the relays are close to

the source.

VI. CONCLUSION

In this work, we have evaluated the throughput and the total

transmission delay of the proposed cross-layer design that

combines ARQ at the link layer and cooperative diversity at

the physical layer. It has been shown that a great improvement

of the QoS in terms of throughput and the total transmission

delay has been witnessed. We have shown that the DF

relaying mode outperforms AF. It has been noticed also that

optimizing the number of available relays Q improves the

performance.

Fig. 3. Throughput of cooperative ARQ protocol using DF relaying

for 20 dB.

Fig. 4. Throughput of cooperative ARQ protocol using AF relaying

for 20 dB.

Fig. 5. Throughput efficiency versus the number of available relays

for = 20 dB.

Thro

ugh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)

Q = 0 : Truncated ARQ (Analytical)

Q = 0 : Truncated ARQ (Simulation)

0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

Th

rou

gh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

Thro

ugh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1

0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0 0 2 4 6 8 10 12 14 16 18 20

SNR, dB

Thro

ugh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

Thro

ugh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

Th

rou

gh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1

0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0 0 2 4 6 8 10 12 14 16 18 20

SNR, dB

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 1 2 3 4 5 6 7

Th

rou

gh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

0.7

DF with ΓR-D = 12 dB


0.6 DF with ΓR-D = 8 dB

AF with ΓR-D = 12 dB


0.5 AF with ΓR-D = 8 dB

0.4

0.3

0.2

0.1

0

0 1 2 3 4 5 6 7 Number of candidate relays Q

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Th

rou

gh

put

eff

icie

ncy (

bit/s

/hz)

1.2

1 0.8

0.6

Q = 7 (Analytical)

Q = 7 (Simulation)

Q = 5 (Analytical)

Q = 5 (Simulation)

Q = 3 (Analytical)

Q = 3 (Simulation)

Q = 2 (Analytical)

Q = 2 (Simulation)

Q = 1 (Analytical)

Q = 1 (Simulation)



0.4

0.2

0

0 2 4 6 8 10 12 14 16 18 20 Es/No, dB

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


To

tal tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Tota

l tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Optimal Q for AF

Optimal Q for DF

735

Fig. 6. Total transmission delay versus the number of available relays

when = 20 dB.

REFERENCES

[1] Laneman, J.N.; Tse, D.N.C.; Wornell, G.W, “Cooperative

diversity in wireless networks: Efficient protocols and outage

behavior”, IEEE Transactions on Information Theory, Vol. 50, No. 12, pp. 3062 – 3080, Novembre 2004.

[2] Nabar, R.U.; Bolcskei, H.; Kneubuhler, F.W.; “Fading relay

channels: performance limits and space-time signal design”, IEEE

Journal on Selected Areas in Communications, Vol: 22, No. 6,

pp. 1099, Août 2004.

[3] Lin Dai Letaief, K.B, “Cross-layer design for combining

cooperative diversity with truncated ARQ in ad-hoc wireless

networks”, IEEE Global Telecommunications Conference,

GLOBECOM '05, St. Louis, MO, 2006.

[4] Hatem Boujemaa, “Delay Analysis of cooperative Truncated

HARQ with Opportunistic Relaying, IEEE Transactions On

Vehicular Technology”, Vol. 58, NO. 9, November 2009.

[5] M.Dianati, X. Ling, K.Naik, and X. Shen, “A node cooperative

ARQ scheme for wireless ad-hoc networks”, IEEE Wireless

Communications and Networking Conference, New Orleans, 2005.

[6] Alouini, M.-S. Goldsmith, A, “A unified approach for

calculating error rates of linearly modulated signals over generalized

fading channels”, in Proc. ICC 98, pp. 459-464, June 1998.

[7] Behrouz Maham, Are Hjorungnes and Giuseppe Abreu,

“Distributed GABBA Space Time Codes in Amplify-and-Forward

Relay Networks”. IEEE on Wireless Communications, Vol. 8, NO. 4,

April, 2009.

[8] H. Shin and J. H. Lee, “Exact symbol error probability of

orthogonal space-time block codes”, in Proc. Globecom’02, pp.

1197-1201, 2002.

[9] W. C. Chan, T. C. Lu, and R. J. Chen, “Pollaczek-Khinchin

formula for the M/G/1 queue in discrete time with vacations,” IEEE

Proc. Comput. Digit Tech., vol. 144, no. 4, pp. 222–226, July 1997

To

tal tr

an

sm

issio

n d

ela

y

6

5.5

5

4.5

4

3.5

3 0 1 2 3 4 5 6 7

Number of candidate relays Q

Tota

l tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Tota

l tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Optimal Q for AF

Optimal Q for DF

To

tal tr

an

sm

issio

n d

ela

y

6

5.5

5

4.5

4

3.5

3 0 1 2 3 4 5 6 7

Number of candidate relays Q

To

tal tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Tota

l tr

ansm

issio

n d

ela

y

6

SNR

= 12 dB

SR

SNR = 10 dB SR

SNR = 8 dB 5.5 SR

5

4.5

4

3.5

3


0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


SNR

SNR

SNR

0.7







0.4

0.3

0.2

0.1

0


Optimal Q for AF

Optimal Q for DF

736

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