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Study of Buffer-Aided Cooperative NOMA using Incremental Relaying in Wireless Networks

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  • The University of Oklahoma Tulsa OK USA

Abstract and Figures

In this paper, a novel design of an incremental cooperative communication with downlink non-orthogonal multiple access is studied and analyzed for a buffer-aided cooperative relay network. The phenomenon of packet diversity is taken into consideration instead of link diversity to overcome the lousy channels. A source multi-casts data packets in the direction of two users, if the direct transmission fails, only then the source requires assistance from the strong user for successful transmission.Additionally, the quality of the relaying channel is validated at every instance for the selection of the best packet. Furthermore, direct and relayed signals are combined at the destination using the maximal ratio combining (MRC) technique. Also, a closed-form expression is derived for the computation of the outage probability at user B along with the delay, throughput and diversity gain. The model illustrates the significance of the proposed scheme in terms of the outage probability, packet diversity and throughput against buffer-less schemes. Index Terms Amplify and forward (AF) relaying, buffer-aided, NOMA, incremental relaying, cooperative communication.
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Study of Buffer-Aided Cooperative NOMA
using Incremental Relaying in Wireless
Networks
Hina Nasir1, Nadeem Javaid2,, Waseem Raza3
1International Islamic University, Islamabad 44000, Pakistan
2COMSATS University Islamabad, Islamabad 44000, Pakistan
3University of Lahore, Lahore 54000, Pakistan
Correspondence: nadeemjavaidqau@gmail.com; https://www.njavaid.com
Abstract
In this paper, a novel design of an incremental cooperative communication with downlink non-
orthogonal multiple access is studied and analyzed for a buffer-aided cooperative relay network. The
phenomenon of packet diversity is taken into consideration instead of link diversity to overcome the lousy
channels. A source multi-casts data packets in the direction of two users, if the direct transmission fails,
only then the source requires assistance from the strong user for successful transmission.Additionally,
the quality of the relaying channel is validated at every instance for the selection of the best packet.
Furthermore, direct and relayed signals are combined at the destination using the maximal ratio com-
bining (MRC) technique. Also, a closed-form expression is derived for the computation of the outage
probability at user B along with the delay, throughput and diversity gain. The model illustrates the
significance of the proposed scheme in terms of the outage probability, packet diversity and throughput
against buffer-less schemes.
Index Terms
Amplify and forward (AF) relaying, buffer-aided, NOMA, incremental relaying, cooperative com-
munication.
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I. INTRODUCTION
Cooperative communication is a method of supporting source by a relay or a collection of
relays in conveying its data to a known target. It develops the spatial diversity gain, increases
the capacity and throughput, maximizes the probability of coverage and reduces the probability
of error and outage. In the existing literature, cooperative communication is divided into two
broad classifications: regular and incremental cooperative communication [1]. In the former,
relay always forwards a replica of the source’s message to the target. Whereas, in the latter,
relay supports the source only when the direct transmission is not successful [1]–[3]. Also, relays
are distinguished as regenerative or non-regenerative incremental scheme, known as conventional
scheme. Regenerative relays use decode and forward (DF) relaying protocol and non-regenerative
relays use amplify and forward (AF) relaying protocol. Generally, nodes in traditional cooperative
communication function in half-duplex transmission mode in which they cannot send and receive
packets concurrently. The source multi-casts in the first time slot to the picked relay and the
same relay transmits the received signal in the second time slot (in case of unsuccessful direct
transmission) regardless of the channel conditions. The adoption of a single relay begins channel
mismatch problem, since the quality of the corresponding channels of the relay may not always
be the best [4]. Accurately, when the AF relaying protocol is used, only data is decoded at
the destination. Thus, the overall success of transmission solely depends on the quality of the
available links between the source and target.
To alleviate the problem as mentioned earlier, a novel approach involving buffer-aided cooper-
ative communication [4]–[8] offers many advantages, such as improved diversity gain compared
to the buffer-less communication. It also enables the selection of the most reliable channel for
transmission, which demands the attainment of channel state information (CSI). The most reliable
channel is the one having the strongest signal to noise ratio (SNR). Besides, storing packets in
buffers leads to additional delay and the design demands the constant monitoring of the buffer
state. Thus, the design complexity is usually raised for buffer-aided cooperative protocols [4].
Although buffers allow full diversity gain, however, due to half-duplex constraint, the spectral
efficiency is not achieved.
On the other hand, non-orthogonal multiple access (NOMA) is a viable answer to meet the
high spectrum and connectivity demands of 5th generation networks. It can serve various users
simultaneously by exploiting the power domain [9]–[12]. It allows communication resources to be
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shared among various users in time, frequency or code domain. In a typical downlink cooperative
NOMA network scenario, the source sends a superimposed signal to multiple users and all
users receive interfering signals from a common source. In particular, the source broadcasts a
superimposed signal to the two users. The user having better channel conditions being a powerful
user decodes weak user’s signal and then use successive interference cancellation to decode its
signal. Then the powerful user acts as a relay to forward the weak user’s signal. Besides, the
weak user can directly decode its signal. [13].
Numerous work is done in literature considering NOMA [9]–[17] and orthogonal multiple
access (OMA) [7], [8], [19]–[25]. Combining NOMA with buffer-aided relays has proven to be
effective in increasing the system’s performance [17].
Most of the existing literature with buffers is focused either on relay selection or packet
selection. Also, in the literature, the buffer is accessed as a queue, i.e., first in first out manner.
However, there is a chance that a packet lying at the head of the buffer may not be the best to
match the instantaneous channel conditions of the relay to destination hop. The scheme in [26]
focused on this topic and reduced the overall outage probability. The authors suggested the notion
of a channel to packet matching. According to this notion, the packets which encountered adverse
source-relay channel must move from the reasonable relay-destination channel and vice versa.
This scheme is mentioned as AF-dual-hop in the rest of the paper. However, they concentrated on
the dual-hop network ignoring the significance of the direct link between source and destination.
The direct link can significantly reduce outage by improving signal quality using the advantages
of spatial diversity. Also, it helps in reducing the delay at high SNR. A buffer-aided cooperative
communication scheme is proposed in [27], which is based on the concept of packet diversity
instead of link diversity1.The work in [27] presents the theoretical analysis of the outage
probability, delay and diversity order. It is based on buffer-aided orthogonal multiple access
(OMA). Also, it gives no information about the graphical representation of results for analysis.
Taking motivation from [8], [13] and [26], a buffer-aided cooperative NOMA communication
scheme is proposed in this work. We mapped the idea of the channel to packet matching on
the incremental cooperative downlink NOMA system. Also, the graphical representation of the
findings is presented along with the discussion of the results and comparison with the existing
schemes. The network consists of a source and two users. User A acts as a relay to user B
1This work is an extension to work presented in [27].
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with is the intended destination. Finite length buffers are equipped at both users. The proposed
scheme works in two stages. In the first stage, the source multi-casts all the packets to the user
B that are also overheard by the user A. If the transmission is successful, user A drops the
packet. Otherwise, the packets are stored in the buffers of user A and the user B along with
their respective channel conditions. The first stage ends when the buffers are filled. In the second
stage, based on the instantaneous channel situations of link between user A and user B, a packet
is picked from the buffer at the user A, amplified and transmitted to the destination. At the
destination, the direct and the relayed transmissions are joined using maximal ratio combining
(MRC). The selection criterion for a packet is based on the notion of the channel to packet
matching. The contributions in this paper are summarized as follows:
1) A packet selection scheme is suggested for a buffer-aided three-node network using AF
incremental relaying cooperative NOMA communication. The proposed scheme considers
direct transmission capability. The AF-dual-hop scheme incorporated a buffer at the relay
node only. Our proposed network has data buffers both at the users. The buffer at the user
A is used to offer packet diversity and the buffer at the user B is used to combine the
direct transmission and the relayed transmission.
2) The closed-form expression for the outage probability is determined for the suggested
scheme. Moreover, throughput and end-to-end delay are also determined.
3) The diversity gain analysis in terms of the spatial diversity and packet diversity is carried
out for the proposed scheme.
4) Results are presented in comparison to the conventional scheme [3] and AF-dual-hop
scheme [26].
The rest of the article is prepared as follows. Section II reveals similar work in this domain;
Section III gives the system model for the suggested scheme. The performance analysis in terms
of the outage probability, delay, throughput and diversity gain is given in Section IV. Numerical
results and discussions are given in Section V, and Section VI concludes the paper.
II. LITERATURE REVIEW
Some of the research work accomplished for buffer-aided cooperative communication is
presented in this section. The authors proposed an idea of non-linear two-dimensional channel
probability space (CPS) for a buffer-aided dual-hop network in [28]. CPS division method acti-
vates the most suitable channel to reduce the end-to-end energy dissipation and outage probability.
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Same authors in [5] further explored the benefits of CPS in three dimensions known as non-
linear transmission activation probability space (TAPS). Moreover, a linear multi-dimensional
TAPS system is also proposed in [29]. This system is designed for a buffer-aided multi-relay
cooperative communication network. It also exploits the instantaneous channel condition for
the activation of the most appropriate channel for packet transmission. In this scheme, authors
explore enhancement in the energy dissipation and outage probability as compared to buffer-less
opportunistic routing schemes.
In [6], a buffer-aided scheme is proposed for a three-node network, assuming that the buffer
status is known at the source node. The source probabilistically accesses the channel to maximize
the throughput. Another work in [30] considered a dual-hop relay network and designed a
relaying scheme for imperfect CSI. They proposed three states for relay nodes: transmit, receive
and silent. The states are assigned depending on the imperfect channel state of the link and
the required acquisition overhead. The authors also provided an optimal trade-off between
the overhead of information acquiring and channel quality. In [31]–[33], some buffer-aided
cooperative communication techniques are proposed for two-way relaying in which 2 users
transfer data with each other with the aid of a relay. They have either a finite or an infinite
relay buffers and sending scheme is reliant on the instantaneous signal strength. The outage
probability performance of is also studied for mobile cooperative networks in [34]. The authors
studied optimal and sub optimal transmit antenna selection schemes and derived closed-form
expression for the outage probability.
Many of the schemes available in the literature on buffer-aided relay selection involve in-
stantaneous strength of the wireless link. The authors suggested a relay selection scheme for
a DF buffer-aided cooperative relaying network based on the combination of one and two slot
transmission routines. They considered finite buffers at the relay nodes. The relay choice is reliant
on the instantaneous channel quality only [7]. Furthermore, they provided a logical structure to
model the evolving relay buffers utilizing Markov chain and examined the proposed scheme
concerning the outage probability. The authors in [20] and [21] also worked on relay selection
of a DF relaying network. The relay selection choice includes both the channel quality and
current buffer standing. The scheme shows improvement in the outage probability and delay.
Another approach involving buffer status based relay selection is proposed in [22] known as
max-weight. In this policy, the authors assigned a weight to each link based on buffer status
and select the best relay with the most significant weight amongst all links. They derived the
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closed-form expressions for the outage probability and diversity gain and achieved the complete
diversity at buffer size 3 and above in contrast to the max-link AF relay selection scheme.
Considering the delay in buffer-aided cooperative relaying, authors in [35]–[37] proposed relay
selection schemes focusing on the reduced packet delay. They prioritized relay-destination link
and achieved notable improvement in packet delay in comparison to max-link AF scheme. It is
studied in [24] that majority of the prominent works of the buffer-aided relay selection focus on
the DF relaying technique. Keeping this in view, they introduced a relay selection strategy for
AF relaying system. They considered both symmetric and asymmetric channel arrangements to
investigate the outage probability performance. The scheme in [24] is enhanced in [8] by the
incorporation of direct link. They studied performance for the outage probability, throughput and
delay in comparison to the max-link AF scheme. A new scheme based on packet selection is
proposed in [26] which is proposed for a buffer-aided dual-hop network. Their objective was
to reduce the overall system outage by introducing the channel to packet matching notion. The
purpose is to let the packets that faced a lousy channel in the first hop go for right channel in the
next-hop so that the overall system performance is enhanced. A similar concept was exploited
in [27] in which authors introduced a direct link and derived a closed-form representation for
the outage probability. However, this work is only the analytical analysis with no graphical
description of results.
The current literature on NOMA is discussed in the forthcoming discussion. In [9], a coopera-
tive NOMA network is investigated for device-to-device communication. The authors considered
both AF and DF modes for relay with and without wireless power transfer capability and derived
the closed-form expressions for the outage probability to show the effectiveness of the proposed
strategies. The work in [10] exploits cooperative NOMA for wireless powered relay and the
authors derived a closed-form expression for the outage probability to prove the efficiency of
NOMA over OMA systems. In [11], NOMA is also explored for cognitive relaying with hardware
impairments to evaluate the practical aspects of the system. The authors derive the closed form
expression for the outage probability. Another work considered NOMA for secrecy performance
in the system of the Internet of things. The secrecy outage probability is derived to show the
performance of NOMA over OMA systems [12]. The performance of downlink NOMA for
incremental relaying cooperative communication is studied and analyzed for three-node network
with source and two users. The authors find optimal power allocation strategies at the source to
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minimize the outage probability [13]
The NOMA with multiple relays in a cellular system is also explored for hybrid decode-
amplify and forward relaying in [14]. The authors claimed that high throughput efficiency is
achieved at high SNR. In [15], the authors explored cooperative NOMA with a direct link using
DF relaying technique. The authors suggested three relaying schemes utilizing both direct and
relayed transmission to enhance the outage performance of the system for far users. The work
in [16] studied the performance of NOMA in the downlink cooperative system. The authors
proposed a strategy to communicate with two mobile users using AF relay to achieve better
spectral efficiency and user fairness.
Another work in [17] considered NOMA with buffer-aided relaying with and without the
availability of CSI at the relays. The buffer-aided relaying for downlink NOMA is considered
with a direct link in [18]. The authors targeted throughput maximization and derive closed-form
expressions for the throughput.
III. SYS TE M MOD EL
A single cooperative arrangement of a source node (S), user A (UA) and user B (UB) is
considered as given in Fig. 1. UAis a near and treated as strong user. UBis far and treated as
weak user. All nodes operates in a half-duplex communication style, i.e., it either transmits or
receives. Communication between S and users takes place via a direct connection or an indirect
connection. UAand UBare equipped with buffers BAand BBof finite length B (packets),
respectively. Buffers provide random access and data can be transmitted from any location in
the buffer. The information rate is r0bits/s/Hz. MRC method is employed at the destination to
mix the received signals.
S
B...21
UB
UA
B...21
BA
BB
B
B
Fig. 1: System model for buffer-aided three node relay network with S, UAand UB.
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The Rayleigh fading channel is studied. h1,h2and h3are the fading coefficients of source-user
B (SUB), source-user A (SUA) and user A-user B (UAUB) channels, respectively.
Data packets are transferred based on time slots with a duration tseconds each. It is assumed
that the fading envelope of a hop remains fixed for a time slot; however, it may differ for
different time slots. Moreover, the channel is also undermined with additive white Gaussian
noise (AWGN) with mean, zero and variance, No.
A. The proposed transmission scheme
The transmission process of the proposed scheme has 2 stages. In stage 1, source sends a
reference signal to both users to estimate the CSI of the received signals. Based on the received
signal, UBestimates the channel between itself and Sand compares it with predefined threshold
γth = 2ro1, where rois the information rate in bits/s/Hz. If it is greater than threshold, it
sends acknowledgement to Sand UA. Upon receiving this acknowledgement, Sperforms direct
transmission and sends a superimposed signal to UAand UB. On successful decoding, the S
continues with the next transmission. The equation of the received signal at UBis written as,
yUB=pa1Psxsh1+pa2Psxsh1+n1.(1)
where, yUBis the received signal at UB,Psis the power from S,xsis the transmitted signal
from source, a1and a2are the power allocation factors for UAand UB, respectively and n1is
the channel noise. On the other hand, if UBis unable to decode the received signal, it sends
negative acknowledgement to Sand UA. Upon this negative acknowledgement, Sbroadcasts a
superimposed signal to UAand UB. The signal along with its CSI is stored in buffers BAand BB,
respectively. UAamplifies the received signal according to the gain defined as G=qPr
Ps|h2|2+N0
and stores it in buffer. This process continues until both the buffers are full. The equation of
received signal at UAis written as
yUA=pa1Psxsh2+pa2Psxsh2+n2.(2)
where, yUAis the received signal at UA, and n2is the channel noise.
In the second stage, UAtransmits and UBreceives. Based on the instantaneous strength of
UAUBchannel, UBpicks from BAsuch that (3) is satisfied. At the same time, UBalso picks
the same packet from its buffer, BB.
γD> γ1+γ2γ3
1 + γ2+γ3.(3)
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According to (3), a packet is picked such that its end-to-end SNR, defined as γD, leads to the
successful packet reception at the UB. The decision of successful reception is based on the SNR
threshold, γth, which is the minimum SNR required for the correct decoding of the signal at
intended destination.
The signals received at UBin the second stage is mathematically expressed as:
yU0
B=pPrGyUAh3+n3.(4)
where, yU0
Bis the signal received at UBin stage 2 and n3is channel noise. Both signals, yUB
and yU0
Bare combined at the end using maximal ratio combining as,
yD=yUB+yU0
B.(5)
Fig. 2 shows the transmission process of the proposed scheme in the first and second stage. The
4
3
2
1
BA
BB
4
3
2
1
Phase 1
21
22
23
24
11
12
13
14
D
Phase 2
3
12
S
Fig. 2: The proposed transmission scheme of a buffer-aided cooperative NOMA.
packets from Sare stored in BAand BBwith their respective CSI in stage 1. In stage 2, the
packet satisfying (3) is picked from BAand forwarded to D. The same packet copy is accessed
from BBand both the signals are combined using MRC.
The instantaneous Signal to interference noise rations (SINR) of SUB,SUAand
SNR of UAUBlinks are represented by γ1,γ1and γ3, respectively. Where γ1=a2ρsh2
1
a1ρsh2
1+1 ,
γ2=a2ρsh2
2
a1ρsh2
2+1 and γ3=ρrh2
3, respectively. Where ρs=Ps/N0and ρr=Pr/N0.The complexity
of the proposed scheme is derived as follows. In the best-case scenario, the destination node
decodes the received information in stage 1, and sources continue with the next packet without
UA’s assistance. Therefore, the complexity, in this case, is O(1). However, in the worst-case
scenario, the destination is unable to decode the information. All the packets are stored in the
buffer until it is filled. The complexity of stage 1 equals O(L). In stage 2, the scheme has to make
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a selection out of B packets stored in the buffer for B time slots. Therefore, the complexity of
stage 2 is O(B×B). Hence, the overall complexity of the scheme is O(B+B2).The scheme in
[26] being having the same 2 stage transmission scheme has the complexity of O(B2). However,
this scheme is not obeying incremental relaying. Therefore, the proposed system is better when
the direct link has high SNR.
IV. PERFORMANCE ANA LYSI S
In the proposed scheme, the AF relaying is used. Therefore, the only destination decodes the
data. The signal is acceptable only when the end-to-end SNR is higher than the SNR threshold.
Therefore, it is desired to calculate output SNR at UBwhich is the sum of instantaneous SNR
of SUBlink and the equivalent SNR of the source-user A-user B (SUAUB) links.
Thus, γDis expressed as:
γD=γ1+γSUAUB,(6)
where, γSUAUBis the equivalent SNR of SUAUBlinks. The equivalent SNR is expressed
as:
γSUAUB=a2γ2γ3
γ2+γ3+a1γ2γ3+ 1 .(7)
Assuming Rayleigh faded channel, the PDF and CDF of a link Xare respectively expressed
as
fγX(γ) = 1
¯γX
eγ/¯γX,(8)
FγX(γ) = 1 eγ/¯γX.(9)
The CDF of the overall SNR of SUAUBis derived as:
FγSUAUB(γth ) = Pa2γ2γ3
γ2+γ3+a1γ2γ3+ 1 γth
= 1Z
γth
fγ3(γ)1Fγ2γth(γ+ 1)
a2γγth a1γγth 
= 1Z
0
fγ3(γ+γth
a2a1γth
)
"1Fγ2
γth(γ+γth
a2a1γth + 1)
γ#dγ . (10)
Let us consider the scenario when the relay has a B number of packets. Based on γ3, the central
node selects a packet among B packets stored at the relay node in a way that the total SNR,
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γD, at the destination is greater than or equal to γth. The outage occurs if all the packets give
no match to γ3. Therefore, using order statistics, Fγ2is expressed as:
Fγ2(γ) = (1 eγ/¯γ2)B.(11)
Putting (11) and (8) with proper indices in (10),
FγSUAUB(γth )=1Z
0
e
γ+γth
a2a1γth
¯γ3
¯γ3"1(1e
γth(γ+γth
a2a1γth+1)
γ)B#
= 1Z
0
e
γ+γth
a2a1γth
¯γ3
¯γ3
×
B
X
b=1 B
b!(1)be
γthb(γ+γth
a2a1γth +1)
γγ2!
= 1+
B
X
b=1 B
b!(1)beγth
¯γ2+b¯γ3(a2a1γth )
¯γ2¯γ3
¯γ3
Z
0
eγthb(γth +(a2a1γth))
γ¯γ2(a2a2γth)γ
¯γ3(12)
Using the identity R
0exp(β
4xαx)dx =qβ
αK1(βα),FγS UAUB(γth)is expressed as:
Fγ3(γth) = 1 +
B
X
b=1 B
b!(1)beγth
¯γ2+b¯γ3
¯γ2¯γ3
¯γ3
2sγthb(γth +a2a1γth γ3
¯γ2(a2a1γth)×
K1 2sγthb(γth +a2a1γth )
¯γ2¯γ3(a2a1γth)!,(13)
where, K1(.)is the modified Bessel function of second kind and first order. In order to simplify
the analysis, the asymptotic high SNR approximation for K1(x)
=1/x is derived, which reduces
(13) to:
FγSUAUB(γth ) = 1+
B
X
b=1 B
b!(1)be
γth( ¯γ2+b¯γ3(a2a1γth ))
¯γ2¯γ3.(14)
The CDF of SNR at UB,FγD(γth), after the application of MRC is expressed as:
FγD(γth) = Zγth
0
FγSUAUB(γ)fγ1(γth γ)
=Zγth
0
e(γthγ)
¯γ1
¯γ1
×(1+
B
X
b=1 B
b!(1)be
γγ2+b¯γ3(a2a1γth))
¯γ2¯γ3!
(15)
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A. End-to-end outage probability
The outage probability is named as the probability when output SNR at UBdrops below the
predefined threshold. More precisely, if the SNR experienced by a packet on direct communi-
cation is less than γth, the packet is collected in the buffers of UAand UB. In the second stage,
based on the instantaneous SNR of UAUBlink, a packet is picked from the buffer at the
relay and transmitted to the destination. At the destination, the same packet is accessed from
BBand both are combined using MRC. However, there is still a chance that the end-to-end
SNR after MRC falls below γth. It is named an outage event. The outage probability, Pout, is
mathematically expressed as:
Pout =Zγth
0
fγD(γ) = FγD(γth).(16)
Where, FγD(γth)is defined in (15).
B. End-to-end delay
In the proposed scheme, a packet may experience the out of order arrival at the destination,
considerable buffer delays and delay spread. These issues arise because a packet is only selected
for transmission if its respective SNR meets the packet selection condition. Two types of delay
in terms of time slots are considered: block delay and packet delay. A time slot is a duration
required by a packet to travel over a link. It is also assumed for the proposed scheme that only
one packet is transmitted during one time slot. The end-to-end delay is expressed as:
Delayx=Dp1+Dp2,(17)
where, Dp1and Dp2are the delays experienced in the stage 1 and stage 2, respectively and
x={Block, P acket}.
1) Block delay: It is a time needed by a bundle of packets to arrive the target from the source.
Considering only the relayed transmission, in the first stage, it takes tBtime slots to fill a buffer
of size Bpackets. Also, it takes tBtime slots for a relay to remove Bpackets from its buffer.
Therefore, the end-to-end block delay becomes:
DelayBlock = 2 tB.(18)
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Now, the direct transmission is considered with the relayed transmission. A link outage, denoted
by σis defined as:
σ=
1p1, γ1γth
p1, γ1> γth
(19)
where, p1= exp(γth/¯γ1)is the probability of successful direct transmission. According to the
proposed scheme, if a packet is received successfully at the destination in the direct transmission,
it is not stored in the buffer and faces a delay of one time slot. Hence, (18) is modified as:
DelayBlock = (1 σ) 2 tB+σtB.(20)
It states that when the direct transmission is successful, i.e., σ=p1and p1= 1, the block delay
is tBtime slots, otherwise, it is 2tBtime slots.
2) Packet delay: The end-to-end-delay of a particular packet is named as packet delay. In the
best-case scenario, a packet is the last one to enter the buffer and the first one to leave. The
packet delay, in this case, is 2 time slots. However, in the worst case, a packet enters the buffer
in the first time slot and waits for the next tB1time slots for the buffer to fill in and finish
with stage 1. Hence, Dp1= (1 + tB1) time slots. In stage 2, only UAUBlink is used for
transmission. Therefore, it takes tBtime slots to empty the buffer. Dp2=tBtime slots give the
delay in stage 2. The total packet delay is expressed as:
DelayP ack et = 2 tB.(21)
Considering the direct link, (21) is modified as:
DelayP ack et = (1 σ)2 tB+σ . (22)
The above equation shows that for an unsuccessful direct transmission, σ= 1 p1and p1= 1,
the packet delay is 2tBtime slots. Otherwise, it is one time slot.
C. Throughput
The amount of packets transmitted per unit time slot is defined as the throughput. It is
mathematically expressed as [3]:
T hr =r0
DelayP aack et
,(23)
Putting (22) in (23), the throughput becomes:
T hr =r0
σ+ 2 tB(1 σ).(24)
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According to (24), the throughput lies between r0/2tBand r0. When the direct transmission is
not successful, the throughput is r0/2tB, otherwise, it is r0.
D. Diversity gain
Considering the packet selection instead of link selection, the diversity gains for the proposed
scheme in terms of both the spatial diversity and packet diversity are derived.
1) Spatial diversity gain: To derive the spatial diversity gain, asymptotic analysis is carried
out. At high SNR, γ1>> γth, the packet is transmitted successfully in the direct transmission and
user A’s assistance is not required. Therefore, the network will benefit from the virtual antenna
array gain but not the diversity gain. Hence, the spatial diversity gain is 1in this case. When
γ1γth, the system will need assistance from UAto transmit the packet to UB. Therefore, the
spatial diversity gain of 1+1 is achieved.
2) Packet diversity gain: The diversity gain is expressed as [38]:
d=lim
¯γh→∞
log Pout
log ¯γh
,(25)
where, ¯γh=Ps/N0is the average SNR of every link. Direct substitution of (16) in (25) in not
helpful to show the packet diversity gain. Rather, the packet diversity gain is derived step wise
by considering the following cases:
γ1> γth: In this case, there is a successful direct transmission. As it is assumed that only
one packet is transmitted in one time slot; therefore, the packet diversity gain is 1.
γ1γth: In this case, direct transmission is not successful. Therefore, the packet and its
respective CSI are stored in the buffers. Since the direct link is not taking part in the packet
selection, therefore, it is ignored for the time being. Let us assume that the probabilities
for packet selection for both SUAand UAUBlinks are the same. The outage in this
scenario will be:
Pout =P(γDγth)
=
B
Y
i=1
P(min(γi
2, γi
3)γth)
= (1 eγth/¯γ2)B+ (1 eγth/¯γ3)B
(1 eγth/¯γ2)B(1 eγth/¯γ3)B.(26)
15
Assuming ¯γ2= ¯γ3= ¯γ, using the approximation 1exxand ignoring the higher order
terms:
pout =γth
¯γB
.(27)
Substituting (27) in (25),
d=Blim
¯γ→∞
log γth
¯γ
log ¯γ.(28)
According to the above equation, the packet diversity gain for the relayed transmission is
B. Now, the assumption of both links having an equal number of choices available to select
the packet is lifted. Indeed, only UAUBlink selects the packet from the buffer at UA.
Therefore, the packet diversity gain reduces to B
2. In [8], the diversity gain is incremented
by 1 in the presence of a direct link. Therefore, the packet diversity gain of the proposed
scheme with the direct link is B
2+ 1.
V. RE SU LTS AND DISCUSSIONS
In order to evaluate the proposed scheme referred as AF-buffer-aided system (AF-BAS), it
is compared with the two existing schemes: conventional scheme (B=1) [3] and AF-dual-hop
packet selection scheme (AF-dual-hop) [26]. To have fair comparison, the cooperative NOMA
is also incorporated in the compared schemes. In the simulations, ¯γ1= ¯γ2= ¯γ3=Ps/N0and
r0= 1 bits/s/Hz. The power allocation factors are set to a1 = 0.8and a2 = 0.2unless
otherwise specified. The performance metrics used for evaluation are the end-to-end outage
probability, end-to-end delay and throughput.
Fig. 3 presents the end-to-end outage probability performance against SNR of the transmitted
signal at user B. In this figure, the outage probability is plotted for different buffer sizes. It is
to note that the proposed scheme, AF-BAS with B=1, represents the conventional incremental
relaying cooperative system and AF-dual-hop with B=1 represents the conventional dual-hop
single relay system. The results show that the outage performance curves of AF-BAS and AF-
dual-hop schemes are better than their respective conventional schemes. The conventional scheme
shows lousy performance because it does not allow packet selection at any stage. The concept of
channel to packet matching tends to reduce the outage probability of AF-dual-hop and AF-BAS
schemes. AF-BAS shows better performance than AF-dual-hop due to the incorporation of the
direct link along with the integration of the MRC technique.
16
There is an improvement in the outage probability when the buffer is increased from 1 to
16; however, there is a small enhancement on the further increase. The increase in buffer size
decreases the outage probability because a large buffer size allows more packets to store in it.
More packets give more choices to search for a good match. Even if a perfect packet match is
not found, the weighted sum of the direct and indirect signals takes the signal out of the outage
event.
0 5 10 15 20 25 30
Average SNR (dB)
10-2
10-1
100
Outage Probability
AF-dual-hop, B=1
AF-BAS, B=1
AF-Dual-hop, B=2
AFBAS, B=2
AF-dual-hop, B=16
AF-BAS, B=16
AF-dual-hop, B=32
AF-BAS, B=32
Fig. 3: End-to-end outage probability versus SNR of the transmitted signal.
0 5 10 15 20 25
Average SNR [dB]
10-3
10-2
10-1
100
Outage Probability
AF-dual-hop
AF-BAS
AF-Maxlink
Fig. 4: End-to-end outage probability versus SNR of the transmitted signal.
17
In Fig. 4, the outage probability of the proposed scheme is further compared with the existing
relay selection scheme, i.e., AF-Maxlink [24] keeping K= 1,a1 = 0 and a2 = 1 to have
a fair comparison. For this plot, the buffer size is kept to B= 3. It is seen that AF-Maxlink
scheme shows better outage as compared to AF-dual-hop scheme. However, the performance
of AF-BAS is best. This is because the AF-BAS is not considering a direct link. AF-Maxlink
shows better outage probability as compared to AF-dual-hop scheme because it is not operated
in two segregated stages, which significantly increases its diversity gain.
0 5 10 15 20 25
Average SNR (dB)
10-4
10-3
10-2
10-1
100
Outage Probability
a1=0.0
a1=0.1
a1=0.2
a1=0.3
a1=0.4
a1=0.5
a1=0.6
a1=0.7
a1=0.8
a1=0.9
Fig. 5: End-to-end outage probability with increasing the power allocation factor of user A.
The Fig. 5 presents the outage probability of the proposed scheme with increasing the power
allocation factor of UAi.e., a1for B= 16. The factor a1is increased from 0 to 0.9. It is
observed that as a1increases, the outage probability decreases because the user A becomes
stronger, causing user B weak. When user B is lousy, there is a minimal probability of success
of direct transmission and most of the time, UA’s assistance is required to transmit UBs message.
Fig. 6 shows the significance of the direct link in the proposed scheme. In this figure, the
outage probability is plotted for different values of γSUBwith a fixed buffer of size 16. The
results illustrate that when γSUB= 0, the system behaves as AF-dual-hop scheme. As SUB
link improves, so is the outage performance. Although the direct link is very unreliable, however,
it can significantly reduce the outage probability as compared to the AF-dual-hop scheme.
To stretch the analysis, we have analyzed the proposed scheme for asymmetric channel
conditions for B= 16 in Fig. 7. In this plot, we considered two real constants αand βto
18
0 5 10 15 20 25
Average SNR (dB)
10-3
10-2
10-1
100
Outage Probability
SUB
=SUA
SUB
=0.8 SUA
SUB
=0.6 SUA
SUB
=0.4 SUA
SUB
=0.2 SUA
SUB
=0
Fig. 6: Significance of direct link: outage with respect to SNR of the transmitted signal.
0 5 10 15 20 25
Average SNR (dB)
10-3
10-2
10-1
100
Outage Probability
sUB
=0, =1, =1
=1, =1
sUB
=0, =1, =3
=1, =3
sUB
=0, =3, =1
=3, =1
Fig. 7: Asymmetric SUAUAUBchannels: outage with respect to SNR of the transmitted signal
for B= 16.
prioritize SUAand UAUBchannels, respectively. It is seen that when α= 3 and β= 1, the SUA
side has high SNR and outage is improved as compared to the case when α= 1 and β= 3.
Additionally, when the direct link is overlooked, i.e., γSUB= 0, the outage probability shows a
similar pattern as observed for γSUB>0. Also, symmetric channel conditions have better outage
probability as compared to asymmetric channels.
In Fig. 8, the average end-to-end packet delay of the proposed scheme versus SNR of the direct
19
0 5 10 15 20 25 30
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Average SNR (dB)
Delay (time slots)
B=1
B=3
B=5
B=7
Fig. 8: Average end-to-end packet delay of the proposed scheme with respect to SNR.
link is shown. For this plot a1 = 0. The proposed scheme is compared with the conventional
scheme marked as B= 1. In this figure, the delay performance is shown in two respects: with
increasing buffer size and with increasing SNR. It is seen that with the increase in buffer size, the
delay of the proposed scheme increases. Specifically, when SNR is very low, the delay increases
linearly with the increase in buffer size. This is because, when a packet enters the buffer, it has
to wait inside buffer until stage 1 is over. In stage 2, again packet has to wait for its turn to get
the favorable relay-destination channel quality. Larger the buffer size, more the packet has to
wait for its turn to be transmitted. In the worst case, the wait is twice the number of time slots
required to fill the buffer of size B. Furthermore, it is observed that with the increase in SNR of
the direct link, the delay of the proposed scheme and the conventional scheme is only 1 time slot.
At high SNR, the direct link has sufficient channel quality to transmit the packet successfully
to the destination in only 1time slot without needing assistance from the relay. Hence, it is
concluded that the proposed scheme offers the delay equal to the conventional scheme with the
added benefits of buffer-aided relaying.
Fig. 9 shows the throughput of the proposed scheme with different buffer sizes against SNR of
the direct link with r0= 1 bits/s/Hz. With B= 1, the proposed scheme behaves as a conventional
scheme giving the maximum throughput of nearly 0.5bits/s/Hz. As the buffer size increases, the
throughput decreases. The reason for the decrease is the two-stage transmission scheme. Larger
the buffer size, more time slots are required to transmit the packet that affects the throughput. At
20
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average SNR (dB)
Throughput (packets/time slot)
B=1
B=3
B=5
B=7
B=9
B=11
B=13
B=15
Fig. 9: Throughput of the proposed scheme with varying buffer size against SNR of the direct
link.
high SNR, the throughput approaches to 1 because of the successful transmission by the direct
link. It is also seen that the decrease in the throughput is tiny when the buffer size is large, i.e.,
10 and above. Hence, it is concluded that there is a performance trade-off in terms of throughput
and buffer size. Larger the buffer size, smaller is the throughput.
VI. CONCLUSION
In this paper, a buffer-aided incremental cooperative NOMA communication system has been
investigated based on AF relaying protocol. The overall system performance has improved by
incorporating the idea of channel to packet matching. Additionally, the proposed scheme has
decreased the outage probability compared to the traditional buffer-aided schemes. However,
in the selection of a data packet from the buffer of a relay, the trade-off between the outage
probability and delay has been observed. Moreover, it has been concluded that the optimal
selection of buffer size helped in achieving a considerable delay. The simulation results showed
the delay of 1 time slot at high SNR, which is equivalent to the conventional incremental
cooperative communication schemes. Also, the symmetric channel conditions have shown better
outage probability as compared to asymmetric channels. Additionally, the analysis of spatial
diversity gain has shown the same behavior in the conventional and proposed schemes. However,
the significant improvement has been evident in packet diversity gain of B
2+ 1 against 1and B
2
21
in conventional buffer-aided schemes. Thus, the less number of data packets are lost, resulting
in higher packet diversity gain and lower average delay at the cost of throughput.
In the future, our focus is on the exploitation of packet selection scheme for NOMA systems
with multiple users and multiple relays.
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... This motivates us to investigate buffer-aided C-NOMA with direct transmission and cooperative transmission between intended users in the IoT. Although the recent work in [36] investigated C-NOMA with bufferaided user cooperation, only unidirectional cooperation from a near user to a far user was considered, and the performance evaluation was focused only on the far user. To the best of the authors' knowledge, this is the first work to investigate bufferaided C-NOMA with coordinated direct transmission and bidirectional buffer-aided cooperative transmission between the intended users. ...
... Based on (35), (36) and the fact thatP 3 1 =P 1 3 = 0, it is easy to obtain the stationary probabilities ofŜ i , denoted bŷ π i , i ∈ [1 : 3], as follows: (35) and (36), θ=ρ −2 holds. Thus, π 1= ρ 0 ,π 2≤ ρ −1 ,π 3≤ ρ −2 . ...
... Based on (35), (36) and the fact thatP 3 1 =P 1 3 = 0, it is easy to obtain the stationary probabilities ofŜ i , denoted bŷ π i , i ∈ [1 : 3], as follows: (35) and (36), θ=ρ −2 holds. Thus, π 1= ρ 0 ,π 2≤ ρ −1 ,π 3≤ ρ −2 . ...
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