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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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