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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