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Outage Probability of Hybrid

Decode-Amplify-Forward Relaying Protocol for

Buffer-Aided Relays

Hina Nasir1,2, Nadeem Javaid3, Waseem Raza4, Muhammad Imran5, Nidal Naseer6

1International Islamic University, Islamabad 44000, Pakistan

2Air University, Islamabad 44000, Pakistan

3COMSATS University Islamabad, Islamabad 44000, Pakistan

4The University of Lahore, Lahore 54000, Pakistan

5College of Applied Computer Science, King Saud University, Saudi Arabia

6College of Engineering, Alfaisal University, Saudi Arabia

Abstract—Buffer-aided cooperative relaying is often investi-

gated either using decode and forward (DF) or amplify and

forward (AF) relaying rules. However, it is seldom investigated

using the hybrid decode-amplify-forward (HDAF) relaying rule.

In this work, the performance of signal-to-noise ratio (SNR)

based HDAF relaying rule is followed for buffer-aided cooperative

relaying. Relay with the best possible corresponding channel is

determined for reception or transmission. When source to relay

hop is the most powerful, data is forwarded to chosen relay and

its SNR is compared against the predeﬁned SNR threshold at

the relay. If it is greater than the threshold, the decoded data is

saved in the corresponding buffer. Otherwise, the ampliﬁed data

is saved in the respective buffer. When relay to destination link

is the most powerful, data is forwarded to the destination. The

famous Markov chain analytical model is used to illustrate the

progression of the buffer state and to get the outage probability

expression. Mathematical and simulation outcomes support our

ﬁndings and prove that the outage probability performance of

the proposed technique beats the existing SNR based buffer-aided

relaying protocols based on DF and AF relaying rules by 2.43

dBs and 8.6 dBs, respectively.

Index Terms—cooperative relaying, buffer-aided, relay selec-

tion, hybrid decode-amplify-forward.

I. INTRODUCTION

Cooperative relaying (CR) allows the source’s data to be

transmitted to the target with the cooperation of intermediate

relays. It has wide applicability in ad-hoc and sensor networks

and their services. The regular CR system picks one relay

to send the source signal to the target in the consecutive

time-slots [1]. This relaying model offers many advantages

in terms of throughput, capacity, coverage, etc. when matched

to the non-cooperative relaying model, however, it has some

weaknesses. The choice of a single relay is a bottleneck

because the excellent source-to-relay (S−R) hop may not

guarantee the excellent relay-to-destination (R−D) hop.

Besides, the set transmission schedule, i.e., the alternate order

of transmission of source and relay, limits the diversity gain

of the system.

The obstacles as stated earlier are eased by the introduction

of data buffers at the relays [2]. The buffers grant freedom

to pick separate relays for receiving and transmitting data

by storing the received data at the relay and transmitting

it whenever the R−Dchannel is favorable. They offer

advantages like increased diversity gain, increased goodput,

increased capacity, etc., as compared to the traditional CR

system. For a buffer-aided CR system, the dominant link on the

grounds of link state is picked for data transmission. When the

dominant link is from S−Rchannels, data is delivered to the

picked relay and saved in the corresponding buffer. Besides,

when the dominant link is from R−Dside, the corresponding

buffer sends data to the destination.

To design a relaying scheme for a buffer-aided system, the

designers keep the following main challenges in mind. First

is the acquisition of channel state information (CSI). Since

the best link in terms of link quality is to be decided in

each time-slot, the CSI needs to be known. Secondly, buffer

status monitoring is needed as the full buffers are incapable of

receiving data and empty buffers are incapable of transferring

data. Therefore, it is essential to keep track of full and empty

buffers to know the link availability. Furthermore, the delay

introduced by incorporation of buffers is a challenging task

because data has to wait inside the buffers un till the respective

R−Dchannel is selected.

The buffer-aided CR schemes can are usually classiﬁed

into ﬁxed and non-ﬁxed transmission models. In a ﬁxed

transmission model, the dominant S−Rlink is picked for

communication in the odd time-slot and the received data from

the source is saved in the particular relay buffer. For the next

time-slot, the dominant R−Dlink is picked for communi-

cation and the corresponding relay sends to the destination

from its buffer [3]. In comparison, in a non-ﬁxed transmission

model, any link can be dominant for data transmission in a

given time-slot [4]. The maximum obtainable diversity gains

in ﬁxed and non-ﬁxed transmission models are Kand 2K,

respectively, where Kis the count of relays.

The famous works in the existing literature addressing the

aforementioned challenges in buffer-aided CR are max-max

[3] and max-link [4] relay selection schemes. These schemes

978-1-5386-8088-9/19/$31.00 ©2019 IEEE

obey ﬁxed and non-ﬁxed transmission models, respectively.

Link state is the only metric in the choice of the most

suitable relay and are based on decode and forward (DF)

relaying. Most of the literature on buffer-aided CR is based

on max-max and max-link relay selection schemes following

DF relaying strategy. In [5], the authors added a direct link

between source and destination in the system model of the

max-link scheme and obtained satisfying diversity gain and

delay performance. The authors in [6] proposed the hybrid of

schemes proposed in [3] and [4] and achieved full diversity

gain of 2Kusing ﬁxed transmission regulation. Another effort

on relay selection based on link quality only is made in [7].

The authors prioritized R−Dover S−Rto reduce queuing

delay and achieved the ideal delay of two time-slots.

The relay choice based only on the link state signiﬁcantly

reduced the outage probability of the system, however, the

outage probability can be more improved if buffer status is

taken into consideration. Full buffers are incapable to receive

data and empty buffers are incapable to transmit data. Thus,

the count of links is decreased. The reduction in the number of

links reduces the diversity gain of the system. The authors in

[8] recommended the buffer status based relay determination

scheme based on the non-ﬁxed transmission model. They

assigned weight to each link based on the available and

occupied buffer space of the corresponding buffer. The link

with the greatest weight is picked for data transmission. The

max-weight scheme achieved reduced outage probability in

comparison to the max-link scheme, however, in case of links

with same weights, random selection is made which may not

guarantee the best link selection. Based on this, the authors in

[9] proposed link priority and link quality as a second selection

metric in relay selection. Another effort on buffer status based

relay selection is made in [10]. In this scheme, the authors

avoid full and empty buffers by taking link quality and buffer

status in relay selection. They also achieved reduced queuing

delay by prioritizing R−Dlink. The same as the previous

attempt, a buffer situation based relay determination scheme

following ﬁxed transmission is given in [11]. The authors made

relay selection on the basis on smallest in shortest out buffer

status and attained diversity gain equal to the number of relays

at a tiny buffer size. The authors in [12] exploit the broadcast

nature of the wireless network and activate multiple S−Rlinks

to reduce delay. Although the delay is reduced to a signiﬁcant

amount in these schemes, however, they compromise on the

diversity gain. There is a diversity-delay trade-off in buffer-

aided cooperative communication. Delay negotiates for the

diversity gain. A low complexity based relay determination

scheme is proposed in [13] to reduce delay by giving priority

to the R−Dlink while preserving the diversity gain. The

authors imposed a threshold for the number of packets in

a buffer. For the minimum of one S−Rtransmission, the

R−Dlink is given priority if the buffer occupancy meets the

threshold.

The authors in [14] explored that many of the present works

in buffer-aided relay determination is based on DF relaying.

They proposed amplify and forward (AF) relaying based max-

link scheme and achieved enhanced diversity and coding gain.

This scheme is enhanced in [15] using buffer status based relay

determination to enhance the outage probability performance

of the system.

Form the literature as mentioned earlier, it is evident that

most of the work in buffer-aided CR either focuses on DF

relaying or on AF relaying. In DF relaying, the transmission

or reception at relay only happens if the signal is decode-

able at the receiving end. The signal is decode-able only if

its quality is greater than the predeﬁned metric such as a

speciﬁc signal to noise ratio (SNR) threshold. If the signal

is corrupted, relays remain silent for both reception and trans-

mission. In HDAF, instead of remaining silent on corrupted

signal quality, relay adaptively switches between the AF or DF

mode to improve the system performance. The HDAF relaying

is mostly explored for buffer-less cooperative relaying. In

[16], the authors presented the SNR based incremental HDAF

cooperative relaying protocol for three node network. The

relays prefer to remain quiet or transmit either in AF or DF

mode, depending on the signal condition. The authors in [17],

[18] examined the performance gain of HDAF protocol over

AF and DF protocols for multiple relays cooperative network.

An HDAF model with the nth best-relay determination scheme

is presented in [19]. In this scheme, the best relay sends to

the destination indiscriminately. However, when the best relay

is not available, the nth best relay is considered.

To the best of the author’s awareness, the buffer-aided

HDAF is still primarily to explore. In [20], the authors

explored HDAF on buffer-aided incremental cooperative re-

laying. The authors used link state as the single metric in relay

determination. This scheme is based on the ﬁxed transmission

model with the consideration of the direct link connecting

source and target in the system model. The authors obtained

the expression for the outage probability for ﬁnite and inﬁnite

length buffers. The scheme achieved the diversity gain equal

to Kand delay of 1+KL/2time-slots, where, Lis the buffer

size.

In this work, we propose a buffer-aided SNR based HDAF

scheme based on non-ﬁxed transmission regulation. The

scheme selects the dominant link on the grounds of link qual-

ity. The link with the highest SNR is selected for transmission

or reception. If the S−Rlink is dominant, data is forwarded

from source to the corresponding relay and compared against

the SNR threshold. If it is higher than the threshold, data is

decoded and saved in the buffer. In contrast, if it is less than

or equal to the threshold, data is ampliﬁed and saved in the

buffer. When the corresponding R−Dlink is dominant, the

decoded or ampliﬁed data saved in the buffer is transmitted

to the destination. We obtain the theoretical equation for the

outage probability by analyzing the inﬁnite and ﬁnite buffers

at the relays. Markov chain based analytical model is used

to model the development of the buffer state and to calculate

the outage probability. The analytical outcomes are conﬁrmed

using thorough Monte Carlo simulations.

Paper organization is as follows. In Section II, we give the

system model, relay selection and outage probability inves-

tigation of the proposed work. In Section III, the numerical

results of the proposed scheme are given. Conclusive remarks

are presented in Section IV.

TABLE I: Numerical notations

Symbol Description

R Set of Relays

S Source

D Destination

S−RSource-to-relay channel

R−DRelay to destination channel

K Number of relays

L Buffer size

ψ(LRk)Number of packets in buffer

γSR SNR of S−Rchannel

γRD SNR of R−Dchannel

Z HDAF threshold at relay

γth Threshold at destination

roinformation rate

Csr Number of open S−Rlinks

Crd Number of open R−Dlinks

II. SY ST EM MO DE L

. . .

R1

R2

S D

RK

LR1

LR2

LRK

L

L

L

Fig. 1: System model for the buffer-aided HDAF scheme

The system design under study is a dual-hop cooperative

relaying network of source S, destination Dand a set Rof

Knumber of relays indicated by R={R1, R2,· · · , RK}as

shown in Fig. 1. The detailed numerical notation is given in

Table I. The direct communication link between Sand Dis

not possible as it is in deep fade and as considered in many of

the existing works [3], [4], [8], [8]–[11], [14]. All nodes are

provided with a separate antenna device and do not support

simultaneous reception and transmission, i.e., they work in

half-duplex mode. Relays are provided with both AF or DF

hardware. Depending upon the channel state, they either work

as AF relay or DF relay. Every relay has a ﬁxed sized data

buffer of maximum Lpackets space to save the received data.

Buffers support ﬁrst in ﬁrst out policy to process data. The

count of elements in a buffer LRk is denoted by ψ(LRk)where

0≤ψ(LRk)≤L. Only a neither empty nor full buffer can

accept and transmit data. When a packet goes into the buffer,

buffer ψ(LRk)gets a unit increment, likewise, when a packet

departs from the buffer, ψ(LRk )gets a unit decrement. An

S−Rlink is supposed to be ’open’ if its respective buffer is

not full and R−Dlink is supposed to be open if its respective

buffer is not empty. The open link means it is available and

open for selection.

Let the channel coefﬁcients between S−R(R−D) hop is

indicated by hSR (hRD ). It is believed that all channels support

independent and identically distributed (i.i.d) Rayleigh fading

where the envelop fading signal for a particular hop is ﬁxed

for a certain time-slot and differs individually from one time-

slot to another. The instantaneous SNRs of S−R(R−D)

hop is given as γSR =Ps|hSR |2/No(γRD =Pr|hRD|2/No).

Where, Ps(Pr) is the transmission power of the source

(relay) node and Nois noise variance of additive white

Gaussian noise with unit mean assumed for the channels.

Transmission rate is assumed to be robits/s/Hz. The average

SNRs of S−R(R−D) hop is ¯γSR =PsE(|hSR|2)/No

(¯γRD =PrE(|hRD|2)/No), where, E(.)is the statistical

average operator. In case of Rayleigh distribution, for any γ,

the probability distribution function (PDF) is expressed as:

fγi(γ) = 1

¯γi

e−γ/¯γi,(1)

and cumulative distribution function (CDF) is depicted as

Fγi(γ) = P r(γi≤γ)=(−e−γ/¯γi+ 1) .(2)

According to the proposed transmission scheme, the dis-

tributed method adopted in [21] is adopted to exchange SNR

information among the relays. The relays are able to decide

whether itself is best for reception or transmission of data.

The data transfer is from Sto Dthrough an intermediary

node called relay. Since each relay has a data storing facility,

we can pick the most dominant link for data transmission

among all open links. The dominant link is the strongest link

among all open links in terms of link quality. When the S−R

link is dominant, data is forwarded from Sto the correspond-

ing R. Upon reception at the relay, the experienced SNR is

matched against the predeﬁned SNR threshold indicated by Z,

where, Z= 2ro−1. If received SNR is higher then Z, it means

that the signal is surely decode-able at the relay. Therefore, the

DF relaying method is adopted and the decoded data is saved

in the buffer. In contrast, if the received SNR is less than

Z, it speciﬁes that data cannot be decode-able and hence, it

is ampliﬁed using the AF relaying method and saved in the

buffer without decoding. The obtained signal at the relay is

analytically represented as:

ySRk=pPsxshSRk+nSRk,(3)

where, xsis the signal transmitted from source, ySRkis the

signal received at relay Rk,nSRkis the channel noise.

Moreover, when the dominant link is from R−Dside, the

buffer transmits from the connected relay to D. Analytically,

the received signal in DF mode is expressed as:

yRkD=pPrxrhRkD+nRkD,(4)

where, yRkDis the received signal at D,xris the decoded,

corrected and transmitted signal from relay and nRkDis the

channel noise. For a relay to work in AF mode, the signal

received at Dis given as:

yRkD=GhRkDySRk+nRkD,(5)

where, Gis the gain factor deﬁned as:

G=sPr

Ps|hSRk|2+No

.(6)

A. Relay Selection

According to the proposed buffer-aided HDAF protocol, in

a given time-slot, the dominant link is picked from all open

links on either sides. The relay selection is analytically stated

as,

R∗= arg max

Rk

[

Rk:ψ(LRk)6=Lk

{|hSRk|2}

[

Rk:ψ(LRk)6=0

{|hRkD|2}

,(7)

where, R∗is the selected relay.

B. Outage Probability Investigation

In this part, we are interested in calculating the outage

probability of the buffer-aided HDAF scheme. In order to

assure the signal reception is successful at the target, we

establish SNR threshold γth = 22ro−1, which is the minimum

threshold below which the signal is not decode-able at the

destination. We ﬁrst ﬁnd the outage probability considering

inﬁnite buffer size. Then, we move towards the practical case

of ﬁnite buffers using Markov modeling.

C. Inﬁnite Buffer Size at Relays

The outage probability of buffer-aided HDAF utilizing the

law of total probability is deﬁned as,

Pout =P r(γSR > Z )PDF +P r (γSR ≤Z)PAF ,(8)

where, PDF (PAF ) is the outage probability of DF (AF)

method. The ﬁrst term in (8) deﬁnes that the signal at relay

is decode-able and relay operates in DF method. The terms

P r(γSR > Z )and P r(γS R ≤Z)are respectively expressed

as,

P r(γSR > Z ) = 1 −[(1 −e−Z/¯γSR )Csr ],(9)

P r(γSR ≤Z) = (1 −e−Z/¯γSR )Csr ,(10)

where, Csr and Crd are the count of open links on S−R

and R−Dsides, respectively. It is to state here that in the

case of inﬁnite (huge) buffer size, the corresponding links of a

relay are always open for data transmission. Therefore, Csr =

Crd =K.

The probability to operate in DF mode is given by,

PDF =P r(γDF

D≤γth|γS R > Z),(11)

where, γDF

Dis the SNR at the destination in case of DF

relaying protocol. Using the law of conditional probability,

PDF =P r(γRD ≤γth , γSR > Z)

P r(γSR > Z ).(12)

Since, γSR and γRD are independent of each other,

PDF =P r(γRD ≤γth )P r(γSR > Z )

P r(γSR > Z )

= (1 −e−γth/¯γRD )Crd .(13)

The second term in (8) deﬁnes that the relay is unable to

decode the signal and it works in AF mode with the probability

to operate expressed as,

PAF =P r(γAF

D≤γth|γS R ≤Z),(14)

where, γAF

Dis the end-to-end equivalent SNR at the destina-

tion for AF relaying protocol deﬁned in [22], [23] as,

γAF

D=γSR γRD

γSR +γRD + 1 .(15)

Putting (15) in (14), we get,

PAF =P r(γSR γRD

γSR +γRD+1 , γSR ≤Z)

P r(γSR ≤Z)(16)

Now, we represent γSR as random variable xand γRD as

random variable y. The probability of HDAF to operate in AF

mode is derived as,

PAF =RZ

0R

(x+1)γth

x−γth

0fγRD (y)fγSR (x)dydx

P r(γSR ≤Z).(17)

Using order statistics, the CDF of γSR following Rayleigh

distribution is given as

FγSR (x) = (1 −e−x/¯γS R )Csr ,(18)

differentiating w.r.t x, we get PDF of γSR as

fγSR (x) = (1 −e−x/¯γSR )Csr−1Csr e−x/¯γSR

¯γSR

.(19)

Using Binomial expansion,

fγSR (x) = Csr

¯γSR

Csr−1

X

m=0 Csr −1

m(−1)me−x/¯γSR e−mx/¯γSR .

(20)

Similarly, PDf of γRD using Binomial expansion is given as

fγRD (y) = Crd

¯γRD

Crd−1

X

n=0 Crd −1

n(−1)ne−y/¯γRD e−ny/¯γRD .

(21)

Putting (20) and (21) in (17), we get,

PAF =1

(1 −e−Z/¯γSR )Csr ×

CrdCsr

(n+ 1)¯γSR

Csr−1

X

m=0

Crd−1

X

n=0 Csr −1

mCrd −1

n

(−1)n+m¯γSR

m+ 1(1 −e−(m+1)Z/¯γSR )−

ZZ

0

e−(m+1)x/¯γSR e

−(n+1)(x+1)γth

(x−γth) ¯γRD dx . (22)

Putting (13), (9), (10) and (22) in (8), we get the outage

probability for the presented buffer-aided HDAF system.

D. Finite and Homogeneous Buffer Size at Relays

Now, we move towards the realistic case of ﬁnite and homo-

geneous buffer size at the relays. Markov modeling is utilized

to get the outage probability. The total number of states of

the Markov chain is (L+ 1)K. Let A∈R(L+1)K×(L+1)K

denote the state transition matrix of the Markov chain. Each

entry Aij =P(sj→si) = P(Xt+1 =si|Xt=sj)in Ais a

probability to transit from state sjto siat time tand (t+ 1),

respectively. The probability of transition relies on the state of

buffer. A relay with (Ψ(LRk) = Lor Ψ(LRk) = 0) cannot

accept or transmit data, respectively. Let csr and crd be the

binary variables for the link availability of S−Rand R−D

hops, respectively. cq= 1, if link is available and cq= 0, if

link is not available, where q∈ {sr, rd}. The link availability

of a relay Rkcan be found as,

csr(Rk) = (1,if 0≤ψ(LRk)≤L−1,

0,otherwise, (23)

crd(Rk) = (1,if 1≤ψ(LRk)≤L,

0,otherwise. (24)

Hence, the total number of open links at S−Rand R−D

sides which compete in the proposed dominant link election

process are respectively expressed as,

Csr =

K

X

a=1

csr(a),(25)

Crd =

K

X

a=1

crd(a).(26)

The state transition matrix entries are denoted by:

Aij =

psj

out,if si=sj,

(1−Psj

out)

Csr (1 −PAct

RD ),if si∈Usj

SR

(1−Psj

out)

Crd PAct

RD ,if si∈Usj

RD,

0,otherwise,

(27)

where, Usj

SR and Usj

RD are the set of states to which sjcan

transit when S−Rand R−Dhops are picked, respectively.

Psj

out is the outage probability for no development in the buffer

state. It is deﬁned in (8). PAct

RD is the probability that R−D

hop is activated when its SNR is greater than the SNR of

S−Rhop. PAct

RD is derived as,

PAct

RD =P r(X < Y ) = Z∞

0

FγSR (x)fγRD (x)dx . (28)

Considering Markov chain as a-periodic, irreducible and col-

umn stochastic, the vector for the probability of steady state

is given by [24]:

π= (Q+A−I)−1q, (29)

where, π= [π1, ..., π(L+1)K]T,Qij = 1 ∀i, j and

q= [1,1, ..., 1]T, and I∈R(L+1)K×(L+1)Kis the identity

matrix. The structure of the Markov chain states that when

there is no development in the buffer state, an outage happens.

Accordingly, the system’s outage probability is analytically

displayed as [4]:

Pout =

(L+1)K

X

i=1

πipsi

out =diag(A)π . (30)

III. RES ULTS AN D ARGUMENTS

The outage probability assessment of the proposed scheme

is given in this segment. The proposed scheme is referred as

‘Maxlink-HDAF’ in the plots. Maxlink-HDAF is compared

with the existing schemes, i.e., ‘Maxlink-DF’ [4], ‘Maxlink-

AF’ [14] and ‘Maxmax-HDAF’ [20]. The parameter, rois

set to 1bits/sec/Hz everywhere as followed in [3], [4]. The

results are presented for derived analytical expressions and

veriﬁed utilizing thorough Monte-Carlo simulations, i.e., 106

iterations. All the outcomes are based on symmetric channel

conditions.

0 2 4 6 8 10 12 14 16 18

SNR (dB)

10-6

10-4

10-2

100

Outage probability

Maxlink-HDAF (simulation)

Maxlink-HDAF (theory)

Maxmax-HDAF (theory)

Maxmax-HDAF (simulation)

Fig. 2: Outage probability of Maxlink-HDAF and Maxmax-

HADF schemes for K= 3 and L= 3

The investigation of the outage probability of the proposed

Max-link HDAF scheme and Maxmax-HDAF scheme against

average SNR are displayed in Fig. 2. The outcomes are

presented for K= 3 and L= 3. The Maxlink-HDAF scheme

outperforms the Maxmax-HDAF scheme because the latter

follows the ﬁxed transmission model that limits its diversity

gain. While Maxlink-HDAF tends to obtain diversity gain

approximately equal to 3. In this case, the full diversity gain

is not obtained because of the tiny buffer size. There is a huge

chance of buffer overﬂow which lowers the number of open

links. It is seen that the simulation and theoretical and out-

comes coincide with each other that proves our investigation.

Fig. 3 shows the investigation of the outage probability of

the Maxlink-HDAF scheme with Maxlink-DF and Maxlink-

AF schemes against the average SNR. The results are pre-

sented for L= 3 and K= 3. The enhancement in the result of

0 5 10 15

SNR (dB)

10-6

10-4

10-2

100

Outage Probability

Maxlink-HDAF (simulation)

Maxlink-HDAF (theory)

Maxlink-DF (theory)

Maxlink-DF (simulation)

Maxlink-AF (theory)

Maxlink-AF (simulation)

Fig. 3: Outage probability of Maxlink-HDAF, Maxlink-DF and

Maxlink-AF schemes for K= 3 and L= 3

Maxlink-HDAF is evident. For the design obeying DF relaying

solely, when the SNR at relay or destination is lower than the

predeﬁned threshold, the system runs into the outage. In HDAF

protocol, instead of pushing the system into the outage, the

relay switches from DF mode to AF mode and stores the data.

That is why the outage probability is improved. The Maxlink

in DF mode is better than the AF mode. Because in AF mode,

data is decode-able at the destination only. Therefore, there

is a high chance that packet is stored with weak SNR and

ampliﬁed accompanying noise and transmitted to the target.

The improvement of HDAF mode is slightly better than DF

mode because HDAF uses DF mode when SNR is higher than

the threshold at the relay deﬁned as Z.

IV. CONCLUSIONS

This research focuses on the buffer-aided relay selection

using the HDAF relaying rule. The link state, i.e., SNR

is solely used in relay selection. The outage probability is

investigated for the case of symmetric channel conditions.

The following conclusions are derived. The proposed scheme

using HDAF mode achieved a better outage probability in

comparison to SNR based buffer-aided relay selection schemes

using DF or AF relaying rules solely by 2.4 dBs and 8.6 dBs,

respectively.

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