- Email: [email protected]
Wireless powered cooperative communications with direct links over correlated channels
Accepted Manuscript Wireless powered cooperative communications with direct links over correlated channels Dan Deng, Minghui Yu, Junjuan Xia, Zhenyu Na, Junhui Zhao, Qinghai Yang
PII: DOI: Reference:
S1874-4907(18)30051-X https://doi.org/10.1016/j.phycom.2018.03.013 PHYCOM 515
To appear in:
Physical Communication
Received date : 23 January 2018 Revised date : 11 March 2018 Accepted date : 24 March 2018 Please cite this article as: D. Deng, M. Yu, J. Xia, Z. Na, J. Zhao, Q. Yang, Wireless powered cooperative communications with direct links over correlated channels, Physical Communication (2018), https://doi.org/10.1016/j.phycom.2018.03.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Wireless Powered Cooperative Communications with Direct Links over Correlated Channels Dan Denga , Minghui Yua , Junjuan Xiab,∗, Zhenyu Nac , Junhui Zhaod , Qinghai Yange a Guangzhou
Panyu Polytechnic, Guangzhou, P.R. China, 511483. ([email protected]). University, Guangzhou, P.R. China, 510006. ([email protected]). c School of Information Science and Technology, Dalian Maritime University, Dalian 116026, China (e-mail:[email protected]). d School of Information Engineering, East China Jiaotong University, Nanchang, China (email: [email protected]). e State Key Laboratory on ISN, School of Telecommunications Engineering, Xidian University, Xi’an 710071, China, (e-mail:[email protected]) b GuangZhou
Abstract In this paper, we investigate the impact of correlated channels on the wireless powered cooperative networks, where the direct links between the source and destination exist and are correlated with the relaying links. In the considered system, the time switching-based relaying protocol of simultaneous wireless information and power transfer is used. In order to enhance the system performance, a better branch between the relaying link and the direct link is selected. We evaluate the system transmission performance by deriving the closed-form expression on outage probability as well as the asymptotic results for the proposed scheme, in the high regime of transmit power. Based on the theoretical analysis, we investigate the effects of the system parameters, such as channel correlation coefficient, average channel fading power, energy harvesting coefficient and slot allocation coefficient, on the system outage probability. Numerical results are provided to verify the theoretical analysis. Keywords: energy harvesting, cooperative system, correlated channels, selection combination, outage probability
∗ Corresponding
author Email address: [email protected] (Junjuan Xia)
Preprint submitted to Physical Communication
March 29, 2018
1. Introduction In recent years, many wireless techniques have arisen to tackle with the explosively increasing data transmission service[1, 2, 3, 4, 5]. Among these techniques, relaying is a promising technique to increase the wireless cover5
age, improve the transmission capacity without requiring additional transmit power[6, 7]. In addition, energy harvesting (EH) technique, which can collect wireless power from the environment, is a potential solution for future wireless networks [8, 9, 10]. Without battery deployment, energy harvesting scheme can provide low cost and convenient option for long-term low-power communica-
10
tions. Due to the excellent characteristics of energy harvesting, it has attracted much attentions in both academic and industry area [11, 12]. Based on the simultaneous wireless information and power transfer (SWIPT) with perfect and imperfect channel state information, Ref. [13] focused on the transmission
15
power minimum for multiple-input single-output multicasting systems, while optimal mode switching algorithm is studied in [14] . Moreover, joint antenna selection and transmit covariance matrix design optimization problem for energy harvesting systems is investigated in [15]. There are some other extended works on the transmission security for the wireless networks [16, 17, 18, 19].
20
On the other hand, selection diversity has been widely studied to improve the reliability of the wireless links by exploiting the freedom of the multiuser systems[20, 21, 22, 23, 24]. Also, user selection scheme can be joint designed with other emerging wireless technologies. For example, Ref.[9] proposed joint source and relay selection for cooperative non-orthogonal multiple access (NO-
25
MA) systems. Based on the wireless edge caching deployment, Ref.[25] analyzed the outage performance as well as their diversity order and coding gain with different caching placement solutions. While Ref.[26] investigated the secure relay and jammer selection for physical layer security in terms of secrecy outage probability.
30
Moreover, wireless energy harvesting can be compatible with cooperative
2
networks [27]. Considering an amplify-and-forward relaying network with energy constrains, Ref. In [28], the authors proposed both time switching-based and power splitting-based relaying protocols. In particular, at low SNR, the time switching-based protocol outperforms the power splitting-based protocol. As an 35
extension, a time-switching based energy harvesting and information transmission protocol is proposed in [29] using intelligent slot allocation scheme. Results show that the proposed continuous time EH outperforms the fixed time-duration EH scheme. Besides, the outage performance for energy harvesting relay-aided cooperative network is analyzed in [30] by deriving closed-form expression of
40
outage probability. Most of the above works ignoring the direct links from the source to the destinations. In the severe shadowing case, it is reasonable to assume that there is no direct links from the source to the destinations. However, in the moderate shadowing environments, there usually exist direct links which can be useful to
45
improve the performance of the cooperative systems. On the other hand, the theoretical analysis is more complicated due to the combination of the direct links and the relay links [21]. There are some insight works on the role of the direct links for the cooperative systems [31, 32, 33, 34]. In this paper, we investigate the outage probability with selection combina-
50
tion for wireless powered relaying system with the help of a direct links. In the considered system, the time switching-based relaying protocol of simultaneous wireless information and power transfer is used. In order to enhance the system performance, a better branch between the relaying link and the direct link is selected. We derive the closed-form expression on outage probability as well
55
as the asymptotic results for the proposed scheme. Based on the theoretical analysis, we find that the large channel correlation coefficient can be benefit to the outage performance, while it has no effect on the diversity order. Notations: We use CN (µ, σ 2 ) to represent the circularly symmetric complex
Gaussian random variable with mean µ and variance σ 2 , fX (x) and FX (x) 60
denote the probability density function and cumulative distribution function of a random variance X, respectively, EX (·) means the statistical expectation 3
Energy Harvesting Relay
R
S
D Direct Link
Figure 1: System model of Wireless Powered Cooperative Communications with Direct links
function with respect to X, and hR−D denotes the simultaneous channel fading coefficient of the link from R to D.
2. System Model 65
As shown in Fig.1, we consider a decode-and-forward (DF) wireless powered relaying system, which consists of a source station, a wireless powered relay station and a destination, denoted as S, R and D, respectively. It is assumed that each station works in half duplex mode and is equipped with one single antenna due to the equipment size or the power consumption constraint. In addition, all
70
other wireless channels are assumed to be quasi-static Rayleigh block fading[35]. hSR ∼ CN (0, α1 ), hRD ∼ CN (0, α2 ) and hRD ∼ CN (0, β) denote the channel fading coefficients of links S − R, R − D and S − D, respectively. Note that the channel fading coefficients hSR and hRD are assumed to be correlated because of radio scattering or antenna deployment [36, 37, 38].
75
In the considered system, the source station transmits messages to the destination station with the help of the direct link. Similar with Ref. [29, 28], the time switching-based relaying protocol of simultaneous wireless information and
4
Energy Harvesting
S->R S->D Information Transmission
R->D Information Transmission
Figure 2: Time switching-based energy harvesting relaying protocol
power transfer is adopted at the relay station, which is depicted in Fig.2.
1
In the energy harvesting (EH) phase of the relaying protocol, which is the 80
first ξT seconds of the each time slot, the relay station harvests as much as possible energy from the wireless signal transmitted by the source station. ξ ∈ (0, 1) is the time allocation factor for the EH phase, and T is the length of each time slot. The harvested energy can be used in the following information transfer. Specifically, the energy consumed by the receiver of the relay station is
85
negligible compared with the transmission power during the information transfer phase [29]. During the information transfer (IT) phase, the first half part of time
1−ξ 2 T
is used for the transmission from S to R and D, simultaneously. While the second half part 90
1−ξ 2 T
is used for the transmission from R to D. In this phase,
the relay station firstly decodes the signal and forwards to the destination using the energy harvested in the EH phase. At the destination station, in order to improve the quality of service, the selection combination receiver is deployed. That is, the destination station 1
Both time switching-based and power switching-based protocols are widely studied in the
previous works [28, 29, 30]. While in this paper time switching-based protocol is adopted, the reasons are given as follows. First, since only one RF module is needed in time switching-based protocol, it can be easily implemented with lower cost compared with power switching-based protocol. Second, previous works [28] have proved that, at low SNR, time switching-based protocol outperforms the power splitting-based protocol.
5
selects the better link from the relaying link and the direct link.
95
3. Outage Performance Analysis In this section, we will derive the closed-form analytical expressions on the outage probability for the wireless powered relaying system, as well as the asymptotic expressions for large transmission power. Based on the analytical expressions, the effects of the system parameters are revealed.
100
3.1. Analytical Expression First, consider the EH phase in the relaying protocol, the signal received by relay station can be given as rR =
√
PS hSR x + nR ,
(1)
where PS denotes the transmission power of S, x is the transmitted signal from the source station with normalized power, and nR ∼ CN (0, N0 ) is the additive white Gaussian noise (AWGN) signal received by the relay station. Then the signal-to-noise ratio (SNR) at the relay station in the EH phase can be given as γSR = where γ =
PS N0 ,
PS |hSR |2 = γu, N0
(2)
and u = |hSR |2 is the instantaneous channel fading power of
S − R link. In this phase, according to the relaying protocol in Fig.2, the harvested energy by the relay station can be expressed as ER = ηPS uξT,
(3)
where η is the energy conversion efficiency [9]. Similarly, the SNR of the direct link can be given as γSD =
PS |hSD |2 = γw, N0
where w = |hSD |2 is the instantaneous channel fading power of S − D link. 6
(4)
During the second IT phase, by using the harvested energy in EH phase, the relay regenerates the message x and forwards to the destination with power PR . Under the power constraint, we get PR =
ER 1−ξ 2 T
.
(5)
Substituting (3) into (5), we obtain PR = PS u 105
where θ =
2ηξ = PS uθ, 1−ξ
(6)
2ηξ 1−ξ .
In the phase, the signal received at the destination can be given as rD =
√
PR hRD x + nD ,
(7)
where nD ∼ CN (0, N0 ) is the AWGN signal received by D. By using (6), the SNR of R − D can be expressed as γRD =
PR |hRD |2 = γuθv, N0
(8)
Since decode-and-forward scheme is adopted by the relay station, the equivalent SNR of the relaying link can be given as γSRD = min{γSR , γRD } = γu min{1, θv}.
(9)
To enhance the quality of the links, the destination chooses the better link from the relaying link and the direct link. The equivalent SNR of the selected combination receiver at D can be expressed as γsc = max{γSD , γSRD } = γ max{w, u min{1, θv}}
(10)
Then the capacity of the system is obtain as Csc =
1 log2 (1 + γsc ). T
(11)
The outage probability is defined as the probability that the system capacity falls below a given target data rate. Given that the rate requirement is 7
predefined as Ct , the system outage probability is expressed as (12)
Psc = P r{Csc < Ct } = P r{γsc < γt }, where γt = 2T Ct − 1. By substituting (10) into (12), yields Psc = P r{γ max{w, u min{1, θv}} < γt } { { } γt } = P r max w, u min{1, θv} < γ { γt γt } = P r w < , uφ < . γ γ
(13)
where the definition of φ is given as φ = min{1, θv}.
Lemma 1. The probability density function of φ can be given as 1 e− θαx2 , if x < 1, θα2 fφ (x) = 0 , otherwise .
(14)
Proof: see Appendix A.
Lemma 2. Given the definition Am (µ) as follows, µ µ Am (µ) = Eφ {e− φ ( )m } φ
(15)
according to the Chebyshev-Gauss quadrature formula, we have the following approximation Am (µ) ≈ where
110
M π ∑ f (xk , µ, m), M
(16)
k=1
xk = cos (2k−1)π , 2M
2µ 2µ m f (x , µ, m)= e− 1+x k ( k 1+xk )
√
1−x2k − 1+xk 2α2 θ 2α2 θ e
(17) ,
and M is a tradeoff parameter between accuracy and computation complexity. Proof: see Appendix B. Moreover, the joint probability density function can be given as √ 2 ρxy I0 ( ) y x 1 − ρ α1 β α + β fu,w (x, y) = exp(− 1 ), (1 − ρ)α1 β 1−ρ 8
(18)
where ρ ∈ [0, 1) is the power correlation coefficient [39] between u and w, I0 (·) denotes the zero-order modified Bessel function of the first kind, as eq.(8.406) in [40]. 115
Particularly, ρ = 0 indicates that they are mutually independent. Using infinite series expansion as eq.(8.455) in [40] on (18), and ignoring the high order small quantities, I0 (·) can be expressed as I0 (x) =
∞ ∑
k=0
N
∑ x2k x2k ≈ , 4k (k!)2 4k (k!)2
(19)
k=0
where N denotes the truncation parameter, which is a tradeoff parameter between accuracy and computation complexity [39].
Specifically, it has been
proved in [41] that the series converges and the truncation error is exponentially bounded. Thus, the joint probability density function can be re-expressed as fu,w (x, y) ≈
N ∑
ck xk y k e
−α
x 1 (1−ρ)
y
e− β(1−ρ) ,
(20)
k=0
where ck =
ρk . (α1 β)k+1 (1 − ρ)2k+1 (k!)2
(21)
By substituting (20) into (13), yields Psc = Eφ
∫
γt φγ
x=0
≈ Eφ =
∫
N ∑
k=0
γt φγ
x=0
ck
∫
γt γ
fu,w (x, y)dydx.
y=0
∫
{∫
γt γ
N ∑
−α
ck xk y k e
x 1 (1−ρ)
y
e− β(1−ρ) dydx
(22)
y=0 k=0
} y y k e− β(1−ρ) dy Eφ y=0 | {z }| γt γ
{∫
P1
γt φγ
x=0
−α
xk e {z
x 1 (1−ρ)
dx
}
}
P2
Theorem 1. The outage probability of selection combination algorithm for the wireless powered relaying cooperative system can be given as follows Psc ≈
N ∑
k=0
q1
ρk (1 − ρ)[1 − e− γ (
k ∑ ( qγ1 )m
m=0
9
m!
)][1 −
k ∑ Am ( qγ2 )
m=0
m!
],
(23)
where
q = 1 q = 2
γt β(1−ρ) , γt α1 (1−ρ) ,
(24)
and the value of Am (µ) is given by Lemma 2. Proof:
Consider the item of P1 in (22), by using the incomplete gamma
function as eq.(3.381) in [40], we obtain P1 = [β(1 − ρ)](k+1) γ(k + 1,
γt ) γβ(1 − ρ)
(25)
According to the series expansion of incomplete gamma function as eq.(8.352) in [40], that is n ∑ xm )] m! m=0
γ(n + 1, x) = n k![1 − e− γβ(1−ρ) (
γt m k ( ∑ γβ(1−ρ) )
m=0
m!
)]
(27)
Then, we will consider the item of P2 in (22). Similar with the analysis on P1 , by using the incomplete gamma function and its series expansion (26) on P2 , we have γt m } k ( { ∑ γt φγα1 (1−ρ) ) − P2 = Eφ [α1 (1 − ρ)]k+1 k![1 − e φγα1 (1−ρ) ] . m! m=0
(28)
Apply (16) of Lemma 2 on (28), we obtain the analytical expression on P2 as follows γt k A [ { } ∑ m γα1 (1−ρ) ] P2 = [α1 (1 − ρ)]k+1 k![1 − ] . m! m=0
(29)
Substituting (27) and (29) into (22), we obtain the analytical expression on
10
outage probability, i.e. Psc ≈ =
N ∑
k=0 N ∑
k=0
γt
ρk (1 − ρ)[1 − e− γβ(1−ρ) ( k
ρ (1 − ρ) [1 − e
−
q1 γ
(
γt m k ( ∑ γβ(1−ρ) )
k ∑ ( qγ1 )m
m=0
|
m!
m=0
{z
m!
)] [1 − }|
H1
)][1 −
γt k A [ ∑ m γα1 (1−ρ) ]
m=0
k ∑ Am ( qγ2 )
m!
m=0
{z
]
].
}
H2
m!
(30)
This completes the proof of Theorem 1. 3.2. Asymptotic Analysis In order to have a deep insight into the outage performance for wireless 120
powered cooperative system, the asymptotic analysis is present given that the transmission power is large enough. In this case, it is assumed that γ → ∞. Theorem 2. Given that the transmission power of the source station is large enough, the outage probability of wireless powered cooperative system with selection combination is given as follows: ∞ Psc ≈
γt γt [1 − A0 ( )]. γβ α1 γ(1 − ρ)
(31)
Proof: Firstly, consider the first item H1 in (30), we can re-write it as follows q1
H1 = 1 − e− γ ( =1−e
−
q1 γ
(
k ∑ ( qγ1 )m
m=0 ∞ ∑
m!
)
( qγ1 )m m!
m=0
−
∞ ∑ ( qγ1 )m
m=k+1
m!
(32) )
Note that the infinite series expansion of exponential function can be expressed as ex =
∞ ∑ xk
k=0
k!
.
(33)
Applying the series expansion formula on (32), yields q1
q1
H1 = 1 − e− γ [e γ − =e
−
q1 γ
∞ ∑
∞ ∑ ( qγ1 )m
m=k+1 ( qγ1 )m
m=k+1
11
m!
m!
] (34)
When γ → ∞, we can ignoring the high order items, i.e., only k = 0 is selected, q1
H1 ≈ e− γ (
q1 ) γ
(35)
By using the approximation that ex ≈ 1 + x, we can rewrite H1 as q1
H 1 ≈ e− γ (
q1 q1 q1 q1 ) ≈ (1 − ) ≈ . γ γ γ γ
(36)
Thus, the expression on Psc in (22) can be given as ∞ Psc ≈ (1 − ρ)
q1 q2 [1 − A0 ( )]. γ γ
(37)
∞ Substituting the definitions of q1 and q2 in (24) into Psc , we obtain the
asymptotic outage probability in (31) in Theorem 2. Theorem 2 is proved. Based on the Theorem 2, we can make the following corollary. 125
Corollary 1: The asymptotic outage probability of the system is monotone increasing function with respect to the channel correlation coefficient. Proof: According to the definition of A0 (µ) in (15) of Lemma 2, it’s easy to prove that A0 (µ) is a strictly monotone decreasing function with respect ∞ to µ. Thus, Psc is monotone increasing function with respect to the channel
130
correlation coefficient ρ. The reason for this phenomenon is that the large channel correlation coefficient decreases the freedom between the relaying link and the direct link, which results in higher outage probability of the selective combination.
4. Simulation Results 135
In this section, simulation results are provided to verify the presented analysis. We investigate the effects of the system parameters, such as channel correlation coefficient, average channel fading power, energy harvesting coefficient and slot allocation coefficient, on the system outage probability [42, 43, 44, 45, 46].
12
In all simulation setup, we set the predefined requirement rate as Ct = 1bps/Hz, 140
and the truncation parameters are fixed as N = M = 30.
2
Fig.3 depicts the outage probability versus the channel correlation coefficient as a function of the system SNR γ. The system parameters are given as follows. The energy harvesting coefficient is 0.1, and the slot allocation coefficient is set as 0.5. The average channel fading powers of the three links are set the same, 145
i.e., α1 = α2 = 0.1, β = 0.01. And the channel correlation coefficient changes from 0, 0.5 and 0.9. With the setup of the system, we investigate the impact of channel correlation coefficient on the system performance. We can see from this figure that the simulation results match the analytical results in all SNR regions. Specifically, in high SNR region the analytical results converge to the
150
asymptotic line. Moreover, the outage probability increases with large channel correlation coefficient, which coincides with the result of Corollary 1. Besides, with different channel correlation coefficients, the slope of the asymptotic outage remains the same. In other words, although small channel correlation coefficient is benefit to the outage performance, it has no effect on the diversity order.
155
The effect of average channel fading power on outage probability is present in Fig.4. The system setup is given as follows. The energy harvesting coefficient is set as 0.1, the channel correlation coefficient is 0.9, and the slot allocation coefficient is set as 0.5. The average channel fading powers of hSR changes as 0.1, 0.5 and 1.0. While the average channel fading powers of hRD keeps the
160
same with that of hSR , i.e. α1 = α2 , and β = α1 ∗ α2 . We can see from this figure that average channel fading power shows significant impact on the system outage probability. Obviously, large channel fading power will improve the system performance, which coincides with our intuition. 2 Please
kindly note that the definition of M is given in (16) of Lemma 2. M is a tradeoff
parameter between accuracy and computation complexity for Am (µ). While the definition of N is given in (19). N denotes the truncation parameter, which is a tradeoff parameter between accuracy and computation complexity for I0 (x).
13
Outage probability
10 0
10 -1
ρ=0,0.5,0.9
η=0.1, ξ=0.5, α 1 =α 2 =0.1, β=0.01 10
-2
Analytical Simulation Asymptotic
0
5
10
15
20
25
30
35
SNR (dB)
Figure 3: Effect of channel correlation coefficient on outage probability
10 0 α 1 =0.1,0.5,1.0
Outage probability
10 -1
10 -2
10 -3
10 -4
η=0.1, ρ=0.9, ξ=0.5 Analytical Simulation Asymptotic
10 -5
0
5
10
15
20
25
30
35
SNR (dB)
Figure 4: Effect of average channel fading power on outage probability
14
Outage probability
10 0
10
-1
η=0.1,0.2,0.4
ρ=0.9, ξ=0.5, α 1 =α 2 =0.1, β=0.01 Analytical Simulation Asymptotic
10 -2
0
5
10
15
20
25
30
35
SNR (dB)
Figure 5: Effect of energy harvesting coefficient on outage probability
Fig.5 depicts the effect of energy harvesting coefficient on system perfor165
mance. The channel correlation coefficient is 0.9, and the slot allocation coefficient is set as 0.5. The average channel fading powers of the three links are set as α1 = α2 = 0.1, β = 0.01. While the energy harvesting coefficient changes as 0.1, 0.2 and 0.4. From this figure, we can see that large energy harvesting coefficient owns better outage performance. The reason is that the larger en-
170
ergy harvesting coefficient can collects more power used for forwarding wireless signal to the destination. Thus, the outage probability can be improved. Fig.6 depicts the effect of slot allocation coefficient ξ on system performance, where the energy harvesting coefficient is set as 0.1 and the channel correlation coefficient is 0.9. The average channel fading powers of the three links are set
175
the same, i.e., α1 = α2 = β = 1. While the slot allocation coefficient changes as 0.1, 0.2 and 0.4. From this figure, we can see that , in this system setup, large ξ shows better performance than the small one. The reason for this phenomenon is that when ξ is relative small, the bottle neck of the system performance is
15
10
0
Outage probability
10 -1
10
-2
ξ=0.1,0.2,0.4 10 -3
10 -4
η=0.1, ρ=0.9, α 1 =α 2 =β=1.0 Analytical Simulation Asymptotic
10 -5
0
5
10
15
20
25
30
35
SNR (dB)
Figure 6: Effect of slot allocation coefficient on outage probability
the power consumption in the IT phase. 180
3
In this case, large ξ means more
energy can be harvested in the EH phase, and the outage performance can be enhanced.
5. Conclusion In this paper, we investigate outage probability of wireless powered cooperative system over correlated wireless channel, in which the better branch is 185
selected between the relaying link and the direct links. The effect of the system parameters on outage probability is studied by deriving the closed-form analytical expressions as well as the asymptotic expressions for large transmission power. Furthermore, simulation results are provided to verify the theoretical 3 The
slot allocation coefficient ξ is relative small, that is, the allocated time for EH phase
is not enough for the following IT phase. In this case, the transmission powers of both source and the relay are smaller than needed. Thus, the outage probability raises with smaller ξ, and the power consumption in the IT phase become the bottle neck of the system performance.
16
analysis. According to the asymptotic expressions, we find that, although the 190
large channel correlation coefficient can be benefit to the outage performance, it has no effect on the diversity order.
Acknowledgement This work was supported in part by the Science and Technology Program of Guangzhou, China, under Grant 201707010389, in part by the Scientific Re195
search Project of Guangzhou Municipal University under Grant 1201620439, in part by the Qingshanhu Young Scholar Program in GZPYP under Grant 2016Q001, in part by Comba Research Funds under Grant JX-PYP-201501 and Grant H2017007, in part by Guangdong big data technology research center for intelligent vocational education.
200
Appendix A. Proof of Lemma 1 According to the definition of φ, we can obtain the following cumulative distribution function Fφ (x) = P r{φ < x} = P r{min{1, θv} < x}
(A.1)
= 1 − P r{min{1, θv} ≥ x}. In the case of x ≥ 1, we have Fφ (x) = 1. While for the case of x < 1, we have Fφ (x) = 1 − P r{min{1, θv} ≥ x} = 1 − P r{θv ≥ x}
(A.2)
x
= 1 − e− θα2 . Taking a derivative on (A.1), we can get the probability density function of φ as in Lemma 1.
17
Appendix B. Proof of Lemma 2 According to the definition of Am (µ), using the probability density function of φ as in (14) of Lemma 1, we obtain µ µ Am (µ) = Eφ {e− φ ( )m } φ ∫ 1 µ µ = e− x ( )m fφ (x)dx x 0 ∫ 1 µ µ 1 − θαx 2 dx = e− x ( )m e x θα 2 0
Note that the Chebyshev-Gauss quadrature formula, that is ∫ 1 M ∑ g(x) √ dx ≈ Hk g(xk ), 1 − x2 −1 k=1 205
where xk = cos (2k−1)π and Hk = 2M
(B.1)
(B.2)
π M.
By applying the Chebyshev-Gauss quadrature and simple mathematical derivation on (B.1), we can obtain the (16) and (17) in Lemma 2. References [1] F. Zhou, L. Fan, X. Lei, G. Luo, H. Zhang, J. Zhao, Edge caching with 210
transmission schedule for multiuser multirelay networks, IEEE Communications Letters PP (99) (2018) 1–4. [2] G. Huang, D. Tang, Wireless information and power transfer in two-way OFDM amplify-and-forward relay networks, IEEE Communications Letters 20 (8) (2016) 1563–1566.
215
[3] L. Fan, X. Lei, N. Yang, T. Q. Duong, G. K. Karagiannidis, Secure multiple amplify-and-forward relaying with cochannel interference, IEEE Journal of Sel. Topics in Sig. Proc. 10 (8) (2016) 1494–1505. [4] G. Liu, H. Liu, H. Chen, C. Zhou, L. Shu, Position-based adaptive quantization for target location estimation in wireless sensor networks using one-
220
bit data, Wireless Communications and Mobile Computing 16 (8) (2016) 929–941. 18
[5] R. Zhao, Y. Yuan, L. Fan, Y. He, Secrecy performance analysis of cognitive decode-and-forward relay networks in Nakagami-m fading channels, IEEE Trans. Commun. 65 (2) (2017) 549–563. 225
[6] J. Li, X. Jiang, Y. Yan, W. Yu, S. S. Song, M. H. Lee, Low complexity detection for quadrature spatial modulation systems, Wireless Personal Communications 95 (4) (2017) 4171–4183. [7] W. Tan, M. Matthaiou, S. Jin, X. Li, Spectral efficiency of DFT-based processing hybrid architectures in massive MIMO, IEEE Wireless Commun.
230
Lett. 6 (5) (2017) 586–589. [8] N. Zhao, F. R. Yu, V. C. M. Leung, Wireless energy harvesting in interference alignment networks, IEEE Communications Magazine 53 (6) (2015) 72–78. [9] D. Deng, L. Fan, X. Lei, W. Tan, D. Xie, Joint user and relay selection for
235
cooperative noma networks, IEEE Access 5 (1) (2017) 20220–20227. [10] J. Guo, N. Zhao, F. R. Yu, X. Liu, V. C. M. Leung, Exploiting adversarial jamming signals for energy harvesting in interference networks, IEEE Trans. Wireless Communications 16 (2) (2017) 1267–1280. [11] N. Zhao, S. Zhang, F. R. Yu, Y. Chen, A. Nallanathan, V. C. M. Leung,
240
Exploiting interference for energy harvesting: A survey, research issues, and challenges, IEEE Access 5 (2017) 10403–10421. [12] N. Zhao, F. R. Yu, V. C. M. Leung, Opportunistic communications in interference alignment networks with wireless power transfer, IEEE Wireless Commun. 22 (1) (2015) 88–95.
245
[13] M. R. A. Khandaker, K. K. Wong, Swipt in miso multicasting systems, IEEE Wireless Communications Letters 3 (3) (2014) 277–280. [14] L. Liu, R. Zhang, K. C. Chua, Wireless information transfer with opportunistic energy harvesting, IEEE Transactions on Wireless Communications 12 (1) (2013) 288–300. 19
250
[15] S. Zhao, Q. Li, Q. Zhang, J. Qin, Antenna selection for simultaneous wireless information and power transfer in mimo systems, IEEE Communications Letters 18 (5) (2014) 789–792. [16] G. Liu, B. Xu, H. Chen, C. Zhang, X. Hu, Energy-efficient scheduling for distributed estimation in wireless sensor and actuator networks with
255
kriging, Ad Hoc & Sensor Wireless Networks 27 (3-4) (2015) 197–222. [17] G. Huang, W. Tu, Optimal resource allocation in wireless-powered OFDM relay networks, Computer Networks 104 (2016) 94–107. [18] G. Liu, J. Yao, Y. Liu, H. Chen, D. Tang, Channel-aware adaptive quantization method for source localization in wireless sensor networks, Internation-
260
al Journal of Distributed Sensor Networks 11 (2015) 214081:1–214081:13. [19] G. Huang, W. Tu, Wireless information and energy transfer in nonregenerative OFDM AF relay systems, Wireless Personal Communications 94 (4) (2017) 3131–3146. [20] G. Pan, H. Lei, Y. Deng, L. Fan, J. Yang, Y. Chen, Z. Ding, On secrecy
265
performance of MISO SWIPT systems with TAS and imperfect CSI, IEEE Trans. Commun. 64 (9) (2016) 3831–3843. [21] L. Fan, S. Zhang, T. Q. Duong, G. K. Karagiannidis, Secure switch-andstay combining (SSSC) for cognitive relay networks, IEEE Trans. Commun. 64 (1) (2016) 70–82.
270
[22] L. Fan, X. Lei, N. Yang, T. Q. Duong, G. K. Karagiannidis, Secrecy cooperative networks with outdated relay selection over correlated fading channels, IEEE Trans on Vehicular Technology 66 (8) (2017) 7599–7603. [23] X. Lai, W. Zou, X. Li, L. Fan, Multiuser energy harvesting relaying system with direct links, IET Commun. 11 (12) (2017) 1846–1852.
275
[24] X. Wang, H. Zhang, L. Fan, Y. Li, Performance of distributed switchand-stay combining for cognitive relay networks with primary transceiver, Wireless Personal Commun. 97 (2) (2017) 3031–3042. 20
[25] M. Tao, E. Chen, H. Zhou, W. Yu, Content-centric sparse multicast beamforming for cache-enabled cloud ran, IEEE Transactions on Wireless Com280
munications 15 (9) (2016) 6118–6131. [26] H. Hui, A. Swindlehurst, G. Li, J. Liang, Secure relay and jammer selection for physical layer security, Signal Processing Letters, IEEE 22 (8) (2015) 1147–1151. [27] Y. Luo, J. Zhang, K. B. Letaief, Relay selection for energy harvesting co-
285
operative communication systems, in: Global Communications Conference, 2013, pp. 2514–2519. [28] A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy, Relaying protocols for wireless energy harvesting and information processing, IEEE Transactions on Wireless Communications 12 (7) (2013) 3622–3636.
290
[29] A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy, Wireless-powered relays in cooperative communications: Time-switching relaying protocols and throughput analysis, IEEE Transactions on Communications 63 (5) (2015) 1607–1622. [30] T. Li, P. Fan, K. B. Letaief, Outage probability of energy harvesting relay-
295
aided cooperative networks over rayleigh fading channel, IEEE Transactions on Vehicular Technology 65 (2) (2016) 972–978. [31] F. Shi, W. Tan, J. Xia, D. Xie, L. Fan, X. Liu, Hybrid cache placement for physical-layer security in cooperative networks, IEEE Access 6 (2018) 8098–8108.
300
[32] V. N. Q. Bao, T. Q. Duong, D. B. D. Costa, G. C. Alexandropoulos, A. Nallanathan, Cognitive amplify-and-forward relaying with best relay selection in non-identical rayleigh fading, IEEE Communications Letters 17 (3) (2013) 475–478.
21
[33] X. Liu, X. Zhang, D. Yang, Outage probability analysis of multiuser 305
amplify-and-forward relay network with the source-to-destination links, IEEE Communications Letters 15 (2) (2011) 202–204. [34] F. R. V. Guimaraes, D. B. D. Costa, T. A. Tsiftsis, C. C. Cavalcante, G. K. Karagiannidis, Multiuser and multirelay cognitive radio networks under spectrum-sharing constraints, IEEE Transactions on Vehicular Technology
310
63 (1) (2014) 433–439. [35] J. Li, M. Wen, X. Jiang, W. Duan, Space-time multiple-mode orthogonal frequency division multiplexing with index modulation, IEEE Access 5 (2017) 23212–23222. [36] X. Lai, W. Zou, D. Xie, X. Li, L. Fan, DF relaying networks with randomly
315
distributed interferers, IEEE Access 5 (2017) 18909–18917. [37] W. Tan, S. Jin, C. Wen, T. Jiang, Spectral efficiency of multi-user millimeter wave systems under single path with uniform rectangular arrays, EURASIP J. Wireless Comm. and Networking 181 (2017, DOI:10.1186/s13638-017-0966-4) 1–13.
320
[38] F. Zhou, L. Fan, N. Wang, G. Luo, J. Tang, W. Chen, A cache-aided communication scheme for downlink coordinated multipoint transmission, IEEE Access 6 (2018) 1416–1427. [39] L. Fan, R. Zhao, F. K. Gong, N. Yang, G. Karagiannidis, Secure multiple amplify-and-forward relaying over correlated fading channels, IEEE
325
Transactions on Communications 7 (65) (2017) 2811–2820. [40] I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products, 7th Ed, Academic Press,Elsevier Inc, San Diego, California 92101-4495, USA, 2007. [41] X. Sun, J. Wang, W. Xu, C. Zhao, Performance of secure communications over correlated fading channels, IEEE Signal Processing Letters 19 (8)
330
(2012) 479–482.
22
[42] J. Yang, H. Wu, G. Huang, Y. Liang, Y. Liao, Modeling and coupling effect evaluation of thermal conductivity of ternary opacifier/fiber/aerogel composites for super-thermal insulation, Materials and Design 133 (5) (2017) 224–236. 335
[43] Y. Liang, H. Wu, G. Huang, J. Yang, H. Wang, Thermal performance and service life of vacuum insulation panels with aerogel composite cores, Energy and Buildings 154 (2017) 606–617. [44] J. Yang, H. Wu, M. Wang, et al., Prediction and optimization of radiative thermal properties of nano TiO2 assembled fibrous insulations, Interna-
340
tional Journal of Heat and Mass Transfer 117 (2018) 729–739. [45] J. Yang, H. Wu, M. Wang, S. He, H. Huang, Prediction and optimization of radiative thermal properties of ultrafine fibrous insulations, Applied Thermal Engineering 104 (2016) 394–402. [46] J. Yang, H. Wu, S. He, M. Wang, Prediction of thermal conductivity of
345
fiber/aerogel composites for optimal thermal insulation, Journal of Porous Media 18 (10) (2015) 971–984.
23
Dan Den ng received h his Bachelor and Ph.D. deegrees from University of Science andd Technologgy of China, in n 2003 and 2 2008, respecttively, both ffrom Department of Elecctronic Enginneering and Information Science. From 2008 to 2014, he was with Co omba Telecom Ltd. in Gu angzhou Chiina, as a 4, he has joined Guangzhoou Panyu Po olytechnic, w where he is cuurrently an A Associate Directorr. Since 2014 Professo or. His researrch interestss include MIM MO commun nication and physical‐layeer security in n next‐ generatiion wireless communicattion systemss. He has pub blished 29 pa apers in interrnational jou urnals and conferences. Alsso, he holds 19 patents, and has servved as a mem mber of Techhnical Program Committtees for seveeral conferen nces.
Junjuan Xia received d the bachelo or degree froom the department of co omputer scieence from Tia anjin d the master degree from m the department of elecctronic engin neering Universiity in 2003, aand obtained from Shaantou University in 2015 5. Now she w works for the school of Co omputer Scieence and Educatio onal Softwarre, Guangzho ou Universityy as a laborattory enginee er. Her currennt research iinterests include w wireless cach hing, physica al‐layer secu rity, cooperaative relaying g and interfeerence mode eling.
ZHENYU U NA received d the B.S. degree and thee M.S. degre ee in communication enggineering from the Harbin Institute of TTechnology, C China, in 20004 and 2007,, respectivelyy, and the Phh.D. degree in mmunication n engineeringg from the Communication Researchh Center, Harrbin informattion and com Institutee of Technolo ogy, in 2010.. He is currenntly an Assocciate Professor with the SSchool of Information Science and Techno ology, Dalian Maritime Un niversity, China. His reseearch interests
include ssatellite com mmunications and netwoorking, OFDM M, non‐orthogonal multiccarrier transm missions, NOMA o over satellitee, wireless po owered com munication n networks.
Qinghai Yang receiveed his B.S. de egree in Com mmunication n Engineering g from Shanddong Universsity of China in 1998 8, M.S. degreee in Informaation and Communicatio n Systems frrom Technology, Jinan, C University, Ch hina in 2001,, and Ph. D. i n Communiccation Engine eering from Inha Universsity, Xidian U Korea in n 2007 with u university‐president awa rd. From 200 07 to 2008, h he was a reseearch fellow w with Ultra‐wideband Wireeless Communication Reesearch Center, Inha Univversity. Sincee 2008, he ha as been dian Universitty. His current research iinterests include the field ds of autonoomic communication, with Xid content delivery nettworks and LLTE‐A techniqques. Junhui ZZhao received d the B.S. de egree from XXi'an Universiity of Techno ology, Xi'an, China, in 200 06; the M.S. deggree from Ch hongqing University, Choongqing, Chin na, in 2009; a and the Ph.D D. degree fro om Wayne SState University, Detroit,, MI, USA, in 2014, all in e electrical engineering. SSince 2014, h he has been an Assistant Prrofessor in th he Departmeent of Electrical and Com mputer Engineeering and University of New Haven , West Haven, CT, USA. H His research interests incclude Computer Science, U modelin ng and contro ol of renewable/alternattive energy syystems, distrributed geneeration, micrro grid, and pow wer system vvoltage stability.
PII: DOI: Reference:
S1874-4907(18)30051-X https://doi.org/10.1016/j.phycom.2018.03.013 PHYCOM 515
To appear in:
Physical Communication
Received date : 23 January 2018 Revised date : 11 March 2018 Accepted date : 24 March 2018 Please cite this article as: D. Deng, M. Yu, J. Xia, Z. Na, J. Zhao, Q. Yang, Wireless powered cooperative communications with direct links over correlated channels, Physical Communication (2018), https://doi.org/10.1016/j.phycom.2018.03.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Wireless Powered Cooperative Communications with Direct Links over Correlated Channels Dan Denga , Minghui Yua , Junjuan Xiab,∗, Zhenyu Nac , Junhui Zhaod , Qinghai Yange a Guangzhou
Panyu Polytechnic, Guangzhou, P.R. China, 511483. ([email protected]). University, Guangzhou, P.R. China, 510006. ([email protected]). c School of Information Science and Technology, Dalian Maritime University, Dalian 116026, China (e-mail:[email protected]). d School of Information Engineering, East China Jiaotong University, Nanchang, China (email: [email protected]). e State Key Laboratory on ISN, School of Telecommunications Engineering, Xidian University, Xi’an 710071, China, (e-mail:[email protected]) b GuangZhou
Abstract In this paper, we investigate the impact of correlated channels on the wireless powered cooperative networks, where the direct links between the source and destination exist and are correlated with the relaying links. In the considered system, the time switching-based relaying protocol of simultaneous wireless information and power transfer is used. In order to enhance the system performance, a better branch between the relaying link and the direct link is selected. We evaluate the system transmission performance by deriving the closed-form expression on outage probability as well as the asymptotic results for the proposed scheme, in the high regime of transmit power. Based on the theoretical analysis, we investigate the effects of the system parameters, such as channel correlation coefficient, average channel fading power, energy harvesting coefficient and slot allocation coefficient, on the system outage probability. Numerical results are provided to verify the theoretical analysis. Keywords: energy harvesting, cooperative system, correlated channels, selection combination, outage probability
∗ Corresponding
author Email address: [email protected] (Junjuan Xia)
Preprint submitted to Physical Communication
March 29, 2018
1. Introduction In recent years, many wireless techniques have arisen to tackle with the explosively increasing data transmission service[1, 2, 3, 4, 5]. Among these techniques, relaying is a promising technique to increase the wireless cover5
age, improve the transmission capacity without requiring additional transmit power[6, 7]. In addition, energy harvesting (EH) technique, which can collect wireless power from the environment, is a potential solution for future wireless networks [8, 9, 10]. Without battery deployment, energy harvesting scheme can provide low cost and convenient option for long-term low-power communica-
10
tions. Due to the excellent characteristics of energy harvesting, it has attracted much attentions in both academic and industry area [11, 12]. Based on the simultaneous wireless information and power transfer (SWIPT) with perfect and imperfect channel state information, Ref. [13] focused on the transmission
15
power minimum for multiple-input single-output multicasting systems, while optimal mode switching algorithm is studied in [14] . Moreover, joint antenna selection and transmit covariance matrix design optimization problem for energy harvesting systems is investigated in [15]. There are some other extended works on the transmission security for the wireless networks [16, 17, 18, 19].
20
On the other hand, selection diversity has been widely studied to improve the reliability of the wireless links by exploiting the freedom of the multiuser systems[20, 21, 22, 23, 24]. Also, user selection scheme can be joint designed with other emerging wireless technologies. For example, Ref.[9] proposed joint source and relay selection for cooperative non-orthogonal multiple access (NO-
25
MA) systems. Based on the wireless edge caching deployment, Ref.[25] analyzed the outage performance as well as their diversity order and coding gain with different caching placement solutions. While Ref.[26] investigated the secure relay and jammer selection for physical layer security in terms of secrecy outage probability.
30
Moreover, wireless energy harvesting can be compatible with cooperative
2
networks [27]. Considering an amplify-and-forward relaying network with energy constrains, Ref. In [28], the authors proposed both time switching-based and power splitting-based relaying protocols. In particular, at low SNR, the time switching-based protocol outperforms the power splitting-based protocol. As an 35
extension, a time-switching based energy harvesting and information transmission protocol is proposed in [29] using intelligent slot allocation scheme. Results show that the proposed continuous time EH outperforms the fixed time-duration EH scheme. Besides, the outage performance for energy harvesting relay-aided cooperative network is analyzed in [30] by deriving closed-form expression of
40
outage probability. Most of the above works ignoring the direct links from the source to the destinations. In the severe shadowing case, it is reasonable to assume that there is no direct links from the source to the destinations. However, in the moderate shadowing environments, there usually exist direct links which can be useful to
45
improve the performance of the cooperative systems. On the other hand, the theoretical analysis is more complicated due to the combination of the direct links and the relay links [21]. There are some insight works on the role of the direct links for the cooperative systems [31, 32, 33, 34]. In this paper, we investigate the outage probability with selection combina-
50
tion for wireless powered relaying system with the help of a direct links. In the considered system, the time switching-based relaying protocol of simultaneous wireless information and power transfer is used. In order to enhance the system performance, a better branch between the relaying link and the direct link is selected. We derive the closed-form expression on outage probability as well
55
as the asymptotic results for the proposed scheme. Based on the theoretical analysis, we find that the large channel correlation coefficient can be benefit to the outage performance, while it has no effect on the diversity order. Notations: We use CN (µ, σ 2 ) to represent the circularly symmetric complex
Gaussian random variable with mean µ and variance σ 2 , fX (x) and FX (x) 60
denote the probability density function and cumulative distribution function of a random variance X, respectively, EX (·) means the statistical expectation 3
Energy Harvesting Relay
R
S
D Direct Link
Figure 1: System model of Wireless Powered Cooperative Communications with Direct links
function with respect to X, and hR−D denotes the simultaneous channel fading coefficient of the link from R to D.
2. System Model 65
As shown in Fig.1, we consider a decode-and-forward (DF) wireless powered relaying system, which consists of a source station, a wireless powered relay station and a destination, denoted as S, R and D, respectively. It is assumed that each station works in half duplex mode and is equipped with one single antenna due to the equipment size or the power consumption constraint. In addition, all
70
other wireless channels are assumed to be quasi-static Rayleigh block fading[35]. hSR ∼ CN (0, α1 ), hRD ∼ CN (0, α2 ) and hRD ∼ CN (0, β) denote the channel fading coefficients of links S − R, R − D and S − D, respectively. Note that the channel fading coefficients hSR and hRD are assumed to be correlated because of radio scattering or antenna deployment [36, 37, 38].
75
In the considered system, the source station transmits messages to the destination station with the help of the direct link. Similar with Ref. [29, 28], the time switching-based relaying protocol of simultaneous wireless information and
4
Energy Harvesting
S->R S->D Information Transmission
R->D Information Transmission
Figure 2: Time switching-based energy harvesting relaying protocol
power transfer is adopted at the relay station, which is depicted in Fig.2.
1
In the energy harvesting (EH) phase of the relaying protocol, which is the 80
first ξT seconds of the each time slot, the relay station harvests as much as possible energy from the wireless signal transmitted by the source station. ξ ∈ (0, 1) is the time allocation factor for the EH phase, and T is the length of each time slot. The harvested energy can be used in the following information transfer. Specifically, the energy consumed by the receiver of the relay station is
85
negligible compared with the transmission power during the information transfer phase [29]. During the information transfer (IT) phase, the first half part of time
1−ξ 2 T
is used for the transmission from S to R and D, simultaneously. While the second half part 90
1−ξ 2 T
is used for the transmission from R to D. In this phase,
the relay station firstly decodes the signal and forwards to the destination using the energy harvested in the EH phase. At the destination station, in order to improve the quality of service, the selection combination receiver is deployed. That is, the destination station 1
Both time switching-based and power switching-based protocols are widely studied in the
previous works [28, 29, 30]. While in this paper time switching-based protocol is adopted, the reasons are given as follows. First, since only one RF module is needed in time switching-based protocol, it can be easily implemented with lower cost compared with power switching-based protocol. Second, previous works [28] have proved that, at low SNR, time switching-based protocol outperforms the power splitting-based protocol.
5
selects the better link from the relaying link and the direct link.
95
3. Outage Performance Analysis In this section, we will derive the closed-form analytical expressions on the outage probability for the wireless powered relaying system, as well as the asymptotic expressions for large transmission power. Based on the analytical expressions, the effects of the system parameters are revealed.
100
3.1. Analytical Expression First, consider the EH phase in the relaying protocol, the signal received by relay station can be given as rR =
√
PS hSR x + nR ,
(1)
where PS denotes the transmission power of S, x is the transmitted signal from the source station with normalized power, and nR ∼ CN (0, N0 ) is the additive white Gaussian noise (AWGN) signal received by the relay station. Then the signal-to-noise ratio (SNR) at the relay station in the EH phase can be given as γSR = where γ =
PS N0 ,
PS |hSR |2 = γu, N0
(2)
and u = |hSR |2 is the instantaneous channel fading power of
S − R link. In this phase, according to the relaying protocol in Fig.2, the harvested energy by the relay station can be expressed as ER = ηPS uξT,
(3)
where η is the energy conversion efficiency [9]. Similarly, the SNR of the direct link can be given as γSD =
PS |hSD |2 = γw, N0
where w = |hSD |2 is the instantaneous channel fading power of S − D link. 6
(4)
During the second IT phase, by using the harvested energy in EH phase, the relay regenerates the message x and forwards to the destination with power PR . Under the power constraint, we get PR =
ER 1−ξ 2 T
.
(5)
Substituting (3) into (5), we obtain PR = PS u 105
where θ =
2ηξ = PS uθ, 1−ξ
(6)
2ηξ 1−ξ .
In the phase, the signal received at the destination can be given as rD =
√
PR hRD x + nD ,
(7)
where nD ∼ CN (0, N0 ) is the AWGN signal received by D. By using (6), the SNR of R − D can be expressed as γRD =
PR |hRD |2 = γuθv, N0
(8)
Since decode-and-forward scheme is adopted by the relay station, the equivalent SNR of the relaying link can be given as γSRD = min{γSR , γRD } = γu min{1, θv}.
(9)
To enhance the quality of the links, the destination chooses the better link from the relaying link and the direct link. The equivalent SNR of the selected combination receiver at D can be expressed as γsc = max{γSD , γSRD } = γ max{w, u min{1, θv}}
(10)
Then the capacity of the system is obtain as Csc =
1 log2 (1 + γsc ). T
(11)
The outage probability is defined as the probability that the system capacity falls below a given target data rate. Given that the rate requirement is 7
predefined as Ct , the system outage probability is expressed as (12)
Psc = P r{Csc < Ct } = P r{γsc < γt }, where γt = 2T Ct − 1. By substituting (10) into (12), yields Psc = P r{γ max{w, u min{1, θv}} < γt } { { } γt } = P r max w, u min{1, θv} < γ { γt γt } = P r w < , uφ < . γ γ
(13)
where the definition of φ is given as φ = min{1, θv}.
Lemma 1. The probability density function of φ can be given as 1 e− θαx2 , if x < 1, θα2 fφ (x) = 0 , otherwise .
(14)
Proof: see Appendix A.
Lemma 2. Given the definition Am (µ) as follows, µ µ Am (µ) = Eφ {e− φ ( )m } φ
(15)
according to the Chebyshev-Gauss quadrature formula, we have the following approximation Am (µ) ≈ where
110
M π ∑ f (xk , µ, m), M
(16)
k=1
xk = cos (2k−1)π , 2M
2µ 2µ m f (x , µ, m)= e− 1+x k ( k 1+xk )
√
1−x2k − 1+xk 2α2 θ 2α2 θ e
(17) ,
and M is a tradeoff parameter between accuracy and computation complexity. Proof: see Appendix B. Moreover, the joint probability density function can be given as √ 2 ρxy I0 ( ) y x 1 − ρ α1 β α + β fu,w (x, y) = exp(− 1 ), (1 − ρ)α1 β 1−ρ 8
(18)
where ρ ∈ [0, 1) is the power correlation coefficient [39] between u and w, I0 (·) denotes the zero-order modified Bessel function of the first kind, as eq.(8.406) in [40]. 115
Particularly, ρ = 0 indicates that they are mutually independent. Using infinite series expansion as eq.(8.455) in [40] on (18), and ignoring the high order small quantities, I0 (·) can be expressed as I0 (x) =
∞ ∑
k=0
N
∑ x2k x2k ≈ , 4k (k!)2 4k (k!)2
(19)
k=0
where N denotes the truncation parameter, which is a tradeoff parameter between accuracy and computation complexity [39].
Specifically, it has been
proved in [41] that the series converges and the truncation error is exponentially bounded. Thus, the joint probability density function can be re-expressed as fu,w (x, y) ≈
N ∑
ck xk y k e
−α
x 1 (1−ρ)
y
e− β(1−ρ) ,
(20)
k=0
where ck =
ρk . (α1 β)k+1 (1 − ρ)2k+1 (k!)2
(21)
By substituting (20) into (13), yields Psc = Eφ
∫
γt φγ
x=0
≈ Eφ =
∫
N ∑
k=0
γt φγ
x=0
ck
∫
γt γ
fu,w (x, y)dydx.
y=0
∫
{∫
γt γ
N ∑
−α
ck xk y k e
x 1 (1−ρ)
y
e− β(1−ρ) dydx
(22)
y=0 k=0
} y y k e− β(1−ρ) dy Eφ y=0 | {z }| γt γ
{∫
P1
γt φγ
x=0
−α
xk e {z
x 1 (1−ρ)
dx
}
}
P2
Theorem 1. The outage probability of selection combination algorithm for the wireless powered relaying cooperative system can be given as follows Psc ≈
N ∑
k=0
q1
ρk (1 − ρ)[1 − e− γ (
k ∑ ( qγ1 )m
m=0
9
m!
)][1 −
k ∑ Am ( qγ2 )
m=0
m!
],
(23)
where
q = 1 q = 2
γt β(1−ρ) , γt α1 (1−ρ) ,
(24)
and the value of Am (µ) is given by Lemma 2. Proof:
Consider the item of P1 in (22), by using the incomplete gamma
function as eq.(3.381) in [40], we obtain P1 = [β(1 − ρ)](k+1) γ(k + 1,
γt ) γβ(1 − ρ)
(25)
According to the series expansion of incomplete gamma function as eq.(8.352) in [40], that is n ∑ xm )] m! m=0
γ(n + 1, x) = n k![1 − e− γβ(1−ρ) (
γt m k ( ∑ γβ(1−ρ) )
m=0
m!
)]
(27)
Then, we will consider the item of P2 in (22). Similar with the analysis on P1 , by using the incomplete gamma function and its series expansion (26) on P2 , we have γt m } k ( { ∑ γt φγα1 (1−ρ) ) − P2 = Eφ [α1 (1 − ρ)]k+1 k![1 − e φγα1 (1−ρ) ] . m! m=0
(28)
Apply (16) of Lemma 2 on (28), we obtain the analytical expression on P2 as follows γt k A [ { } ∑ m γα1 (1−ρ) ] P2 = [α1 (1 − ρ)]k+1 k![1 − ] . m! m=0
(29)
Substituting (27) and (29) into (22), we obtain the analytical expression on
10
outage probability, i.e. Psc ≈ =
N ∑
k=0 N ∑
k=0
γt
ρk (1 − ρ)[1 − e− γβ(1−ρ) ( k
ρ (1 − ρ) [1 − e
−
q1 γ
(
γt m k ( ∑ γβ(1−ρ) )
k ∑ ( qγ1 )m
m=0
|
m!
m=0
{z
m!
)] [1 − }|
H1
)][1 −
γt k A [ ∑ m γα1 (1−ρ) ]
m=0
k ∑ Am ( qγ2 )
m!
m=0
{z
]
].
}
H2
m!
(30)
This completes the proof of Theorem 1. 3.2. Asymptotic Analysis In order to have a deep insight into the outage performance for wireless 120
powered cooperative system, the asymptotic analysis is present given that the transmission power is large enough. In this case, it is assumed that γ → ∞. Theorem 2. Given that the transmission power of the source station is large enough, the outage probability of wireless powered cooperative system with selection combination is given as follows: ∞ Psc ≈
γt γt [1 − A0 ( )]. γβ α1 γ(1 − ρ)
(31)
Proof: Firstly, consider the first item H1 in (30), we can re-write it as follows q1
H1 = 1 − e− γ ( =1−e
−
q1 γ
(
k ∑ ( qγ1 )m
m=0 ∞ ∑
m!
)
( qγ1 )m m!
m=0
−
∞ ∑ ( qγ1 )m
m=k+1
m!
(32) )
Note that the infinite series expansion of exponential function can be expressed as ex =
∞ ∑ xk
k=0
k!
.
(33)
Applying the series expansion formula on (32), yields q1
q1
H1 = 1 − e− γ [e γ − =e
−
q1 γ
∞ ∑
∞ ∑ ( qγ1 )m
m=k+1 ( qγ1 )m
m=k+1
11
m!
m!
] (34)
When γ → ∞, we can ignoring the high order items, i.e., only k = 0 is selected, q1
H1 ≈ e− γ (
q1 ) γ
(35)
By using the approximation that ex ≈ 1 + x, we can rewrite H1 as q1
H 1 ≈ e− γ (
q1 q1 q1 q1 ) ≈ (1 − ) ≈ . γ γ γ γ
(36)
Thus, the expression on Psc in (22) can be given as ∞ Psc ≈ (1 − ρ)
q1 q2 [1 − A0 ( )]. γ γ
(37)
∞ Substituting the definitions of q1 and q2 in (24) into Psc , we obtain the
asymptotic outage probability in (31) in Theorem 2. Theorem 2 is proved. Based on the Theorem 2, we can make the following corollary. 125
Corollary 1: The asymptotic outage probability of the system is monotone increasing function with respect to the channel correlation coefficient. Proof: According to the definition of A0 (µ) in (15) of Lemma 2, it’s easy to prove that A0 (µ) is a strictly monotone decreasing function with respect ∞ to µ. Thus, Psc is monotone increasing function with respect to the channel
130
correlation coefficient ρ. The reason for this phenomenon is that the large channel correlation coefficient decreases the freedom between the relaying link and the direct link, which results in higher outage probability of the selective combination.
4. Simulation Results 135
In this section, simulation results are provided to verify the presented analysis. We investigate the effects of the system parameters, such as channel correlation coefficient, average channel fading power, energy harvesting coefficient and slot allocation coefficient, on the system outage probability [42, 43, 44, 45, 46].
12
In all simulation setup, we set the predefined requirement rate as Ct = 1bps/Hz, 140
and the truncation parameters are fixed as N = M = 30.
2
Fig.3 depicts the outage probability versus the channel correlation coefficient as a function of the system SNR γ. The system parameters are given as follows. The energy harvesting coefficient is 0.1, and the slot allocation coefficient is set as 0.5. The average channel fading powers of the three links are set the same, 145
i.e., α1 = α2 = 0.1, β = 0.01. And the channel correlation coefficient changes from 0, 0.5 and 0.9. With the setup of the system, we investigate the impact of channel correlation coefficient on the system performance. We can see from this figure that the simulation results match the analytical results in all SNR regions. Specifically, in high SNR region the analytical results converge to the
150
asymptotic line. Moreover, the outage probability increases with large channel correlation coefficient, which coincides with the result of Corollary 1. Besides, with different channel correlation coefficients, the slope of the asymptotic outage remains the same. In other words, although small channel correlation coefficient is benefit to the outage performance, it has no effect on the diversity order.
155
The effect of average channel fading power on outage probability is present in Fig.4. The system setup is given as follows. The energy harvesting coefficient is set as 0.1, the channel correlation coefficient is 0.9, and the slot allocation coefficient is set as 0.5. The average channel fading powers of hSR changes as 0.1, 0.5 and 1.0. While the average channel fading powers of hRD keeps the
160
same with that of hSR , i.e. α1 = α2 , and β = α1 ∗ α2 . We can see from this figure that average channel fading power shows significant impact on the system outage probability. Obviously, large channel fading power will improve the system performance, which coincides with our intuition. 2 Please
kindly note that the definition of M is given in (16) of Lemma 2. M is a tradeoff
parameter between accuracy and computation complexity for Am (µ). While the definition of N is given in (19). N denotes the truncation parameter, which is a tradeoff parameter between accuracy and computation complexity for I0 (x).
13
Outage probability
10 0
10 -1
ρ=0,0.5,0.9
η=0.1, ξ=0.5, α 1 =α 2 =0.1, β=0.01 10
-2
Analytical Simulation Asymptotic
0
5
10
15
20
25
30
35
SNR (dB)
Figure 3: Effect of channel correlation coefficient on outage probability
10 0 α 1 =0.1,0.5,1.0
Outage probability
10 -1
10 -2
10 -3
10 -4
η=0.1, ρ=0.9, ξ=0.5 Analytical Simulation Asymptotic
10 -5
0
5
10
15
20
25
30
35
SNR (dB)
Figure 4: Effect of average channel fading power on outage probability
14
Outage probability
10 0
10
-1
η=0.1,0.2,0.4
ρ=0.9, ξ=0.5, α 1 =α 2 =0.1, β=0.01 Analytical Simulation Asymptotic
10 -2
0
5
10
15
20
25
30
35
SNR (dB)
Figure 5: Effect of energy harvesting coefficient on outage probability
Fig.5 depicts the effect of energy harvesting coefficient on system perfor165
mance. The channel correlation coefficient is 0.9, and the slot allocation coefficient is set as 0.5. The average channel fading powers of the three links are set as α1 = α2 = 0.1, β = 0.01. While the energy harvesting coefficient changes as 0.1, 0.2 and 0.4. From this figure, we can see that large energy harvesting coefficient owns better outage performance. The reason is that the larger en-
170
ergy harvesting coefficient can collects more power used for forwarding wireless signal to the destination. Thus, the outage probability can be improved. Fig.6 depicts the effect of slot allocation coefficient ξ on system performance, where the energy harvesting coefficient is set as 0.1 and the channel correlation coefficient is 0.9. The average channel fading powers of the three links are set
175
the same, i.e., α1 = α2 = β = 1. While the slot allocation coefficient changes as 0.1, 0.2 and 0.4. From this figure, we can see that , in this system setup, large ξ shows better performance than the small one. The reason for this phenomenon is that when ξ is relative small, the bottle neck of the system performance is
15
10
0
Outage probability
10 -1
10
-2
ξ=0.1,0.2,0.4 10 -3
10 -4
η=0.1, ρ=0.9, α 1 =α 2 =β=1.0 Analytical Simulation Asymptotic
10 -5
0
5
10
15
20
25
30
35
SNR (dB)
Figure 6: Effect of slot allocation coefficient on outage probability
the power consumption in the IT phase. 180
3
In this case, large ξ means more
energy can be harvested in the EH phase, and the outage performance can be enhanced.
5. Conclusion In this paper, we investigate outage probability of wireless powered cooperative system over correlated wireless channel, in which the better branch is 185
selected between the relaying link and the direct links. The effect of the system parameters on outage probability is studied by deriving the closed-form analytical expressions as well as the asymptotic expressions for large transmission power. Furthermore, simulation results are provided to verify the theoretical 3 The
slot allocation coefficient ξ is relative small, that is, the allocated time for EH phase
is not enough for the following IT phase. In this case, the transmission powers of both source and the relay are smaller than needed. Thus, the outage probability raises with smaller ξ, and the power consumption in the IT phase become the bottle neck of the system performance.
16
analysis. According to the asymptotic expressions, we find that, although the 190
large channel correlation coefficient can be benefit to the outage performance, it has no effect on the diversity order.
Acknowledgement This work was supported in part by the Science and Technology Program of Guangzhou, China, under Grant 201707010389, in part by the Scientific Re195
search Project of Guangzhou Municipal University under Grant 1201620439, in part by the Qingshanhu Young Scholar Program in GZPYP under Grant 2016Q001, in part by Comba Research Funds under Grant JX-PYP-201501 and Grant H2017007, in part by Guangdong big data technology research center for intelligent vocational education.
200
Appendix A. Proof of Lemma 1 According to the definition of φ, we can obtain the following cumulative distribution function Fφ (x) = P r{φ < x} = P r{min{1, θv} < x}
(A.1)
= 1 − P r{min{1, θv} ≥ x}. In the case of x ≥ 1, we have Fφ (x) = 1. While for the case of x < 1, we have Fφ (x) = 1 − P r{min{1, θv} ≥ x} = 1 − P r{θv ≥ x}
(A.2)
x
= 1 − e− θα2 . Taking a derivative on (A.1), we can get the probability density function of φ as in Lemma 1.
17
Appendix B. Proof of Lemma 2 According to the definition of Am (µ), using the probability density function of φ as in (14) of Lemma 1, we obtain µ µ Am (µ) = Eφ {e− φ ( )m } φ ∫ 1 µ µ = e− x ( )m fφ (x)dx x 0 ∫ 1 µ µ 1 − θαx 2 dx = e− x ( )m e x θα 2 0
Note that the Chebyshev-Gauss quadrature formula, that is ∫ 1 M ∑ g(x) √ dx ≈ Hk g(xk ), 1 − x2 −1 k=1 205
where xk = cos (2k−1)π and Hk = 2M
(B.1)
(B.2)
π M.
By applying the Chebyshev-Gauss quadrature and simple mathematical derivation on (B.1), we can obtain the (16) and (17) in Lemma 2. References [1] F. Zhou, L. Fan, X. Lei, G. Luo, H. Zhang, J. Zhao, Edge caching with 210
transmission schedule for multiuser multirelay networks, IEEE Communications Letters PP (99) (2018) 1–4. [2] G. Huang, D. Tang, Wireless information and power transfer in two-way OFDM amplify-and-forward relay networks, IEEE Communications Letters 20 (8) (2016) 1563–1566.
215
[3] L. Fan, X. Lei, N. Yang, T. Q. Duong, G. K. Karagiannidis, Secure multiple amplify-and-forward relaying with cochannel interference, IEEE Journal of Sel. Topics in Sig. Proc. 10 (8) (2016) 1494–1505. [4] G. Liu, H. Liu, H. Chen, C. Zhou, L. Shu, Position-based adaptive quantization for target location estimation in wireless sensor networks using one-
220
bit data, Wireless Communications and Mobile Computing 16 (8) (2016) 929–941. 18
[5] R. Zhao, Y. Yuan, L. Fan, Y. He, Secrecy performance analysis of cognitive decode-and-forward relay networks in Nakagami-m fading channels, IEEE Trans. Commun. 65 (2) (2017) 549–563. 225
[6] J. Li, X. Jiang, Y. Yan, W. Yu, S. S. Song, M. H. Lee, Low complexity detection for quadrature spatial modulation systems, Wireless Personal Communications 95 (4) (2017) 4171–4183. [7] W. Tan, M. Matthaiou, S. Jin, X. Li, Spectral efficiency of DFT-based processing hybrid architectures in massive MIMO, IEEE Wireless Commun.
230
Lett. 6 (5) (2017) 586–589. [8] N. Zhao, F. R. Yu, V. C. M. Leung, Wireless energy harvesting in interference alignment networks, IEEE Communications Magazine 53 (6) (2015) 72–78. [9] D. Deng, L. Fan, X. Lei, W. Tan, D. Xie, Joint user and relay selection for
235
cooperative noma networks, IEEE Access 5 (1) (2017) 20220–20227. [10] J. Guo, N. Zhao, F. R. Yu, X. Liu, V. C. M. Leung, Exploiting adversarial jamming signals for energy harvesting in interference networks, IEEE Trans. Wireless Communications 16 (2) (2017) 1267–1280. [11] N. Zhao, S. Zhang, F. R. Yu, Y. Chen, A. Nallanathan, V. C. M. Leung,
240
Exploiting interference for energy harvesting: A survey, research issues, and challenges, IEEE Access 5 (2017) 10403–10421. [12] N. Zhao, F. R. Yu, V. C. M. Leung, Opportunistic communications in interference alignment networks with wireless power transfer, IEEE Wireless Commun. 22 (1) (2015) 88–95.
245
[13] M. R. A. Khandaker, K. K. Wong, Swipt in miso multicasting systems, IEEE Wireless Communications Letters 3 (3) (2014) 277–280. [14] L. Liu, R. Zhang, K. C. Chua, Wireless information transfer with opportunistic energy harvesting, IEEE Transactions on Wireless Communications 12 (1) (2013) 288–300. 19
250
[15] S. Zhao, Q. Li, Q. Zhang, J. Qin, Antenna selection for simultaneous wireless information and power transfer in mimo systems, IEEE Communications Letters 18 (5) (2014) 789–792. [16] G. Liu, B. Xu, H. Chen, C. Zhang, X. Hu, Energy-efficient scheduling for distributed estimation in wireless sensor and actuator networks with
255
kriging, Ad Hoc & Sensor Wireless Networks 27 (3-4) (2015) 197–222. [17] G. Huang, W. Tu, Optimal resource allocation in wireless-powered OFDM relay networks, Computer Networks 104 (2016) 94–107. [18] G. Liu, J. Yao, Y. Liu, H. Chen, D. Tang, Channel-aware adaptive quantization method for source localization in wireless sensor networks, Internation-
260
al Journal of Distributed Sensor Networks 11 (2015) 214081:1–214081:13. [19] G. Huang, W. Tu, Wireless information and energy transfer in nonregenerative OFDM AF relay systems, Wireless Personal Communications 94 (4) (2017) 3131–3146. [20] G. Pan, H. Lei, Y. Deng, L. Fan, J. Yang, Y. Chen, Z. Ding, On secrecy
265
performance of MISO SWIPT systems with TAS and imperfect CSI, IEEE Trans. Commun. 64 (9) (2016) 3831–3843. [21] L. Fan, S. Zhang, T. Q. Duong, G. K. Karagiannidis, Secure switch-andstay combining (SSSC) for cognitive relay networks, IEEE Trans. Commun. 64 (1) (2016) 70–82.
270
[22] L. Fan, X. Lei, N. Yang, T. Q. Duong, G. K. Karagiannidis, Secrecy cooperative networks with outdated relay selection over correlated fading channels, IEEE Trans on Vehicular Technology 66 (8) (2017) 7599–7603. [23] X. Lai, W. Zou, X. Li, L. Fan, Multiuser energy harvesting relaying system with direct links, IET Commun. 11 (12) (2017) 1846–1852.
275
[24] X. Wang, H. Zhang, L. Fan, Y. Li, Performance of distributed switchand-stay combining for cognitive relay networks with primary transceiver, Wireless Personal Commun. 97 (2) (2017) 3031–3042. 20
[25] M. Tao, E. Chen, H. Zhou, W. Yu, Content-centric sparse multicast beamforming for cache-enabled cloud ran, IEEE Transactions on Wireless Com280
munications 15 (9) (2016) 6118–6131. [26] H. Hui, A. Swindlehurst, G. Li, J. Liang, Secure relay and jammer selection for physical layer security, Signal Processing Letters, IEEE 22 (8) (2015) 1147–1151. [27] Y. Luo, J. Zhang, K. B. Letaief, Relay selection for energy harvesting co-
285
operative communication systems, in: Global Communications Conference, 2013, pp. 2514–2519. [28] A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy, Relaying protocols for wireless energy harvesting and information processing, IEEE Transactions on Wireless Communications 12 (7) (2013) 3622–3636.
290
[29] A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy, Wireless-powered relays in cooperative communications: Time-switching relaying protocols and throughput analysis, IEEE Transactions on Communications 63 (5) (2015) 1607–1622. [30] T. Li, P. Fan, K. B. Letaief, Outage probability of energy harvesting relay-
295
aided cooperative networks over rayleigh fading channel, IEEE Transactions on Vehicular Technology 65 (2) (2016) 972–978. [31] F. Shi, W. Tan, J. Xia, D. Xie, L. Fan, X. Liu, Hybrid cache placement for physical-layer security in cooperative networks, IEEE Access 6 (2018) 8098–8108.
300
[32] V. N. Q. Bao, T. Q. Duong, D. B. D. Costa, G. C. Alexandropoulos, A. Nallanathan, Cognitive amplify-and-forward relaying with best relay selection in non-identical rayleigh fading, IEEE Communications Letters 17 (3) (2013) 475–478.
21
[33] X. Liu, X. Zhang, D. Yang, Outage probability analysis of multiuser 305
amplify-and-forward relay network with the source-to-destination links, IEEE Communications Letters 15 (2) (2011) 202–204. [34] F. R. V. Guimaraes, D. B. D. Costa, T. A. Tsiftsis, C. C. Cavalcante, G. K. Karagiannidis, Multiuser and multirelay cognitive radio networks under spectrum-sharing constraints, IEEE Transactions on Vehicular Technology
310
63 (1) (2014) 433–439. [35] J. Li, M. Wen, X. Jiang, W. Duan, Space-time multiple-mode orthogonal frequency division multiplexing with index modulation, IEEE Access 5 (2017) 23212–23222. [36] X. Lai, W. Zou, D. Xie, X. Li, L. Fan, DF relaying networks with randomly
315
distributed interferers, IEEE Access 5 (2017) 18909–18917. [37] W. Tan, S. Jin, C. Wen, T. Jiang, Spectral efficiency of multi-user millimeter wave systems under single path with uniform rectangular arrays, EURASIP J. Wireless Comm. and Networking 181 (2017, DOI:10.1186/s13638-017-0966-4) 1–13.
320
[38] F. Zhou, L. Fan, N. Wang, G. Luo, J. Tang, W. Chen, A cache-aided communication scheme for downlink coordinated multipoint transmission, IEEE Access 6 (2018) 1416–1427. [39] L. Fan, R. Zhao, F. K. Gong, N. Yang, G. Karagiannidis, Secure multiple amplify-and-forward relaying over correlated fading channels, IEEE
325
Transactions on Communications 7 (65) (2017) 2811–2820. [40] I. Gradshteyn, I. Ryzhik, Table of Integrals, Series, and Products, 7th Ed, Academic Press,Elsevier Inc, San Diego, California 92101-4495, USA, 2007. [41] X. Sun, J. Wang, W. Xu, C. Zhao, Performance of secure communications over correlated fading channels, IEEE Signal Processing Letters 19 (8)
330
(2012) 479–482.
22
[42] J. Yang, H. Wu, G. Huang, Y. Liang, Y. Liao, Modeling and coupling effect evaluation of thermal conductivity of ternary opacifier/fiber/aerogel composites for super-thermal insulation, Materials and Design 133 (5) (2017) 224–236. 335
[43] Y. Liang, H. Wu, G. Huang, J. Yang, H. Wang, Thermal performance and service life of vacuum insulation panels with aerogel composite cores, Energy and Buildings 154 (2017) 606–617. [44] J. Yang, H. Wu, M. Wang, et al., Prediction and optimization of radiative thermal properties of nano TiO2 assembled fibrous insulations, Interna-
340
tional Journal of Heat and Mass Transfer 117 (2018) 729–739. [45] J. Yang, H. Wu, M. Wang, S. He, H. Huang, Prediction and optimization of radiative thermal properties of ultrafine fibrous insulations, Applied Thermal Engineering 104 (2016) 394–402. [46] J. Yang, H. Wu, S. He, M. Wang, Prediction of thermal conductivity of
345
fiber/aerogel composites for optimal thermal insulation, Journal of Porous Media 18 (10) (2015) 971–984.
23
Dan Den ng received h his Bachelor and Ph.D. deegrees from University of Science andd Technologgy of China, in n 2003 and 2 2008, respecttively, both ffrom Department of Elecctronic Enginneering and Information Science. From 2008 to 2014, he was with Co omba Telecom Ltd. in Gu angzhou Chiina, as a 4, he has joined Guangzhoou Panyu Po olytechnic, w where he is cuurrently an A Associate Directorr. Since 2014 Professo or. His researrch interestss include MIM MO commun nication and physical‐layeer security in n next‐ generatiion wireless communicattion systemss. He has pub blished 29 pa apers in interrnational jou urnals and conferences. Alsso, he holds 19 patents, and has servved as a mem mber of Techhnical Program Committtees for seveeral conferen nces.
Junjuan Xia received d the bachelo or degree froom the department of co omputer scieence from Tia anjin d the master degree from m the department of elecctronic engin neering Universiity in 2003, aand obtained from Shaantou University in 2015 5. Now she w works for the school of Co omputer Scieence and Educatio onal Softwarre, Guangzho ou Universityy as a laborattory enginee er. Her currennt research iinterests include w wireless cach hing, physica al‐layer secu rity, cooperaative relaying g and interfeerence mode eling.
ZHENYU U NA received d the B.S. degree and thee M.S. degre ee in communication enggineering from the Harbin Institute of TTechnology, C China, in 20004 and 2007,, respectivelyy, and the Phh.D. degree in mmunication n engineeringg from the Communication Researchh Center, Harrbin informattion and com Institutee of Technolo ogy, in 2010.. He is currenntly an Assocciate Professor with the SSchool of Information Science and Techno ology, Dalian Maritime Un niversity, China. His reseearch interests
include ssatellite com mmunications and netwoorking, OFDM M, non‐orthogonal multiccarrier transm missions, NOMA o over satellitee, wireless po owered com munication n networks.
Qinghai Yang receiveed his B.S. de egree in Com mmunication n Engineering g from Shanddong Universsity of China in 1998 8, M.S. degreee in Informaation and Communicatio n Systems frrom Technology, Jinan, C University, Ch hina in 2001,, and Ph. D. i n Communiccation Engine eering from Inha Universsity, Xidian U Korea in n 2007 with u university‐president awa rd. From 200 07 to 2008, h he was a reseearch fellow w with Ultra‐wideband Wireeless Communication Reesearch Center, Inha Univversity. Sincee 2008, he ha as been dian Universitty. His current research iinterests include the field ds of autonoomic communication, with Xid content delivery nettworks and LLTE‐A techniqques. Junhui ZZhao received d the B.S. de egree from XXi'an Universiity of Techno ology, Xi'an, China, in 200 06; the M.S. deggree from Ch hongqing University, Choongqing, Chin na, in 2009; a and the Ph.D D. degree fro om Wayne SState University, Detroit,, MI, USA, in 2014, all in e electrical engineering. SSince 2014, h he has been an Assistant Prrofessor in th he Departmeent of Electrical and Com mputer Engineeering and University of New Haven , West Haven, CT, USA. H His research interests incclude Computer Science, U modelin ng and contro ol of renewable/alternattive energy syystems, distrributed geneeration, micrro grid, and pow wer system vvoltage stability.