Performance analysis of cooperative based multi hop transmission protocols in underlay cognitive radio with hardware impairment

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Performance analysis of cooperative based multi hop transmission protocols in underlay cognitive radio with hardware impairment. n this paper, we study performances of multi-hop transmission protocols in underlay cognitive radio (CR) networks under impact of transceiver hardware impairment. In the considered protocols, cooperative communication is used to enhance reliability of data transmission at each hop on an established route between a secondary source and a secondary destination.
c
VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28
Performance Analysis of Cooperative-based Multi-hop
Transmission Protocols in Underlay Cognitive Radio with
Hardware Impairment
Tran Trung Duy*, Vo Nguyen Quoc Bao
Wireless Communication Lab,
Posts and Telecommunications Institute of Technology (PTIT), Vietnam
Abstract
In
this
paper,
we
study
performances
of
multi-hop
transmission
protocols
in
underlay
cognitive
radio
(CR) networks under impact of transceiver hardware impairment.
In the considered protocols, cooperative
communication is used to enhance reliability of data transmission at each hop on an established route between
a secondary source and a secondary destination.
For performance evaluation, we derive exact and asymptotic
closed-form expressions of outage probability and average number of time slots over Rayleigh fading channel.
Then, computer simulations are performed to verify the derivations. Results present that the cooperative-based
multi-hop transmission protocols can obtain better performance and diversity gain, as compared with multi-hop
scheme using direct transmission (DT). However, with the same number of hops, these protocols use more time
slots than the DT protocol.
2015 Published by VNU Journal of Sciences.
Manuscript communication: received 01 May 2015, revised 10 June 2015, accepted 25 June 2015.
Corresponding author: Tran Trung Duy, trantrungduy@ptithcm.edu.vn.
Keywords:
Hardware Impairment, Underlay Cognitive Radio, Cooperative Communication, Outage Probability.
1. Introduction
cluster-based cooperative protocol for multi-hop
transmission was proposed and analyzed. In this
In wireless networks such as adhoc networks
protocol,
the cluster node with the maximum
[1]
and
wireless
sensor
networks
[2],
multi-
instantaneous
channel
gain
will
serve
as
the
hop
relaying
scenarios
are
used
widely
due
sender for the next cluster. In [8, 9, 10, 11, 12],
to
far
distances
between
source
node
and
the
authors
proposed
cooperative
routing
destination
node.
In
conventional
multi-hop
protocols
in
which
intermediate
nodes
on
scheme,
the
direct
transmission
(DT)
is
used
the
established
route
exploit
the
cooperative
to
relay
the
source’s
data
to
the
destination
communication
to
forward
the
source
data.
[3, 4].
Although the implementation of the DT
Although
performances
of
these
protocols
protocol
is
easy
in
practice,
its
performance
significantly
are
enhanced,
as
compared
with
significantly
degrades
in
fading
environments
the
DT
protocol,
their
implementation
which
[4].
To enhance performances for the multi-
requires a high synchronization between all the
hop
schemes,
in
published
literature
such
as
intermediate nodes, is a very dicult work.
[5, 6], the authors proposed multi-hop diversity
Recently,
multi-hop
relaying
protocols
in
relaying protocols in which a relay is selected
cognitive radio (CR) networks have gained much
to cooperate with the transmitter at each hop
attention as an ecient method to enhance the
to
forward
the
data
to
next
hop.
In
[7],
a
coverage
and
channel
capacity
for
secondary
16
T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28
networks.
Dierent
with
the
conventional
We
propose
two
multi-hop
protocols
in
wireless networks, transmit powers of secondary
which either conventional cooperative (CC)
users are limited by interference thresholds given
protocol
or
incremental
cooperative
(IR)
by
primary
users
(PU)
[13,
14].
Due
to
protocol
[27]
is
used
to
enhance
quality
the limited power,
performances of multi-hop
of the data transmission at each hop.
In
CR
protocols
significantly
degrades
[15,
16],
the CC protocol, the receiver at each hop
especially in CR schemes with multiple PUs [17].
is equipped with maximal ratio combining
Again, cooperative communication protocols are
(MRC) technique to combine the received
employed to enhance quality of service (QoS) for
data [27]. In the IR protocol, the relay link
the secondary networks.
In [18, 19], underlay
is only used if the quality of the direct link is
cooperative routing protocols with and without
poor [27].
using combining techniques were proposed and
analyzed, respectively. Results in [18, 19]
presented that the proposed schemes provide an
impressive performance gain as compared with
the DT model.
We derive exact closed-form expressions of
outage probability for the proposed schemes
over Rayleigh fading channels. Moreover,
we also derive an exact expression of
average number of the time slots for the IR
So far, almost published works related to the
multi-hop networks assumed that the transceivers
protocol. Then, Monte-Carlo simulations
are presented to verify our derivations.
are perfect. However, in practice, they are
suered from impairments due to I/Q imbalance,
high power amplifier non-linearities and phase
noise [20]. Due to the hardware noises, the
channel capacity obtained at high signal-to-noise
To provide more insights into the system
performance, we also derive the asymptotic
outage probability where both diversity and
coding gains are obtained.
ratio (SNR) region is limited [21]. In [22, 23], the
Finally, we compare the performance of the
authors considered two-way relaying protocols
proposed protocols with the DT protocol to
under the presence of the hardware impairments
show the advantages of our schemes.
over Rayleigh fading channel and Nakagami-
m fading channel, respectively. Works in [24]
and [25] proposed relay selection methods to
obtain diversity order as well as compensate
the performance loss due to the hardware
impairment. To the best of our knowledge, the
most related to our work is the cognitive decode-
and-forward relaying protocol proposed in [26].
The rest of this paper is organized as follows.
The system model of the proposed protocols
is described in Section II. In Section III, the
expressions of the outage probability and the
average number of time slots are derived. The
simulation results are shown in Section III.
Finally, this paper is concluded in Section V.
However,
the authors in [26] only considered
the dual-hop network with selection combining
technique at the destination. Moreover, only
2. System Model
outage probability of the proposed scheme was
Figure
1
illustrates
the
system
model
of
evaluated in [26], while other important metrics
the
proposed
cooperative-aided
multi-hop
such as diversity gain and spectrum eciency
transmission
protocols
in
underlay
cognitive
were not considered.
In this paper, we study
radio.
In this figure, the secondary source T0
performances
of
cooperative-based
multi-hop
transmits its data to the secondary destination TM
protocols in underlay CR networks under the
via a multi-hop model. We assume that an M-hop
impact of the hardware impairment.
The main
route
between
the
secondary
source
and
the
contributions of this paper can be summarized as
secondary destination (with M 1 intermediate
follows:
nodes,
i.e.,
T1,T2,...,TM1)
is
established
by
T
T
T
T
T
i
i
T
T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28
17
at the ith hop with three dierent techniques
R1
R2
RM
(see Fig. 2), i.e., conventional cooperation
(CC), incremental cooperation (IR) and direct
0
1
2
TM1
TM
transmission (DT).
In the CC protocol, the data transmission at
the ith hop is split into two time slots. At the first
time slot, node Ti1, which is assumed to receive
Data links
PU
Interference links
the source data successfully before, transmits the
source data to node Ti and relay Ri. At the end
of the first time slot, relay Ri attempts to decode
Fig. 1: Cooperative-aided multi-hop transmission protocol
in underlay cognitive radio.
the received data. If the decoding at this node
is successful, it forwards the decoded data to Ti
at the second time slot. Then, node Ti combines
the data received from Ti1 and Ri by using MRC
technique.
If the relay Ri cannot receive the
source data successfully, it will not retransmit the
h i1,Ri
i1
hT1,PU
Ri
hRi ,PU
hRi ,T
i
data to Ti, and in this case, node Ti will decode
the source data from the data received from Ti1.
In the IR protocol, node Ti1 also broadcasts
the source data to Ti and Ri at the first time
slot. Then, nodes Ti and Ri try to decode the
received data. If Ti can decode the data correctly,
it sends back an ACK message to Ti and Ri to
inform the decoding status. In this case, the data
PU
transmission at this hop is successful and hence
the relay Ri does nothing. If the decoding at Ti
is unsuccessful, it generates a NACK message
to request a retransmission from Ri.
The relay
Fig. 2: Cooperative communication at the ith hop.
Ri then uses the second time slot to forward the
source data to Ti if this node can decode the
source data successfully.
In this case, node Ti
some methods on network layer such as Adhoc
On-demand Distance Vector (AODV) [28].
At each hop on the routing path, a secondary
relay is used to help the communication at that
hop. We denote Ri as the relay of the ith hop,
i ∈ {1,2,...,M}. In underlay cognitive radio, the
transmit power of all secondary transmitters must
satisfy the interference threshold given at the
primary user (PU) [29]1.
We assume that all of the nodes are equipped
with only a antenna and operate on half-duplex
mode. Next, we consider the data transmission
again attempts to decode the source data. If it
fails again, the data is dropped at this hop. The
advantage of the IR protocol, as compared with
the CC protocol, is that when the quality of the
Ti1 Ti link is good, the IR only uses one
time slot to transmit the data, which enhances the
spectrumeciency. Moreover, intheIRprotocol,
the receiver Ti does not use any combining
techniques to combine the received data, which
reduces the complexity of the decoding process
at this node.
In the DT protocol, node Ti1 directly
transmits the source data to node Ti. In this
1In Fig. 1, for ease of presentation, we would not show
the interference links between the secondary relays and the
primary user.
scheme, if Ti cannot decode the data successfully,
the data is dropped at this hop. We can observe
that the DT protocol only uses one time slot at
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Performance analysis of cooperative based multi hop transmission protocols in underlay cognitive radio with hardware impairment. n this paper, we study performances of multi-hop transmission protocols in underlay cognitive radio (CR) networks under impact of transceiver hardware impairment. In the considered protocols, cooperative communication is used to enhance reliability of data transmission at each hop on an established route between a secondary source and a secondary destination..

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VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 Performance Analysis of Cooperative-based Multi-hop Transmission Protocols in Underlay Cognitive Radio with Hardware Impairment Tran Trung Duy*, Vo Nguyen Quoc Bao Wireless Communication Lab, Posts and Telecommunications Institute of Technology (PTIT), Vietnam Abstract In this paper, we study performances of multi-hop transmission protocols in underlay cognitive radio (CR) networks under impact of transceiver hardware impairment. In the considered protocols, cooperative communication is used to enhance reliability of data transmission at each hop on an established route between a secondary source and a secondary destination. For performance evaluation, we derive exact and asymptotic closed-form expressions of outage probability and average number of time slots over Rayleigh fading channel. Then, computer simulations are performed to verify the derivations. Results present that the cooperative-based multi-hop transmission protocols can obtain better performance and diversity gain, as compared with multi-hop scheme using direct transmission (DT). However, with the same number of hops, these protocols use more time slots than the DT protocol. 2015 Published by VNU Journal of Sciences. Manuscript communication: received 01 May 2015, revised 10 June 2015, accepted 25 June 2015. Corresponding author: Tran Trung Duy, trantrungduy@ptithcm.edu.vn. Keywords: Hardware Impairment, Underlay Cognitive Radio, Cooperative Communication, Outage Probability. 1. Introduction In wireless networks such as adhoc networks [1] and wireless sensor networks [2], multi-hop relaying scenarios are used widely due to far distances between source node and destination node. In conventional multi-hop scheme, the direct transmission (DT) is used to relay the source’s data to the destination [3, 4]. Although the implementation of the DT protocol is easy in practice, its performance significantly degrades in fading environments [4]. To enhance performances for the multi-hop schemes, in published literature such as cluster-based cooperative protocol for multi-hop transmission was proposed and analyzed. In this protocol, the cluster node with the maximum instantaneous channel gain will serve as the sender for the next cluster. In [8, 9, 10, 11, 12], the authors proposed cooperative routing protocols in which intermediate nodes on the established route exploit the cooperative communication to forward the source data. Although performances of these protocols significantly are enhanced, as compared with the DT protocol, their implementation which requires a high synchronization between all the intermediate nodes, is a very difficult work. [5, 6], the authors proposed multi-hop diversity Recently, multi-hop relaying protocols in relaying protocols in which a relay is selected to cooperate with the transmitter at each hop cognitive radio (CR) networks have gained much attention as an efficient method to enhance the to forward the data to next hop. In [7], a coverage and channel capacity for secondary 16 T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 networks. Different with the conventional • We propose two multi-hop protocols in wireless networks, transmit powers of secondary users are limited by interference thresholds given which either conventional cooperative (CC) protocol or incremental cooperative (IR) by primary users (PU) [13, 14]. Due to protocol [27] is used to enhance quality the limited power, performances of multi-hop of the data transmission at each hop. In CR protocols significantly degrades [15, 16], especially in CR schemes with multiple PUs [17]. Again, cooperative communication protocols are employed to enhance quality of service (QoS) for the CC protocol, the receiver at each hop is equipped with maximal ratio combining (MRC) technique to combine the received data [27]. In the IR protocol, the relay link the secondary networks. In [18, 19], underlay is only used if the quality of the direct link is cooperative routing protocols with and without using combining techniques were proposed and analyzed, respectively. Results in [18, 19] presented that the proposed schemes provide an impressive performance gain as compared with the DT model. So far, almost published works related to the multi-hop networks assumed that the transceivers are perfect. However, in practice, they are suffered from impairments due to I/Q imbalance, high power amplifier non-linearities and phase noise [20]. Due to the hardware noises, the channel capacity obtained at high signal-to-noise ratio (SNR) region is limited [21]. In [22, 23], the authors considered two-way relaying protocols under the presence of the hardware impairments over Rayleigh fading channel and Nakagami-m fading channel, respectively. Works in [24] and [25] proposed relay selection methods to obtain diversity order as well as compensate the performance loss due to the hardware impairment. To the best of our knowledge, the most related to our work is the cognitive decode-and-forward relaying protocol proposed in [26]. However, the authors in [26] only considered the dual-hop network with selection combining technique at the destination. Moreover, only poor [27]. • We derive exact closed-form expressions of outage probability for the proposed schemes over Rayleigh fading channels. Moreover, we also derive an exact expression of average number of the time slots for the IR protocol. Then, Monte-Carlo simulations are presented to verify our derivations. • To provide more insights into the system performance, we also derive the asymptotic outage probability where both diversity and coding gains are obtained. • Finally, we compare the performance of the proposed protocols with the DT protocol to show the advantages of our schemes. The rest of this paper is organized as follows. The system model of the proposed protocols is described in Section II. In Section III, the expressions of the outage probability and the average number of time slots are derived. The simulation results are shown in Section III. Finally, this paper is concluded in Section V. 2. System Model outage probability of the proposed scheme was Figure 1 illustrates the system model of evaluated in [26], while other important metrics the proposed cooperative-aided multi-hop such as diversity gain and spectrum efficiency transmission protocols in underlay cognitive were not considered. In this paper, we study performances of cooperative-based multi-hop protocols in underlay CR networks under the radio. In this figure, the secondary source T0 transmits its data to the secondary destination TM via a multi-hop model. We assume that an M-hop impact of the hardware impairment. The main route between the secondary source and the contributions of this paper can be summarized as secondary destination (with M −1 intermediate follows: nodes, i.e., T1,T2,...,TM−1) is established by T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 17 R1 R2 RM at the ith hop with three different techniques (see Fig. 2), i.e., conventional cooperation (CC), incremental cooperation (IR) and direct 0 1 2 TM1 TM transmission (DT). In the CC protocol, the data transmission at the ith hop is split into two time slots. At the first Data links PU Interference links Fig. 1: Cooperative-aided multi-hop transmission protocol in underlay cognitive radio. Ri h i1,Ri hRi ,T hRi ,PU i1 i hT1,PU PU Fig. 2: Cooperative communication at the ith hop. some methods on network layer such as Adhoc On-demand Distance Vector (AODV) [28]. At each hop on the routing path, a secondary relay is used to help the communication at that hop. We denote Ri as the relay of the ith hop, i ∈ {1,2,...,M}. In underlay cognitive radio, the transmit power of all secondary transmitters must satisfy the interference threshold given at the primary user (PU) [29]1. We assume that all of the nodes are equipped with only a antenna and operate on half-duplex mode. Next, we consider the data transmission 1In Fig. 1, for ease of presentation, we would not show the interference links between the secondary relays and the primary user. time slot, node Ti−1, which is assumed to receive the source data successfully before, transmits the source data to node Ti and relay Ri. At the end of the first time slot, relay Ri attempts to decode the received data. If the decoding at this node is successful, it forwards the decoded data to Ti at the second time slot. Then, node Ti combines the data received from Ti−1 and Ri by using MRC technique. If the relay Ri cannot receive the source data successfully, it will not retransmit the data to Ti, and in this case, node Ti will decode the source data from the data received from Ti−1. In the IR protocol, node Ti−1 also broadcasts the source data to Ti and Ri at the first time slot. Then, nodes Ti and Ri try to decode the received data. If Ti can decode the data correctly, it sends back an ACK message to Ti and Ri to inform the decoding status. In this case, the data transmission at this hop is successful and hence the relay Ri does nothing. If the decoding at Ti is unsuccessful, it generates a NACK message to request a retransmission from Ri. The relay Ri then uses the second time slot to forward the source data to Ti if this node can decode the source data successfully. In this case, node Ti again attempts to decode the source data. If it fails again, the data is dropped at this hop. The advantage of the IR protocol, as compared with the CC protocol, is that when the quality of the Ti−1 → Ti link is good, the IR only uses one time slot to transmit the data, which enhances the spectrumefficiency. Moreover, intheIRprotocol, the receiver Ti does not use any combining techniques to combine the received data, which reduces the complexity of the decoding process at this node. In the DT protocol, node Ti−1 directly transmits the source data to node Ti. In this scheme, if Ti cannot decode the data successfully, the data is dropped at this hop. We can observe that the DT protocol only uses one time slot at 18 T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 each hop. However, the data transmission at each hop of this protocol is less reliable than that of the CC and IR protocols. Similar to [29, 30, 31], the transmit power PX is limited by the interference threshold Ith at the PU as follows: Hereafter, we denote CC (or IR or DT) as the multi-hop transmission scheme in which the CC PX = Ith/γX,PU, (4) (or IR or DT) technique is used to transmit the data at each hop. We also assume that the density of secondary users in secondary network is high enough so that each hop on the routing path can select a secondary relay for the cooperation. 3. Performance Evaluation 3.1. Channel model Let us denote hX,Y as the channel coefficient between nodes X and Y, where X,Y ∈ {Ti−1,Ri,Ti,PU} and i ∈ {1,2,...,M}. Assume that hX,Y follows Rayleigh distribution, hence, channel gain γX,Y, i.e., γX,Y = |hX,Y|2, is an exponential random variable (RV). As presented in [6, eq. (1)], the cumulative density function (CDF) and the probability density function (PDF) of γX,Y can be given, respectively, as FγX,Y (z) =1 −exp −λX,Yz, (1) fγX,Y (z) =λX,Yexp −λX,Yz , (2) where λX,Y = dβ with dX,Y being the distance between X and Y and β being the path-loss exponent. 3.2. Signal-to-noise and interference ratio (SNIR) formulation Considering the communication between the transmitter X and the receiver Y, X ∈ {Ti−1,Ri}, Y ∈ {Ti,Ri}, the data received at Y can be expressed by rY = pPXhX,Y x +ηt +ηr +gY, (3) where PX is transmit power of X, x is the source data, ηt is hardware noise caused by the impairment in the transmitter X, ηr is noise from the hardware impairment in the receiver Y and gY is Gaussian noise at Y, which is modeled as Gaussian RV with zero-mean and variance σ2. Considering the hardware noises ηt and ηr , they can be theoretically modeled as in [21]: ηX ∼ CN 0,κXPX , (5) ηr ∼ CN 0,κr PX|hX,Y|2 , (6) where CN (a,b) indicates circularly-symmetric complex Gaussian distributed variables in which a and b are mean and variances, respectively, κt and κr , κt ,κr ≥ 0, characterize the level of hardware impairments in the transmitter X and receiver Y, respectively. For ease of presentation and analysis, we assume that all of the nodes have the same structure so that their hardware impairment levels are same, i.e., κt = κ1 and κr = κ2. However, if the hardware impairment levels are different, the obtained results in this paper are still used to derive the upper-bound and lower-bound expressions of the outage probability for the considered protocols. From (3)-(5), the instantaneous signal-to-noise and interference ratio (SNIR) received at Y can be expressed as γX,YIth/γX,PU X,Y (κ1 +κ2)γX,YIth/γX,PU +σ2 By using (7), we can obtain the instantaneous SNIR of the Ti−1 → Ti, Ti−1 → Ri and Ri → Ti links, respectively as QγTi−1,Ti/γTi−1,PU i−1 i κQγTi−1,Ti/γTi−1,PU +1 QγTi−1,Ri/γTi−1,PU i−1 i κQγTi−1,Ri/γTi−1,PU +1 ΨRi,Ti = κQγRRi,/γRRi,PU 1, (8) where Q = Ith/σ2 and κ = κt + κr . Moreover, if MRC combiner is used, the SNIR received at Ti can be obtained as [29, eq. (8)] ΨMRC = ΨTi−1,Ti +ΨRi,Ti. (9) T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 19 3.3. Outage probability analysis In this subsection, we derive exact and asymptotic expressions of outage probability for the considered protocols. Outage probability is defined as the probability that the received SNIR at a receiver is less than a predetermined threshold, i.e., γth. With this definition, a receiver can be assumed to decode the data successfully if its received SNIR is above the threshold γth. Otherwise, this node cannot receive the data correctly. 3.3.1. DT protocol In this protocol, the outage probability at the ith hop can be given by OutDT = PrΨTi−1,Ti < γth. (10) Substituting ΨTi−1,Ti in (8) into (10) yields 1; if κ≥1/γ Outi =Pr γTi−1,PU < (1−κγth)Q ;if κ<1/γth . (11) We can observe from (11) that when the hardware impairment level κ is larger than 1/γth, the communication between Ti−1 and Ti is always in outage. For κ < 1/γth, the outage probability can be calculated by using [29, eq. (3)] as OutDT = λTi−1,Tiγth +λT1 1,PU (1 −κγth)Q. (12) Due to the independence of hops, the end-to-end outage probability of the DT protocol can be given, similarly as [5, eq. (15)] Pout = 1 −Y1 −OutDT. (13) i=1 By substituting OutDT in (12) into (13), we can obtain an exact closed-form expression of the outage probability for the DT protocol. It is obvious from (12) and (13) that the end-to-end outage probability increases with the increasing of κ and the decreasing of Q. To provide more insights into the outage performance, we next derive an asymptotic expression for Pout at high Q value, i.e., Q → +∞. Indeed, by using the approximation x/(1 + x) x→0 x, i.e., x = λTi−1,Tiγth/ λTi−1,PU (1 −κγth)Q , for (12), we have OutDT Q→+∞ λTii− ,PU 1 −κγth Q. (14) Then, an approximate expression of Pout at high Q values can be given by DT Q→+∞ X DT out i i=1  M  ≈i=1 λTii− ,PU  1 −κγth Q. (15) From (15), the diversity gain of the DT scheme can be easily determined as logPDT DivDT = −Qlim∞ log(Q) ! ! λTi−1,Ti γth 1 λT ,PU 1−κγth Q = −Qlim∞ log(Q) = 1. (16) As shown in (16), the DT scheme obtains the diversity order of 1 but its coding gain is reduced by an amount of GDT = −10log10 (1 −κγth), as compared with the corresponding scheme in which transceiver hardware is perfect. 3.3.2. IR protocol In this protocol, the outage probability at the ith hop can be formulated by OutIR = PrΨTi−1,Ti < γth,ΨTi−1,Ri < γth (17) +Pr ΨTi−1,Ti < γth,ΨTi−1,Ri ≥ γth,ΨRi,Ti < γth . The first term in (17) presents probability that nodes Ri and Ti cannot decode the data correctly in the first time slot, while the second term indicates the event the relay Ri correctly receives the data but the decoding status at Ti at both time slots is unsuccessful. 20 T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 IR λTi−1,PU (1 −κγth)Q λTi−1,PU (1 −κγth)Q i λTi−1,PU (1 −κγth)Q +λTi−1,Tiγth λTi−1,PU (1 −κγth)Q +λTi−1,Riγth λTi−1,PU (1 −κγth)Q λTi−1,PU (1 −κγth)Q + λTi−1,Ti +λTi−1,Ri γth λTi−1,PU (1 −κγth)Q λTi−1,PU (1 −κγth)Q λTi−1,PU (1 −κγth)Q +λTi−1,Riγth λTi−1,PU (1 −κγth)Q + λTi−1,Ti +λTi−1,Ri γth λRi,Tiγth λRi,Tiγth +λRi,PU (1 −κγth)Q (18) Proposition 1: Under the presence of i.e., hardware impairment, if κ ≥ 1/γth then OutIR = 1, and if κ < 1/γth, OutIR can be expressed by an exact closed-form expression as in (18) at the top of next page. logPIR DivIR = −Qlim∞ log(Q) = 2. (21) Proof With κ ≥ 1/γth, we can easily obtain OutIR = 1. For the case where κ < 1/γth, the proof is given in Appendix A. Also, the end-to-end outage probability of the IR protocol can be expressed as Pout = 1 −Y1 −OutIR. (19) i=1 In order to provide useful insights into the system performance such as diversity gain, we derive the asymptotic expression for Pout at high Q values (see Corollary 1 below). Corollary 1: When κ < 1/γth, the end-to-end outage probability Pout can be approximated at high Q region by Moreover, we can see from (20) that due to the hardware impairment, the coding gain loss is GIR = −20log10 (1 −κγth). 3.3.3. CC protocol In this protocol, we can formulate the outage probability at the ith hop as follows: OutCC =PrΨTi−1,Ri < γth,ΨTi−1,Ti < γth +Pr ΨTi−1,Ri ≥ γth,ΨMRC < γth . (22) In the RHS of the equation above, the first term takes the same from with that in (17), while the second term presents the probability that Ri can decode the data correctly but Ti cannot. Next, we will present the exact expression of OutCC via Proposition 2. IR Q→+∞ X λTi−1,Ti out i=1 !Ti−1,PU th 1 −κγth Q2 2λTi−1,Ri λRi,Ti ! λTi−1,PU λRi,PU (20) Proposition 2: If κ ≥ 1/γth, the outage probability OutCC equals 1, otherwise, i.e., κ < 1/γth, an exact closed-form expression of OutCC can be given by (23) (see the top of next page), where a0, a1, a2, b1 and b2 are given by (C.10) in Appendix C. Proof We proved this Corollary in Appendix B. From the results in (20), it can be obtained that the IR protocol provides a diversity order of 2, Proof Also, we easily obtain that OutIR = 1 if κ ≥ 1/γth. In the case that κ < 1/γth, we will present the proof in Appendix C. T.T. Duy, V.N.Q. Bao / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 2 (2015) 15–28 21 OutCC = 1 − λTi−1,PUγth +λTi−1,Tith1 −κγth)Q − λTi−1,PUγth +λTi−1,Rith1 −κγth)Q λTi−1,PUγth b1γth a1 (a2 −γth) λTi−1,PUγth + λTi−1,Ti +λTi−1,Ri (1 −κγth)Q a1 (a1 −γth) (a1 −γth)a2 (23) Similarly, an exact expression of the end-to-end outage probability for the CC protocol is given as

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