Combined Hybrid ARQ and Link Adaptation for

Coded Cooperation in Block-Fading ChannelsMihaly Varga, Mihai Alin Badiu, and Vasile Bota

Abstract—Cooperative hybrid ARQ (HARQ) protocols havebeen widely studied in recent years and they were shown toprovide higher efficiency than cooperative protocols. This paperproposes a joint design within which the HARQ protocol collab-orates with the link adaptation functionality and the cooperativetransmission scheme in order to adapt the behavior of the HARQprotocol to the QoS requirements of the supported services. Asperformance metrics of the HARQ protocol, we use the expectednumber of retransmissions and the expected spectral efficiency.The paper also studies the influence of the protocol parametersupon the performance provided.

Index Terms—Hybrid-ARQ, wireless cooperative communica-tions, link adaptation.

I. INTRODUCTION

FUTURE wireless networks need to accommodate the

rapidly growing traffic amount and to provide various

services with different QoS requirements. These systems

should be designed to fulfill the imposed throughput and delay

constraints in a spectrally efficient way.

In recent years the concept of cooperative communications

was introduced and gained a lot of attention from the research

community. It is already known that cooperative relaying

improve the link performance and reliability by exploiting

the spatial diversity provided by the collaborating node(s)

[1] [2]. Despite this, under certain poor channel conditions,

the cooperative transmission might not succeed delivering

correctly the transmitted block at first attempt.

Automatic Repeat reQuest (ARQ) is a feedback-based

reliable technique widely used in communication systems.

According to the ARQ protocol, which can run at various

layers of the OSI model, the same packet is retransmitted, if

requested by the receiver. The system performance is greatly

improved by a Hybrid ARQ (HARQ) scheme that combines

the ARQ protocol with Forward Error Correction (FEC).

In a system that employs HARQ, the requirement for low

delays, which are proportional to the number of retransmis-

sions performed to successfully provide the data block, and

the need for high spectral efficiency compete with each other.

The low number of retransmissions and the required outage

The authors are with the Communications Department , Technical Uni-versity of Cluj-Napoca, Cluj-Napoca, Romania, e-mail: {Mihaly.Varga, Mi-hai.Badiu, Vasile.Bota}@com.utcluj.ro.

M.Varga was supported by the project ”Develop and support multidis-ciplinary postdoctoral programs in primordial technical areas of nationalstrategy of the research - development - innovation” 4D-POSTDOC, contractno. POSDRU/89/1.5/S/52603, project co-funded from European Social Fundthrough Sectoral Operational Program Human Resources 2007-2013.

This work was supported partially by the European Union within the FP7-ICT-2007-215477 ”CODIV” project.

probability impose the usage of a powerful FEC code, which

involves high redundancy and therefore decreases the spectral

efficiency. On the other hand, a high spectral efficiency can be

obtained by using a low redundancy FEC, which translates into

more decoding errors and a high retransmission probability.

This paper proposes a cooperative HARQ protocol which

operates in conjunction with the link adaptation mechanism to

set, at each retransmission, the parameters of the cooperative

link (modulations on individual links, coding rate, redundancy

type etc.) so as to maximize the spectral efficiency and

to ensure predefined block error rate (BLER) values, after

the initial transmission and each of the subsequent HARQ

retransmissions. Usually, different values for the target out-

age probabilities and different maximum allowed end-to-end

delays are defined for different types of service. Allowing

higher target BLER values after each retransmission would

increase the spectral efficiency and therefore, this paper also

proposes a method to determine these BLER values, based on

the trade-off between spectral efficiency and delay. In order

to satisfy these conditions after each (re)transmission, the link

adaptation mechanism requires a way to estimate the BLER

performance of the composite cooperative link, based on the

instantaneous channel states and cooperative link configuration

parameters. Therefore we also propose a mutual information

(MI)-based link quality model to be employed by the link

adaptation functionality.

In current wireless systems which implement an HARQ

protocol at the physical layer, a straightforward possible

adaptation to the service’s QoS requirements (especially to the

reliability and delay requirements), consists in the employment

or not of the HARQ mechanism. This paper proposes a design

in which the HARQ protocol collaborates with the link adap-

tation functionality and the cooperative transmission scheme

in order to provide a framework for cross-layer optimizations,

which would maximize the spectral efficiency under BLER

and (average and/or maximum) number of retransmissions

constraints.

The rest of the paper is organized as follows: section II de-

scribes the system model and briefly presents the cooperative

relaying scheme; section III describes the proposed coopera-

tive HARQ algorithm and derives its spectral efficiency and the

average number of retransmissions; numerical results obtained

via simulations are presented in section IV and, finally, section

V gives some concluding remarks.

II. HARQ PROTOCOL DESCRIPTION

The proposed HARQ algorithm for relay-enhanced wire-

less communications is employed in a single-source single-

48 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 4, DECEMBER 2011

2

Fig. 1. Cooperative communication model

relay cooperation topology, on top of a Decode&Forward-type

cooperation algorithm, i.e. the Hybrid Distributed Forward

Error Correction (H-DFEC) algorithm. The cooperation is

accomplished by a two phase scheme, namely the broadcast

phase and the relaying phase, respectively (see Figure 1).

The H-DFEC is a cooperative coding algorithm that con-

structs the codeword in a distributed manner, by assembling it

at destination from two groups: one sent by the source during

the broadcast phase, and the second one sent by RN during

the relaying phase. In the broadcast phase the source encodes

I information bits using a convolutional turbo code (CTC) of

mother rate Rm. Out of these coded bits, the rate matching

(RM) algorithm used by the LTE system [3] selects, using

a circular buffer, the corresponding bits such that a desired

coding rate RBP is obtained. The LBP = I/RBP -bit long

codeword is then broadcasted by the source over the Source-

Destination (S −D) and Source-RN (S − RN ) channels. In

the relaying phase, the RN decodes the received block, checks

the integrity of the decoded data (e.g. via Cyclic Redundancy

Check), and then it re-encodes the data using the same CTC

of rate Rm, as the source. Then, it selects from the circular

buffer a number of LRP bits which are transmitted over the

RN-Destination channel. Note that the circular buffer, which

is identical to the one generated by the source, is read with a

given offset, [3]. The content of the additional set of bits sent

by the RN depends on the offset value, thus generating three

types of redundancy:

• a totally different new set of bits (Incremental Redun-

dancy),

• the same set of bits (Repetition Coding ),

• partial repetition, i.e., only some of the bits sent by the

source are repeated (Partial Repetition or Hybrid).

The destination node extracts the Log-Likelihood Ratios

(LLRs) from the signals received over the two channels, then

re-assemblies the circular buffer and, finally combines (adds)

the LLRs of the repeated bits. The LLR flow is then fed to

the turbo decoder, which performs the decoding and checks

the correctness of the decoded block by means of the attached

CRC.

The type-II HARQ algorithm used in this paper, [4] is

schematically shown in Figure 2. It involves an initial cooper-

ative transmission with the H-DFEC algorithm and a variable

number of retransmissions. If, after the initial transmission,

the CRC check at destination indicates a wrongly decoded

message, the destination issues a negative acknowledgment

(NACK-R), designated to the RN, which is received both by

Fig. 2. Functional diagram of the HARQ algorithm

S and RN. Consequently, the RN transmits LRi additional

bits, until the codeword is decoded correctly or the number

of retransmission attempts i reaches q, the maximum allowed

value. The destination combines the retransmitted bits with

the previously received ones, in the same way as in the

initial transmission. If this new aggregated block is decoded

correctly, the destination issues an ACK message, received

by both RN and S. If the decoding process fails after qretransmissions, the destination issues a NACK-A, indicating

that coded-block is lost, and that user is in outage.

If the RN fails to decode correctly the bits received during

the broadcast phase of the initial transmission, it transmits

an empty message to the source and destination. In this case

the source node becomes the HARQ retransmitting node,

generating an HARQ variant of the algorithm, which could

also be used in non-cooperative transmissions.

If the Link Adaptation algorithm decides to use a non-

cooperative scheme, due to a very good source-destination

link, the source acts as the retransmission node, as well.

Other system assumptions are given in the following:

• The HARQ feedback messages, ACK and NACK, have

negligible error-probabilities, due to their small lengths,

and therefore they are assumed to be transmitted over

error-free channels.

• Dedicated fixed relays are used; this ensures a negligible

block error probability of the S-RN links compared with

the error probabilities of other links, due to an appropriate

assignment of the RN, [4] which leads to better S-RN

than S-D channels, and knowing that the modulation and

coding used in the broadcast phase is selected in terms

of S-D channel as well.

• The QAM symbols are transmitted using an OFDMA

scheme, within Radio Resource Units (RRU), i.e. re-

source blocks of fixed frequency-time dimensions.

• Considering mobile destinations, the S-D and RN-D

transmissions are affected by block fading; the fading

coefficients are constant for one radio resource unit,

but are assumed to change from one retransmission to

VARGA et al.: COMBINED HYBRID ARQ AND LINK ADAPTATION FOR CODED COOPERATION IN BLOCK-FADING CHANNELS 49

Fig. 3. Equivalent transmission model for the C-HARQ protocol

another, as commonly considered in literature.

• The destination node has perfect channel state informa-

tion.

We assume that the fading coefficients are uncorrelated

from one retransmission to another, due to the time interval

between two attempts, which is a multiple (at least two)

of the frame period. Then, the initial transmission and the

variable number of retransmissions of the cooperative HARQ

protocol can be modeled, as depicted in Figure 3, by a system

with multiple relays, where the S-RN link has the same

instantaneous channel condition. Denoting by xiα−β the signal

transmitted by node α ∈ {S,RN} to node β ∈ {RN,D}during the i = 0, ..., q-th retransmission (i = 0 denotes the

initial transmission) then the signal yiβ received by the node

β ∈ {RN,D}, during the i-th retransmission should be written

as:

yiβ = hiα−β · √γα−β · xiα−β + niβ (1)

where hiα−β denotes the channel coefficients between nodes

α and β on the i-th retransmission, γα−β is the average signal

to noise ratio of the link α−β and niβ is the complex additive

white Gaussian noise (AWGN) at node β. It is assumed

that coefficients hiα−β are independent identically distributed

(i.i.d.) circularly symmetric complex Gaussian variables with

unity power and distribution CN (0, 1).

III. THE COOPERATIVE HARQ ALGORITHM -

DESCRIPTION AND ANALYSIS

The proposed cooperative HARQ algorithm is designed in

such a way that, after retransmission i, the decoding error

probability, expressed in terms of Block Error Rate (BLER),

is at most pie, with i = 1, . . . , q. This is ensured by the

link adaptation mechanism which, based on the instantaneous

channel conditions on the component links, defines the lengths

of the different messages (LBP , LRP , LRi), their corre-

sponding coding rates, and the QAM modulation orders of

the RRUs occupied during the two cooperation phases and

retransmissions. The link adaptation algorithm also ensures a

BLER of the initial transmission no greater than p0e. Since the

pie target values highly influence the spectral efficiency and

the transmission delay, this paper proposes a methodology to

determine these target values in order to ensure a trade-off

between the performance metrics of the HARQ transmission.

Moreover, to satisfy the BLER conditions, the algorithm

needs to estimate the decoding performance provided by the

multiple-link configurations which are possible (i.e. S-D, S-

RN, RN-D links and their modulation orders and coding rates),

and to select the most appropriate one. For this, the algorithm

employs a BLER performance prediction method based on

mutual information.

The purpose of BLER prediction is to estimate the instan-

taneous performance of a (cooperative or direct) link, based

on current channel conditions and transmission parameters.

There are several approaches in literature, among which the

solution based on mutual information proposed in [5] is the

most appropriate for our scenario. It was shown there that the

BLER performance of CTC codes over fading channels can be

estimated, with an arbitrary good precision, by using the Mean

Mutual Information per coded Bit (MI) as quality metric to

read look-up tables that contain the AWGN performance:

BLERFading ({CSI}) ≈ ψ(MI,Rc, I

)(2)

where ψ (·) is the mapping function that depends on the code

rate Rc and number I of information bits. The MIi

α−β value

is defined as:

MIi

α−β =

N∑n=1

m(n)∑p=1

Im(n),p

(ρiα−β

)

N∑n=1

m (n)

(3)

where: N is the length of message xiα−β expressed in number

of QAM symbols, m (n) is the modulation order of the

nth QAM symbol Im(n),p

(ρiα−β

)is the mutual information

between the input bit of the 2m-QAM mapper and the output

LLR of the pth position in the QAM symbol, ρiα−β is the

instantaneous SNR of the component link α− β experienced

by the ith retransmission,i = 0, ..., q, and is given by:

ρiα−β =∣∣hiα−β

∣∣2 · γα−β (4)

Assuming that the message xiα−β is transmitted using the

same modulation order miα−β on each occupied QAM symbol,

the expression (3) can be rewritten as (5), where Im (·) maps

the SNR to the mutual information domain and, for each

modulation order, can be approximated by analytical functions

[5]:

MIi

α−β = Imiα−β

(ρiα−β

)(5)

After the initial transmission, the ”accumulated” mutual

information can be calculated by using (6):

MI0 (ρ0S−D; ρ0RN−D

)=MI

0

S−D · (LBP − Lrep)

LBP + LRP − Lrep+

+MI

0

RN−D · (LRP − Lrep)

LBP + LRP − Lrep+

+Lrep · I1

(I−11

(MI

0

S−D

)+ I−1

1

(MI

0

RN−D

))

LBP + LRP − Lrep

(6)

50 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 4, DECEMBER 2011

where Lrep is the number of codeword bits repeated in both

cooperation phases of initial transmission.

For a hybrid distributed FEC algorithm, the bits sent by the

RN are of two types:

• a set of bits that are different from the ones transmitted

by S; these provide additional redundancy for the CTC,

and their MI is averaged with the one of the bits sent

by S;

• a set of bits that have already been transmitted by S;

these repeated bits improve their own reliability and the

method to compute their MI given in [6] is considered.

The accumulated MI after the ith retransmission, i =1, ..., q, can be computed recursively, for the combination

techniques used for the two cases mentioned above, by (7),

where Li−1 denotes the length of the codeword at the (i−1)thattempt and LRi denotes the number additional bits carried by

the ith retransmission.

MIi(ρiRN−D;MI

i−1)=MI

i−1 · (Li−1 − Lrep)

Li−1 + LRi − Lrep+

+MI

i

RN−D · (LRi − Lrep)

Li−1 + LRi − Lrep

+Lrep · I1

(I−11

(MI

i−1)+ I−1

1

(MI

i

RN−D

))

Li−1 + LRi − Lrep

(7)

The number of elementary Radio Resource Units (RRU)

occupied by each transmission depends on the codeword

length after the ith attempt, on the modulation orders used

on component links, and on the number of QAM symbols

of the RRU. For a finer granularity of the results, this paper

assumes that the elementary RRU consists of one subcarrier

during one OFDM symbol period, i.e. one QAM symbol. The

employment of a larger elementary RRU would lead to a

coarser granularity, whose effects upon the performance will

be discussed later in the paper. The NRi, representing the

number of RRUs occupied by the current codeword after iretransmissions is:

NR,i =

(LBP

m0S−D

+LRP

m0RN−D

)+

i∑

k=1

LRi

miRN−D

(8)

For the ith transmission, the joint link adaptation and re-

source allocation function selects adaptively, according to (9),

the appropriate coding rate Rci, redundancy type, modulation

orders, and cooperative/non-cooperative transmission, so that

the BLER of the current codeword is smaller or equal to pie,

while minimizing the number of resources required.

NR,0 = Υ0(ρ0S−D, ρ

0RN−D

)=

= minRc0∈(0,1]

m0S−D∈M

m0RN−D∈M

(RRU0

∣∣∣ψ(MI

0, Rc0, I

)= p0e

)

NR,i = Υi(ρ0S−D, ρ

0RN−D, ..., ρ

iRN−D

)=

= minRci∈(0,Rci−1]

m0S−D∈M

m0RN−D∈M

(LRi

miRN−D

∣∣∣ψ(MI

i, Rci, I

)= pie

)(9)

where RRU0 is the number of radio resources used during

the first transmission, and can be expressed as:

RRU0 =LBP

m0S−D

+LRP

m0RN−D

(10)

This choice is based on the previous selections (i.e. Rcj ,

mjα−β ; j = 1, ..., i− 1) and the instantaneous channel condi-

tions, ρjα−β ; j = 1..i, experienced on the component links of

the equivalent model.

The spectral efficiency of a transmission using the HARQ

algorithm is given by:

η =E [I]

E [NR]· NRRU

TRRU ·BWRRU= ηe ·

NRRU

TRRU · BWRRU(11)

where E [I] denotes the expected number of correctly decoded

info bits and E [NR] is the expected number of QAM sym-

bols used to transmit a single coded block, be it positively

acknowledged or lost. TRRU represents the duration in time,

BWRRU the frequency bandwidth, and NRRU the number of

payload QAM symbols of an RRU. Because NRRU , TRRU

and BWRRU are constants of particular systems, it is more

convenient to use an equivalent spectral efficiency ηe , which

expresses as the average number of correctly decoded infor-

mation bits on a QAM symbol. Denoting by pq0 the outage

probability of the HARQ protocol, ηe can be expressed as, [7]

[8]:

ηe =E [I]

E [NR]=I (1− pqo)

E [NR](12)

The expected number of RRUs required transmitting a

coded-block with I information bits can be computed as:

E [NR] = Θ(ξ0, ..., ξq, p

0e, ..., p

qe

)=

= ξ0(1− p0e

)+

q−1∑j=1

[ξj(1− pje

) j−1∏z=0

(pze)

]+ ξq

q−1∏j=0

(pje)

(13)

where ξi; i = 1, ..., q is the average number of resource unit

used for the ith transmission, and is expressed by:

ξi =∫

ρ0S−D

∫ρ0RN−D

· · ·∫

hqRN−D

Υi(ρ0S−D, ρ

0RN−D, ..., ρ

iRN−D

)·

·P(ρ0S−D

)·

i∏j=0

P(ρjRN−D

)δρiRN−D...δρ

0RN−Dδρ

0S−D

(14)

In (14), P(ρiα−β

)is the probability that, during the ith

attempt, the instantaneous signal to noise ratio of channel

α−β is ρiα−β . Taking into account that the fading coefficients

hiα−β are i.i.d. random variables and γα−β is constant during

the HARQ process, we get that ρiα−β is an i.i.d. exponential

variable, i.e., an i.i.d. chi-square variable with two degrees

of freedom; therefore, the probability P(ρiα−β

)can be ex-

pressed as , [9]:

(ρiα−β

)= P

(∣∣hiα−β

∣∣2 =ρiα−β

γα−β

)=

1

2e−

ρiα−β

2·γα−β (15)

If the elementary RRU equals one QAM symbol, the

average number of QAM symbols required to transmit Iinformation bits is expressed by (13). This value mainly

VARGA et al.: COMBINED HYBRID ARQ AND LINK ADAPTATION FOR CODED COOPERATION IN BLOCK-FADING CHANNELS 51

depends on the intermediate block-error probabilities, pie, the

error-probability of the first transmission, p0e and the instan-

taneous qualities of the component links, ρα−β . Due to the

recursion of (7) and (9), the block-error probability of the first

transmission, p0e, affects the message-lengths of all subsequent

retransmissions; therefore, this parameter is the most important

for the performance of the HARQ algorithm.

The spectral efficiency of the transmission without the

HARQ protocol should be obtained by setting q = 0 in (12).

The outage probability pqo of the HARQ protocol, i.e. the

error probability after q retransmissions is given by (16).

pqo =

q∏

i=0

pie (16)

This expression of pqo is derived in the assumption that the

ACK and NACK messages have negligible error probabilities.

The erred ACK/NACK messages might, in the worst case,

generate the loss of that coded block, and therefore the impact

of such erred messages would be the increase of pqo with

the error probabilities of these messages. But, since these

probabilities are assumed to be much smaller than pqo, their

influence is neglected in the section presenting the numerical

results.

IV. NUMERICAL RESULTS

Based on the mathematical model previously derived, this

section evaluates numerically the average number of attempts

(initial transmission plus retransmissions) performed to ac-

knowledge a coded block, with an outage probability pqo,

and the equivalent spectral efficiency ηe of the proposed

cooperative-HARQ algorithm.

First, we propose a method to choose the set of pie block-

error probabilities after each retransmission i. A convenient

way to set the values of pie is to define them as the terms of

a geometrical progression of ratio u ∈ (0; 1) and initial term

p0e:

pie = u · pi−1e = ui · p0e (17)

Replacing (17) in (16), we get the relation that connects the

value of u to the outage probability pqo for a given number of

retransmissions q and the value of the block error probability

of the initial transmission p0e:

pqo = uq(q+1)

2 ·(p0e)q+1

(18)

The smallest value of p0e, which corresponds to the imposed

pair pqo and q can be computed using (18) and the fact that

u ∈ (0, 1). In that case the probability Pci of a correctly

decoded block after the ith retransmission will be:

Pci =(1− pie

) i−1∏

j=0

pje (19)

Based on (19), the average number of attempts performed

to transmit a single block can be expressed as:

Tav

(p0e, p

qo, q)= (i+ 1) · pqo +

q∑

i=0

(i+ 1) · Pci (20)

10-2

10-1

100

1

1.5

2

2.5

3

3.5

pe

0

Ta

v(pe0 ,1

0-2,q

)

q=1

q=2

q=3

q=4

q=5

Fig. 4. Average number of retransmissions vs. block error probability of theinitial transmission.

Fig. 5. Variation of equivalent spectral efficiency with the component channelqualities

Figure 4 presents the variation of Tav with the error proba-

bility of the initial transmission p0e, for different values of the

maximum number of retransmissions allowed, q. As expected,

the average number of attempts grows with the value of p0e for

any given value of q. The variation of q leads to significant

variation of Tav only for high values of p0e, while for low

values of p0e the influence of q is negligible.

Figure 5 illustrates the variation of the equivalent spectral

efficiency with the long-term average SNRs of the S-D and R-

D links, for a transmission with HARQ and for one without

HARQ, used as reference, both having the same imposed

outage probability. The HARQ algorithm used was the co-

operative HARQ, if the link adaptation block chose to use

a cooperative transmission, or a classical HARQ for a non-

cooperative transmission. The modulations used were QPSK,

16 and 64-QAM and the rate of the mother CTC equaled

Rm = 1/3.

Results of Figure 5 show that the use of the HARQ brings

a significant increase of the spectral efficiency. It is greater

for good S-D channels, where cooperation is less likely to be

used, but even for poor S-D channels, where cooperation is

used, the increase in spectral efficiency is notable, especially

for good RN-D channels.

To evaluate the effects of the error probability of the initial

transmission p0e and of the ratio u (17), we used the average

equivalent spectral efficiency ηe as performance metric. Figure

6 presents the variation of this metric vs. the p0e, for different

values of u, when q = 3 and pqo = 10−2. The results show

that, for u smaller than 0.75 but greater than the minimum

value provided by (18) for the given set of p0e and pqo, the

52 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 4, DECEMBER 2011

10-1

2.6

2.8

3

3.2

3.4

log10

(pe

0)

Ke

u=0.9

u=0.75

u=0.5

u=0.25

u=0.1

Fig. 6. Variation of the average spectral efficiency vs. p0e

spectral efficiency provided has small variations with p0e and

that the best performance are obtained for u = 0.5.

When the elementary radio resource unit is composed by

an integer number (greater than one) of QAM symbols, the

equation (17) becomes an inequality given by(17). This is due

to the fact that the length of the messages must be chosen

so that the message fits on an integer number of RRUs. The

link adaptation algorithm computes the minimum length of

the message required to ensure the target pie on the given

channel conditions, and rounds up this computed value to the

closest greater multiple of the elementary RRU. This fact leads

to the transmission, in most cases, of a greater redundancy

that the minimum one required to ensure the target pie, and

therefore the algorithm ensures smaller BLER values that those

imposed, which were used in the theoretical analysis.

The probabilities of the HARQ (with q = 3) to use a

given number of attempts for the acknowledgment of one

coded-block are represented in Figures 7 and 8 for two

values of p0e. The figures present the probabilities obtained

by computer simulations, using the LTE system’s parameters,

referred to the theoretically-computed probabilities (in blue

bars). The differences between the theoretically-computed and

the simulation-resulted probabilities are greater for greater

values of p0e, because in these cases a small amount of

additional redundancy, inserted to fill the ”last” allocated RRU,

leads to a more significant decrease of the BLER actually

provided, which, in turn leads to smaller probabilities of

consequent retransmissions.

pie ≤ ui ·(p0e)q+1

(21)

Figure 9 compares, for the same outage probability, the

efficiency of the HARQ algorithm to the efficiency ensured

by the first transmission.

The improvements brought by HARQ are greater for high

values of p0e, but even for smaller values of p0e, the im-

provement is still worth considering. Depending on the QoS

requirements imposed by higher layers, p0e and u should be set

to provide the highest spectral efficiency, while observing the

delay constraints of the service. Two of most common QoS

requirements are the average delay, which is proportional to

the average number of retransmissions, Tav, and the probabil-

ity of lost a block (which equals pqo), both of them depending

on p0e, u and on q.

0 0.6ep

1 2 3 40

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

0.4

0.831

9.086e-50.0180

0.0020.1411

0.16650.44

Simulated

values

Transmission attempts

Theoretical

values

Fig. 7. Acknowledgment probabilities for each attempt; p0e = 0.6

Simulated

values

Transmission attempts

0 0.3ep

Theoretical

values

1 2 3 40

0.2

0.4

0.6

0.8

1

Pro

ba

bili

ty

0.2365

0.97

0.7

0.0297

0.00851.49e-5

2.37e-40.054

Fig. 8. Acknowledgment probabilities for each attempt; p0e = 0.3

10 -1

10 0

0.5

1

1.5

2

2.5

3

3.5

log 10 (p

e 0 )

K e

u=0.9

u=0.75

u=0.5

u=0.25

u=0.1

With CHARQ

First Transmission

Fig. 9. Variation of the average spectral efficiency vs. p0e ,w/wo HARQ

The methodology derived in this paper can be used to set

these parameters for each type of service, in a cross-layer

design.

V. CONCLUSION

This paper proposed a combination of the HARQ algorithm,

in cooperative and non-cooperative variants, with the link

adaptation mechanism in a cooperative relaying scenario,

which provides means for cross-layer optimizations, by setting

the HARQ parameters, in order to provide the greatest spectral

efficiency while fulfilling the QoS requirements (BLER and

average delay) of the supported services.

VARGA et al.: COMBINED HYBRID ARQ AND LINK ADAPTATION FOR CODED COOPERATION IN BLOCK-FADING CHANNELS 53

It also proposed a cooperative HARQ algorithm whose

performance were evaluated theoretically and by simulations,

using as metrics the average number of retransmissions re-

quired to ensure an imposed outage probability, and the

spectral efficiency provided.

The paper analyzed the influence of the HARQ parameters

upon the spectral efficiency provided and upon the delay in-

serted, and presented a method to establish the domains within

which the parameter’s values do not decrease significantly the

spectral efficiency performance.

The results presented above and those presented in [10]

show that the trade-off between the spectral efficiency and

number of retransmissions, which generate the delay inserted,

can be obtained via a proper choice of the intermediate outage

probabilities.

REFERENCES

[1] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversityin wireless networks: efficient protocols and outage behavior,” IEEE

Trans. Inf. Theory, vol. 50, pp. 3062–3080, 2004.[2] T. E. Hunter and A. Nosratinia, “Cooperative diversity through coding,”

IEEE Trans. Inf. Theory, 2002.[3] Evolved Universal Terrestrial Radio Access (E-UTRA);Multiplexing and

channel coding, 3GPP Standardization Group Std. 3GPP TS 36.212V9.2.0, June 2010.

[4] R. S. Robles, A. Gameiro, E. C. Strinati, D. Ktnas, P. Greco,S. Mayrargue, M. Varga, M. A. Badiu, V. Bota, A. Vlaicu, andC. M. Bota, “Final algorithm evaluation and architecture specifications,”CODIV FP7-ICT-2007-215477, Deliverable, November 2010. [Online].Available: http://www.ict-codiv.eu/private/docs/deliverables/D4.4.pdf

[5] K. Sayana, J. Zhuang, and K. Stewart, “Short term link performancemodeling for ml receivers with mutual information per bit metrics,” inGlobal Telecommunications Conference, 2008, pp. 4313–4318.

[6] M. A. Badiu, V. Mihaly, and B. Vasile, “Link performance predictionmethods for cooperative relaying in wireless networks,” in Wireless

Communication Systems (ISWCS), 2010 7th International Symposium

on, sept. 2010, pp. 556 –560.[7] I. Byun and K. S. Kim, “Cooperative hybrid arq protocols: Unified

frameworks for protocol analysis,” Computing Research Repository, vol.abs/0812.2, 2008.

[8] R. Hoshyar and R. Tafazolli, “Performance evaluation of harq schemesfor cooperative regenerative relaying,” in Communications, 2009. ICC

’09. IEEE International Conference on, june 2009, pp. 1 –6.

[9] I. Stanojev, O. Simeone, and Y. Bar-Ness, “Performance analysis ofcollaborative hybrid-arq protocols over fading channels,” in Sarnoff

Symposium, 2006 IEEE, march 2006, pp. 1 –4.

[10] T. T. Le, S. Mumtaz, A. Silva, N. Chiurtu, D. Castelain,C. Ciochin, V. Bota, M. Varga, C. M. Bota, and M. A. Badiu,“Final system level evaluation results,” CODIV FP7-ICT-2007-215477,Deliverable, November 2010. [Online]. Available: http://www.ict-codiv.eu/private/docs/deliverables/D5.5.pdf

Mihaly Varga received the Dipl. Eng. degree, M.Sc. and Ph.D. degreesin Telecommunications Engineering from the Technical University of ClujNapoca in 2001, 2002 and 2007, respectively. Currently, he is a SeniorLecturer and post-doctoral researcher at the Communication Department ofthe mentioned university. His research interests involve error correcting codes,cooperative communications, wireless networks.

Mihai Alin Badiu received the B.S. degree in electronics and telecommuni-cations engineering from Technical University of Cluj-Napoca, Romania, in2008, and the M.Sc. degree from the same University, in 2010. He is currentlya Ph.D. student at the Technical University of Cluj-Napoca. Between 2008and 2010, he was a Research Assistant at the Communications Departmentof the same University. His current research focuses primarily on cooperativecommunications and advanced signal processing for wireless communications.

Vasile Bota received the M. Sc. and the Ph.D. degrees in Telecommunications,from the ”Politehnica” University of Bucharest, and from the TechnicalUniversity of Cluj-Napoca, respectively. Dr. Bota is currently Professor withthe Communications Department from the Technical University of Cluj-Napoca. His main research interests include coded modulations, cooperativetransmissions, radio resource management and their applications in wirelessand wired communications systems. He has activated in FP7 projects andpublished in international and national journals and conference proceedings.