Computer Networks 137 (2018) 61–68
Contents lists available at ScienceDirect
Computer Networks
journal homepage: www.elsevier.com/locate/comnet
Robust energy harvest balancing optimization with V2X-SWIPT over
MISO secrecy channel
Zhengyu Zhu
a , Zhongyong Wang
a , Zheng Chu
c , ∗, Di Zhang
a , b , ∗, Byonghyo Shim
b
a School of Information Engineering, Zhengzhou University, Zhengzhou 450-001, China b Information System Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea c 5G Innovation Center (5GIC), Institute of Communication Systems (ICS), University of Surrey, Guildford GU2 7XH, United Kingdom
a r t i c l e i n f o
Article history:
Received 21 December 2017
Revised 12 February 2018
Accepted 15 March 2018
Available online 16 March 2018
Keywords:
Vehicle to everything
Physical-layer secrecy
MISO system
SWIPT
Artificial noise
a b s t r a c t
Vehicle to everything (V2X) is emerging as a promising application scenario of fifth generation (5G)
wireless communications. In V2X systems, a series of applications (information transmission, in-car en-
tertainment, etc.) rely on the limited vehicle battery, and the secrecy communication is a vital issue.
However, most prior work limits to the automatic piloting, channel measurement/estimation and high
speed transmissions, seldom study has been done on the battery-limited and secrecy communications
for V2X. In light of this, here we investigate the V2X systems with a battery-limited perspective based on
the multiple-input-single-output (MISO) secrecy channel in the presence of multiple eavesdroppers. The
transmit beamformer and artificial noise (AN) are jointly designed. With the channel uncertainties, by
subjecting to the battery constraints and secrecy rate, a robust energy harvesting (EH) balancing problem
is constructed. The problem is further transformed into a two-level problem, in which we solve the inner-
level problem by exploiting S-Procedure , and the outer-level problem with one-dimensional line search
method. Finally, simulation results are provided to validate the performance of our proposed scheme.
© 2018 Elsevier B.V. All rights reserved.
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1
. Introduction
The 5.9 GHz frequency with a bandwidth 75 MHz has been al-
ocated for intelligent transport systems in 1999 by the US federal
ommunications commission (FCC) . Afterwards, wireless local area
etwork based vehicle communications (WLAN-VC) has been initi-
ted by the American society for testing and materials (ASTM) E
213 standards for vehicle to vehicle (V2V) and vehicle to infras-
ructure (V2I) communications with its first version introduced in
002 and a latest version re-approved in 2010 [1] . Based on the
ork of ASTM, the institute of electrical and electronics engineers
IEEE) 802.11 p standards were initiated for WLAN in vehicular en-
ironments (WAVE) and the dedicated short range communication
DSRC) frequency was allocated for V2X communications. In 2012,
pre-deployment was trailed in Ann Arbor, Michigan, by connect-
ng various transportation devices (i.e., car, motor-bicycle, bus, etc.)
rom different manufactures [2] . In the European side, Comité Eu-
opéen de Normalisation (CEN) and European telecommunications
tandards institute (ETSI) published the first standards for coop-
rative intelligent transport systems (C-ITS) in 2014 [3] . Addition-
∗ Corresponding authors.
E-mail addresses: [email protected] (Z. Chu), [email protected] ,
[email protected] (D. Zhang), [email protected] (B. Shim).
g
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ttps://doi.org/10.1016/j.comnet.2018.03.018
389-1286/© 2018 Elsevier B.V. All rights reserved.
lly, the ITS-Asia-Pacific (ITS-AP) was established around 1996 to
acilitate the collaboration in the Asia Pacific region. Due the lim-
ted coverage area and lower transmission rate of WAVE, in 2016,
GPP R14 further initiated the cellular based V2X study (C-V2X)
4] . The 5G automotive association (5GAA) was established in the
ame year aiming at providing cellular and fifth generation (5G)
ew radio (NR) based V2X services with a joint force from both
ndustry and academia [5] .
In recent years, due to the rapid development of deep learn-
ng (DL) technologies, DL-based traffic device detection has been
tudied in automatic piloting, for instance, [6,7] . With the help of
ecognized and reconstructed objectives on the road, the traffic in-
ormation of vehicles (e.g., speed, acceleration, routing) can be au-
omatically adjusted. On the other hand, to optimize the transmis-
ion of vehicle networks, named data (ND) based software defined
ehicle networks (NDSDVN) has been introduced [8,9] . When com-
ared to prior network architecture, NDSDVN can retrieve request-
ng data from neighboring vehicles and other devices [10] . In the
hysical layer study of vehicle communications, channel estimation
nd measurement have been intensively investigated, for instance,
eometry based deterministic model (GBDM) [11] , non-geometry
ased stochastic model (NGSM) [12] and geometry based stochas-
ic model (GBSM) [13] . With the constraint in cellular systems op-
imal resource allocation method was proposed in [14] . By consid-
62 Z. Zhu et al. / Computer Networks 137 (2018) 61–68
Fig. 1. MISO V2X-SWIPT secrecy system.
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ering the multi-cast services and device-to-device (D2D) commu-
nications [15] , a tradeoff mechanism was obtained with regards to
the cellular resources and communication delay.
On the other hand, the emergence of V2X communications has
led to an continuously increasing demand for wireless applications,
such as ultra-wide radio coverage and ultra-large number of vehi-
cle devices. A promising solution to satisfy this demand is the fifth
generation (5G) wireless technology [16,17] . As one of the main
techniques to combat the battery problem in the 5G wireless com-
munication systems, simultaneous wireless information and power
transmission (SWIPT) allows devices to capture the energy from
environments [18–24] .
Although there have been various studies in V2X, there is
not much work combining simultaneous wireless information and
power transfer (SWIPT) with V2X. Recent work on this is the joint
power allocation and splitting (JoPAS) mechanism [25] , in which a
doubly selective channel was considered. The authors further pro-
posed a sub-optimal power allocation and splitting algorithm to
reduce the computational complexity. However, no work has been
done while on the combination of SWIPT and V2X from a multi-
input-single-output (MISO) secrecy channel. In V2X systems, multi-
ple vehicles can be employed for the V2V transmission with a lim-
ited vehicle battery. Additionally, by using multiple-antenna wire-
tap channel, extra degree of freedom and diversity gains can be ob-
tained [26] . Additionally, we may employ artificial noise (AN) and
cooperative jammer (CJ) to interrupt the eavesdroppers [27,28] . The
AN, on the other hand, can be used for energy harvesting (EH)
from radio frequency (RF) signals sent by the transceiver as well
[29] .
Motivated by the aforementioned discussions, we consider a
novel and practical battery-limited problem of V2X systems, ro-
bust energy harvesting (EH) balance maximization problem , where
the achieved harvested power (from neighboring vehicle, cellu-
lar, pedestrian, etc.) to the target harvested power ratio is max-
imized to achieve the target secrecy rate at vehicular receiver
(VR) and transmit power constraints. In this problem, the har-
vested power is maximized while guaranteeing a balance for the
available power storage space for the energy vehicular receivers
(EVRs). Since the original problem is non-convex by incorporat-
ing the norm-bounded channel uncertainties, and thus cannot be
solved directly, we convert the problem into a two-level problem,
where the inner-level problem is solved by the S-Procedure , and
the out-level problem is solved by the one-dimensional line search
method. Simulation results demonstrate that our proposed robust
scheme outperforms the robust scheme without AN assisted. The
main contributions of this work, can be summarized as 2 folds
• With the massive connected vehicles and limited vehicle bat-
tery of V2X systems, we study the V2X SWIPT with a MISO se-
crecy channel. The limited vehicle battery issue can be partly
alleviated compared to V2V single-input-single-output (SISO)
scenario. Additionally, more degree of freedom and diversity
gains can be obtained via the MISO secrecy channel. On the
other hand, AN and CJ are employed to interrupt the eavesdrop-
pers, and AN is further employed for EH from RF signals.
• We propose a two-level optimization problem to reformulate
this problem. Specifically, the outer-level problem is recast as a
single-variable optimization problem, which can be solved by
one-dimensional line search method, whereas the inner-level
problem is relaxed as a sequence of semi-definite programs
(SDPs) which can be solved by one-dimensional line searching
method. In addition, relaxation tightness of this optimization
problem is provided by showing the optimal solution of the re-
laxed problem is rank-one.
The paper is organized as follows: In Section 2 , we describe the
system model and elaborate the proposed V2X-SWIPT model. In
ection 3 , we introduce the energy harvesting balancing problem,
hereas a two-level optimization mechanism is proposed to solve
he problem. Section 4 is the simulation results section, the perfor-
ance of our proposed system is validated here. We conclude the
aper in Section 5 .
.1. Notation
The upper case boldface letters are used for matrices, where
ower case boldface letters are used for vectors. On the other hand,
· ) H denotes the conjugate transpose. We employ Tr( · ) and E {·}o denote the trace of a matrix and the statistical expectation for
andom variables, respectively. A � 0 indicates that A is a positive
emi-definite matrix. I and (·) −1 denote the identity matrix with
ppropriate size and the inverse of a matrix, respectively. ‖ · ‖ 2 epresents the Euclidean norm of a matrix. � { · } stands for the real
art of a complex number, whereas | A | denotes the determinant of
. [ x ] + represents max { x , 0}.
. System model
A MISO V2X-SWIPT secrecy system consisting of one base sta-
ion (BS), one VR (legitimate user) and K multiantenna EVRs (pas-
ive eavesdropper) is considered in this study. It is assumed that
VRs can receive the information and power simultaneously [30] ,
s shown by Fig. 1 . This system can be extended to the downlink
ystem with multiple VRs that is enabled to receive common mes-
age from the BS. In this paper, we consider the system with one
R case via the MISO secrecy channel. The plural VR case can be
ecomposed into multiple VR cases, which is omitted here for the
ake of convenience.
It is assumed that the BS is equipped with N T transmit anten-
as, where the VR and k -th EVR (i.e., k = 1 , . . . , K) consist of sin-
le antenna, respectively. The channel coefficients between the BS
nd the VR as well as the k -th EVR are denoted by h s ∈ C
N T and
e,k ∈ C
N E,k .
The received signal at the VR and the k -th EVR can be ex-
ressed as
y s = h
H s x + n s ,
e,k = h
H e,k x + n e,k , ∀ k,
here x ∈ C
N T represents the transmitted signal vector. Moreover,
s ∼ CN (0 , σ 2 s ) and n e,k ∼ CN (0 , σ 2
e ) denote the additive Gaussian
oise by the receive antenna at the VR and the k -th EVR, respec-
ively. In order to improve the reliable transmission of our sys-
em, we assume the transmitter employs the transmit beamform-
ng with AN, which act as the information bearer to introduce in-
erference to the EVRs, and energy-carrying to be harvested by the
R. In this case, the transmit signal vector x can be expressed as
= q s + w , (1)
Z. Zhu et al. / Computer Networks 137 (2018) 61–68 63
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here s ∈ C (E {| s | 2 } = 1) is the information-bearing signal in-
ended for the VR, q ∼ CN (0 , Q s ) denote the transmit beamform-
ng, and w ∼ CN (0 , W ) represents the energy-carrying AN, which
s composed of multiple energy beams. Thus, the minimum secrecy
ate can be expressed as
s =
[ log
(1 +
h
H s Q s h s
h
H s Wh s + σ 2
s
)
− max k
log
(1 +
h
H e,k
Q s h e,k
h
H e,k
Wh e,k + σ 2 e
)] + . (2)
In addition, the harvested power for the k -th EVR can be ob-
ained as
e,k = ηk h
H e,k (Q s + W ) h e,k , ∀ k, (3)
here 0 ≤ηk ≤ 1 denotes the ratio for converting the received RF
nergy to electrical energy for the k -th EVR, without loss of gener-
lity, we assume that ηk = 1 throughout this study.
In the sequel, we will give description of the robust energy har-
esting (EH) balancing maximization problem in this MISO V2X-
WIPT secrecy system based on channel uncertainty. The solution
f this problem is given afterwards. Particularly, the minimum har-
ested power of the k -th EVR is balanced while satisfying the min-
mum secrecy rate and the transmit power constraints.
. Problem formulation and robust design algorithm
In this section, we consider the EH balancing maximization
roblem, where the harvested power is maximized subject to the
ecrecy rate and the transmit power constraints, which is given
s
max Q s , W
min
k
P e,k
E k
s.t. R s ≥ R̄ s ,
Tr (Q s + W ) ≤ P, Q s � 0 , W � 0 , ∀ k,
(4)
here R̄ s is the predefined secrecy rate, P denotes the target trans-
it power, and E k represents the target harvested power of the
-th EVR. As noticed, in wireless transmission, it is not always pos-
ible to have the perfect CSI for all channel coefficients at the BS
ue to channel estimation and quantization errors. Thus, we con-
ider the EH balancing maximization problem based on an imper-
ect CSI by incorporating the channel uncertainties.
.1. Channel uncertainty model
Here, we model the imperfect CSI based on the deterministic
odels. The actual channel can be modelled as
h s = h̄ s + e s ,
e,k = h̄ e,k + e e,k , ∀ k,
here h̄ s and h̄ e,k are the estimated channel corresponding to the
R and the k -th EVR, respectively, which are available at the BS,
hereas e s and e e, k are the channel errors associated with these
hannels, which are bounded as
e s ‖ 2 ≤ ε s , ‖ e e,k ‖ 2 ≤ ε e,k , ∀ k, (5)
here εs and εe, k are channel error bounds associated with the
hannels of VR and the k -th EVR.
.2. Robust EH balancing maximization
By exploiting the channel uncertainties model, the robust EH
alance maximization problem can be recast as
max Q s , W
min
k min
e e,k
( ̄h e,k + e e,k ) H (Q s + W )( ̄h e,k + e e,k )
E k
.t. log
(1 +
( ̄h s + e s ) H Q s ( ̄h s + e s )
( ̄h s + e s ) H W ( ̄h s + e s ) + σ 2 s
)
− log
(1 +
( ̄h e,k + e e,k ) H Q s ( ̄h e,k + e e,k )
( ̄h e,k + e e,k ) H W ( ̄h e,k + e e,k ) + σ 2 e
)≥ R̄ s , ∀ k,
Tr (Q s + W ) ≤ P, Q s � 0 , W � 0 .
(6)
We note that the problem (6) is non-convex in terms of channel
ncertainties and non-convex secrecy rate constraint. The problem
annot be solved directly. In order to give solution to this problem,
e first employ a slack variable t to reformulate the secrecy rate
onstraint as follows
f (t) = max Q s , W
min
k min
e e,k
( ̄h e,k + e e,k ) H (Q s + W )( ̄h e,k + e e,k )
E k
s.t. log
(1 +
( ̄h s + e s ) H Q s ( ̄h s + e s )
( ̄h s + e s ) H W ( ̄h s + e s ) + σ 2 s
)+ log (t ) ≥ R̄ s ,
(7a)
1 +
( ̄h e,k + e e,k ) H Q s ( ̄h e,k + e e,k )
( ̄h e,k + e e,k ) H W ( ̄h e,k + e e,k ) + σ 2 e
≤ 1
t , (7b)
Tr (Q s + W ) ≤ P, Q s � 0 , W � 0 . (7c)
here f ( t ) stands for the optimal value of the problem (7) with a
unction of t . Note that since the function f ( t ) is different to obtain
closed-form expression, numerical evaluation of f ( t ) is feasible.
emark 1. Suppose that ( Q
∗s , W
∗) is the optimal solution to prob-
em (6) , and we define t ∗ so that the following equality holds
og
(1 +
( ̄h s + e s ) H Q
∗s ( ̄h s + e s )
( ̄h s + e s ) H W
∗( ̄h s + e s ) + σ 2 s
)+ log (t ∗) = R̄ s , (8)
hen, the optimal solution Q
∗s , W
∗ is also the optimal solution to
roblem (7).
The objective of the outer-level problem is to find the optimal
alue of t , It is observed that the following theorem holds
heorem 1. The problem (6) is equivalent to the following problem
max t
f (t)
.t. t min ≤ t ≤ 1 . (9)
roof. See Appendix A.1 . �
From Theorem 1 , the problem (6) can be addressed by solving
9) instead. For a given t , the optimal value of f ( t ) can be obtained
y solving the problem (7). Thus, we consider one-dimensional line
earch algorithm to find the optimal value of t , for which the key
tep is to determine the lower and upper bound of t from the
chieved secrecy rate R s > 0, it is verified that the upper bound of
is equal to 1 from the constraint (7b) . Now, we determine the
ower bound t min via (7a)
≥(
1 +
( ̄h s + e s ) H Q s ( ̄h s + e s )
( ̄h s + e s ) H W ( ̄h s + e s ) + σ 2 s
)−1
≥(
1 +
( T r [( ̄h s + e s )( ̄h s + e s ) H Q s ]
σ 2 s
)−1
64 Z. Zhu et al. / Computer Networks 137 (2018) 61–68
Algorithm 1 Proposed algorithm to problem (14).
1. Set a lower and upper bound of the targeted secrecy rate τmin
and τmax , and a desired solution accuracy δ (very small value).
2. Outer Iteration loop begin
3. Initialize t = t min .
If t ≤ t max , then
(a) Inner Iteration loop begin
(b) Setting τ = (τmin + τmax ) / 2 .
(c) Solving problem (14).
if problem (14) is feasible
then τ = τmin .
else
then τ = τmax .
end
(d) Until τmax − τmin ≤ δ, break .
(e) Inner Iteration loop end
Update t := t + t .
4. Outer Iteration loop end
5. The optimal value ( τ , Q s , W ) can be obtained via arg max t
f (t) .
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≥(
1 +
( Tr [ Q s ] Tr [( ̄h s + e s )( ̄h s + e s ) H ]
σ 2 s
)−1
≥(
1 +
P (‖ ̄h s + e s ‖
2 2
σ 2 s
)−1
≥(
1 +
P (‖ ̄h s ‖ 2 + ε s ) 2
σ 2 s
)−1
= t min . (10)
It can be easily observed that problem (7) is still non-convex
for a given t in terms of the channel uncertainties. To convert the
problem into a tractable one, we consider the following equivalent
modifications via a standard epigraph variable τ :
max Q s , W ,τ
τ
s.t. ( ̄h e,k + e e,k ) H (Q s + W )( ̄h e,k + e e,k ) ≥ τE k , ∀ k,
( ̄h s + e s ) H [ tQ s − (2
R̄ s − t) W ]( ̄h s + e s ) − (2
R̄ s − t) σ 2 s ≥ 0 ,
( ̄h e,k + e e,k )[ tQ s − (t −1 − 1) W ]( ̄h e,k + e e,k ) ≤ (t −1 − 1) σ 2 e , ∀ k,
Tr (Q s + W ) ≤ P, Q s � 0 , W � 0 . (11)
In order to remove the impact led by the channel uncertainties,
the following lemma is used.
Lemma 1. ( S-Procedure ) [31] : Let f k (x ) (k = 1 , 2) be
f k (x ) = x
H A k x + 2 �
{b
H k x
}+ c k , (12)
where A k = A
H k
∈ C
n ×n , b k ∈ C
n ×1 and c k ∈ R . The implication
f 1 ( x ) ≥ 0 �⇒ f 2 ( x ) ≥ 0 holds if and only if there exists μ≥ 0 such that[A 2 b 2
b
H 2 c 2
]− μ
[A 1 b 1
b
H 1 c 1
]� 0 , (13)
provided there exists a point ˜ x with f 1 ( ̃ x ) > 0 . �
By exploiting S-Procedure shown in Lemma 1 , problem (11) can
be reformulated as (14) on the top of next page.
max �
τ (14a)
s.t. Tr (Q s + W ) ≤ P, [αe,k I + (Q s + W ) (Q s + W ) ̄h e,k
h̄
H e,k
(Q s + W ) h̄
H e,k
(Q s + W ) ̄h e,k − τE k − αe,k ε 2 e
]� 0 , ∀ k,
(14b)
⎡
⎣
λs I +
(tQ s − (2 R̄ s − t) W
) (tQ s − (2 R̄ s − t) W
)h̄ s
h̄ H s
(tQ s − (2 R̄ s − t) W
)h̄ H s
(tQ s − (2 R̄ s − t) W
)h̄ s − (2 R̄ s − t) σ 2
s − λs ε 2 s
⎤
⎦
� 0 , (14c)
⎡
⎣
λe,k I −(
Q s − (t −1 − 1) W
)−(
Q s − (t −1 − 1) W
)h̄ e,k
−h̄ H e,k
(Q s − (t −1 − 1) W
)−h̄ H
e,k
(Q s − (t −1 − 1) W
)h̄ e,k + (t −1 − 1) σ 2
e − λe,k ε 2 e,k
⎤
⎦
� 0 , (14d)
{ Q s � 0 , W � 0 , αe,k ≥ 0 , λs ≥ 0 , λe,k ≥ 0 , τ ≥ 0 } ∈ �. (14e)
We can observe that problem (14) is quasi-convex and can be
solved by interior-point method for a given t and the optimal solu-
tion to problem (14) can be achieved through the bisection method
over τ . In this regard, the optimal solution to the original problem
(4) can be generally obtained via one-dimension line search algo-
rithm over t to check whether the problem (14) is feasible or not.
he proposed algorithm solving the original problem is summa-
ized in Algorithm 1 .
Now, we turn our attention to the tightness analysis of the re-
axation. It is more challenging to show the optimal solution to
14). First, let τ ∗ be the optimal value of the above problem, and
e claim the following power minimization problem can return
he same optimal solution to (14) ( Q s , W ) in [27] ,
in
�Tr (Q s + W )
s.t. (14 b) with τ ∗, (14 c) , (14 d) , (14 e ) . (15)
hus, we will show that the alternative problem (15) has rank-one
olution with the following theorem :
heorem 2. Providing that problem (15) is feasible for given τ ∗ and t,
he optimal solution ( Q s , W ) can be obtained by solving the problem
n (15) , and rank( Q s ) ≤ 1 .
roof. See Appendix A.2 . �
emark 2. By exploiting Theorem 2 , it is observed that the opti-
al solution of problem (15) is rank-one. If we obtain rank( Q s ) > 1
y solving the problem (14), then the solution can be obtained via
he alternative problem (15) and this optimal solution also satisfies
ank( Q s ) ≤ 1. �
. Numerical results
In this section, we present the simulation results to validate the
erformance of the proposed robust design algorithm. We consider
MISO V2X-SWIPT secrecy channel for Rayleigh flat-fading envi-
onments with zero-mean and unit variance. We assume that the
ystem model consists of one BS, one VR, and three EVRs. Indeed,
ome other configurations can be employed with different num-
er of EVRs, however, the results will be similar, the only differ-
nce is the computation complexity. In our simulations, the BS is
quipped with five transmit antennas (i.e., N T = 5 ), where the VR
nd the EVRs consist of single antenna each of them. In addition,
he normalized noise power of the VR and the EVRs are assumed
i.e., σ 2 s = σ 2
e = 1 ), for the sake of compactness. Also, channel error
ector is bounded as 0.05 (i.e., ε s = ε e,k = 0 . 05 , ∀ k ).
First, we evaluate the harvested power with target harvested
ower threshold for each EH EVR in Fig. 2 . The target har-
ested power threshold for each EVR employed in the EH bal-
nce maximization is assumed to be E = 10 W, E = 20 W, and
1 2Z. Zhu et al. / Computer Networks 137 (2018) 61–68 65
Fig. 2. The comparison of the achieved harvested power with the target harvested
power for each EH EVR.
Fig. 3. The achieved harvested power with the different transmit power values.
E
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Fig. 4. The achieved harvested power with the different target secrecy rates.
Fig. 5. The energy harvesting balance with the different transmit powers.
Fig. 6. The harvested power with the different ε.
3 = 30 W. From this figure, one can easily observe that the
H balance is achieved by employing the proposed algorithm in
lgorithm 1 , since the harvested power for each EH EVR is propor-
ional to their target harvested power values.
Next, we evaluate the EH performance with different transmit
owers and the target secrecy rates in Figs. 3 and 4 . Fig. 3 is the re-
ult of harvested power with different transmit power values. One
an observe that the harvested power increases with the transmit
ower, and the perfect CSI based scheme outperforms the imper-
ect CSI based scheme. This is due to the constant value of harvest
oefficient with η, as defined previously. The harvested power with
he target secrecy rate is shown in Fig. 4 , which confirms the har-
ested power decreases with the target secrecy rate.This confirmed
hat our proposal can secure the transmission procedure as well. In
ddition, we compare our proposed robust scheme with the robust
cheme without AN assisted here. It is obviously seen that our pro-
osed scheme can harvest the more power than the scheme with-
ut the AN, since the AN is not only employed to confuse the EVR
o achieve the target secrecy rate, but also involved in the energy
arvesting.
66 Z. Zhu et al. / Computer Networks 137 (2018) 61–68
A
p
L
w
d
A
N
w
�
B[
W
[
L
m
n
r
The EH balance ratio is further evaluated, whose result is given
by Fig. 5 . Observation from this figure confirms that the EH balance
ratio increases with the transmit power, which implies the har-
vested power can be enhanced by improving the transmit power.
Moreover, the robust scheme with AN outperforms that without
AN in terms of the EH balance ratio, and the gap of the EH balance
ratio between the our proposed robust scheme with AN and with-
out AN becomes larger with high transmit power value regime.
This is mainly due to the fact that a portion of the harvested en-
ergy at the EVRs can be provided by the AN signal.
Finally, the harvested power with the error bound (i.e., ε) is
evaluated in Fig. 6 . As seen in this figure, one can observe that the
harvested power of the imperfect CSI decreases with ε, whereas
the harvested power of the perfect CSI based scheme will not
change with ε. This is because that when ε is increased, the ac-
curacy of the estimated channel become worse.
5. Conclusions
Considering the limited vehicle battery issue, we presented a
novel robust EH balancing optimization problem for a V2X-SWIPT
with a MISO secrecy channel. For secrecy consideration, we ex-
ploited an AN scheme to interrupt the eavesdroppers without any
structural restriction. By incorporating the channel uncertainties,
the harvested power is balanced subject to the secrecy rate con-
straint and the transmit power constraints. To solve this non-
convex problem, we first converted it into a two-level optimization
problem. One-dimensional line search method has been employed
to solve the outer-level problem. Afterwards, the inner-level prob-
lem has been reformulated as a sequence of SDPs, which can be
solved by the bisection method. In addition, we prove that the re-
laxation is tight, i.e., the optimal solution of the relaxed problem
is rank-one. Simulation results have been provided to validate the
performance of our proposed scheme.
Acknowledgments
This work was supported by the National Nature Science Foun-
dation of China under grant ( 61571402 , 61771431 , 61601516 ). The
work of D. Zhang and B. Shim was supported by the NRF grant
funded by the Korean government (MSIP2014R1A5A1011478).
Appendix A
A.1. Proof of Theorem 1
In order to prove Theorem 1 , it is assumed that ϕ 1 and ϕ 2 are
optimal values of problem (6) and problem (9) , respectively. Firstly,
we show that problem (9) can obtain the optimal value of problem
(6) (i.e., ϕ 2 ≥ϕ 1 ). It can be easily verified that the following equal-
ity holds:
ϕ 1 = f (t ∗) , (16)
where t ∗ is the optimal value of t in (6) . On the other hand, it
follows ϕ 2 = max τ≥0
f (τ ) ≥ f (t ∗) . Thus, we have ϕ 2 ≥ϕ 1 .
Secondly, in order to prove that problem (6) can achieve the
optimal value of problem (9) (i.e., ϕ 1 ≥ϕ 2 ). It is assumed that t †
is the optimal variable value of problem (9) , and w
† is the optimal
solution of problem (7) with τ = τ † . It can be easily observed from
(7a), (7b) , and (7c) that w
† is also a feasible solution of problem
(6) , thus, ϕ 1 ≥ϕ 2 .
We combine these two parts, it includes ϕ 1 = ϕ 2 . This com-
pletes the proof. �
.2. Proof of Theorem 2
We first consider the Lagrange dual function of the associated
ower minimization problem (15) as follows:
(Q s , W , Z , Y , R e,k , T s , T e,k ) = Tr (Q s ) + Tr (W ) − Tr (ZQ s )
− Tr (YW ) −K ∑
k =1
Tr (R e,k A e,k ) −K ∑
k =1
Tr [ R e,k H
H e,k (Q s + W ) H e,k ]
− Tr (T s B s ) − Tr (T s H
H s [ tQ s − (2
R̄ s − 1) W ] H s
)−
K ∑
k =1
Tr (T e,k A e,k )
+
∑ K
k =1 Tr
(T e,k H
H e,k [ Q s − (t −1 − 1) W ] H e,k
), (17)
here Z ∈ H
N T + , Y ∈ H
N T + , R e,k ∈ H
N T + , T s ∈ H
N T + , and T e,k ∈ H
N T + are
ual variables of Q s , W , (14b), (14c) , and (14d) , in addition,
e,k =
[αe,k I 0
0
H −τ ∗E k − αe,k ε 2 e,k
], H e,k =
[I h̄ e,k
],
B s =
[λs I 0
0
H −(2
R̄ s − t) σ 2 s − λs ε 2 s
], H s =
[I h̄ s
],
B e,k =
[λe,k I 0
0
H (t −1 − 1) σ 2 e − λe,k ε
2 e,k
], ∀ k.
ext, we consider the following related KKT conditions:
∂L
∂Q s = I − Z −
K ∑
k =1
H e,k R e,k H
H e,k − tH s T s H
H s
+
K ∑
k =1
H e,k T e,k H
H e,k = 0 , (18a)
ZQ s = 0 , (B s + H
H s [ tQ s − (2
R̄ s − 1) W ] H s
)T s = 0 , (18b)
R e,k � 0 , T s � 0 , T e,k � 0 . (18c)
Then, by denoting � = I +
∑ K k =1 H e,k T e,k H
H e,k
− ∑ K k =1 H e,k R e,k H
H e,k
,
e have
− tH s T s H
H s = Z . (19)
y considering the following two facts:
I 0
]H
H s = I ,
[I 0
]B s = λs
(H s −
[0 h̄ s
]). (20)
e pre-multiply [I 0
]and post-multiply H
H s by
(B s + H
H s [ tQ s −
(2 R̄ s − 1) W ] H s
)T s = 0 , which yields
I 0
]B s T s H
H s +
[I 0
]H
H s [ tQ s − (2
R̄ s − 1) W ] H s T s H
H s = 0 ,
⇒ λs
(H s −
[0 h̄ s
])T s H
H s + [ tQ s − (2
R̄ s − 1) W ] H s T s H
H s = 0 ,
⇒
(λs I + [ tQ s − (2
R̄ s − 1) W ] )H s T s H
H s = λs
[0 h̄ s
]T s H
H s . (21)
emma 2. If a block hermitian matrix P =
[P 1 P 2
P 3 P 4
]� 0 , then the
ain diagonal matrices P 1 and P 4 are always PSD matrices [32] . �
From Lemma 2 , we claim λs I + [ tQ s − (2 R̄ s − 1) W ] � 0 , which is
onsingular. In this case, we have from (21) ,
ank (H s T s H
H s )
= rank [(
λs I + [ tQ s − (2
R̄ s − 1) W ] )H s T s H
H s
]= rank
(λs
[0 h̄ s
]T s H
H s
)= rank
([0 h̄ s
])≤ 1 . (22)
Z. Zhu et al. / Computer Networks 137 (2018) 61–68 67
L
i
r
h
o
r
l
h
i
c
h
t
R
[
[
[
[
[
[
[
[
[
[
emma 3. Let P 1 and P 2 be two same size matrices, then the follow-
ng matrix inequality holds:
ank (P 1 − P 2 ) ≥ rank (P 1 ) − rank (P 2 ) . (23)
The proof of Lemma 3 is easy to be follow, which is omitted
ere for brevity. From Lemma 3 , (19) and (22) , we have Z ≥ N T − 1 ,
n condition that rank (�) = N T . However, it is easily verified that
ank( Z ) = N T , since Q s = 0 is not the optimal solution of the prob-
em (15) when rank( Z ) is a full rank matrix. Thus, only rank( Z )
olds true. From Q s Z = 0 , we have rank (Q s ) = 1 . Now, the remain-
ng task is to show � is positive-definite matrix (i.e., � � 0 ). By
onsidering that � � 0 must hold true by contradiction, which
ave been shown in [30] . Thus, we can claim rank (Q s ) = 1 holds
rue here.
This completes the proof. �
eferences
[1] ASTM, standard specification for telecommunications and information ex-change between roadside and vehicle systems - 5 GHz band dedicated short
range communications (DSRC) medium access control (MAC) and physicallayer (PHY) specifications [online:] https://compass.astm.org/download/e2213.
33568.pdf ., ASTM International (2010). [2] T. A. A. News, U.s. launches smart-car project in ann arbor with
thousands of vehicles that talk to each other [online:] http://www.
annarbor.com/business-review/reinventing-the-automobile-ann-arbor- deployment- to- facilitate- conversations- between- nearly- 30 0 0-cars/ , 2012.
[3] ETSI, CEN and ETSI deliver first set of standards for cooperative intelligenttransport systems (C-ITS) [online:] http://www.etsi.org/news-events/news/
753- 2014- 02- joint- news- cen- and- etsi- deliver- first- set- of- standards- for- cooperative-intelligent-transport-systems-c-its , 2014.
[4] S. Chen , J. Hu , Y. Shi , L. Zhao , LTE-V: A TD-LTE-Based V2X solution for future
vehicular network, IEEE Internet Things J. 3 (6) (2016) 997–1005 . [5] S. Chen , J. Hu , Y. Shi , Y. Peng , J. Fang , R. Zhao , L. Zhao , Vehicle-to-everything
(V2X) services supported by LTE-Based systems and 5G, IEEE Commun. Stan-dards Mag. 1 (2) (2017) 70–76 .
[6] W. Liu , M. Zhang , Z. Luo , Y. Cai , An ensemble deep learning method for vehicletype classification on visual traffic surveillance sensors, IEEE Access 5 (2017)
24417–24 425 .
[7] T. Zhou , P. Krenbl , M. Aubry , Q. Huang , A .A . Efros , Learning Dense Correspon-dence via 3D-guided Cycle Consistency, in: 2016 IEEE Conference on Computer
Vision and Pattern Recognition (CVPR), 2016, pp. 117–126 . [8] S.H. Ahmed , S.H. Bouk , D. Kim , D.B. Rawat , H. Song , Named data networking
for software defined vehicular networks, IEEE Commun. Mag. 55 (8) (2017)60–66 .
[9] S.H. Ahmed , S.H. Bouk , M.A. Yaqub , D. Kim , H. Song , DIFS: distributed inter-
est forwarder selection in vehicular named data networks, IEEE Trans. Intell.Transp. Syst. (99) (2017) 1–5 .
[10] S.H. Ahmed , S.H. Bouk , M.A. Yaqub , D. Kim , H. Song , J. Lloret , Codie: controlleddata and interest evaluation in vehicular named data networks, IEEE Trans.
Veh. Technol. 65 (6) (2016) 3954–3963 . [11] J. Maurer , T. Fuegen , W. Wiesbeck , A ray-optical channel model for vehicular
Ad-Hoc networks, in: 11th European Wireless Conference, 2005, pp. 1–7 .
[12] G. Acosta-Marum , M.A. Ingram , Six time- and frequency- selective empiricalchannel models for vehicular wireless LANs, IEEE Veh. Technol. Mag. 2 (4)
(2007) 4–11 . [13] A.S. Akki , F. Haber , A statistical model of mobile-to-mobile land communica-
tion channel, IEEE Trans. Veh. Technol. 35 (1) (1986) 2–7 . [14] H. Peng , D. Li , Q. Ye , K. Abboud , H. Zhao , W. Zhuang , X. Shen , Resource alloca-
tion for cellular-based inter-vehicle communications in autonomous multipla-toons, IEEE Trans. Veh. Technol. 66 (12) (2017) 11 249–11 263 .
[15] Z. Zhou , C. Gao , C. Xu , T. Chen , D. Zhang , S. Mumtaz , Energy-efficient stable
matching for resource allocation in energy harvesting-based device-to-devicecommunications, IEEE Access 5 (2017) 15184–15196 .
[16] D. Zhang , Y. Liu , Z. Ding , Z. Zhou , A. Nallanathan , T. Sato , Performance analysisof non-regenerative massive-MIMO-NOMA relay systems for 5G, IEEE Trans.
Commun. 65 (11) (2017) 4777–4790 . [17] Y. Wang , C. Li , Y. Huang , D. Wang , T. Ban , L. Yang , Energy-efficient optimization
for downlink massive MIMO FDD systems with transmit-side channel correla-
tion, IEEE Trans. Veh. Technol. 65 (9) (2016) 7228–7243 . [18] Z. Zhu , Z. Chu , Z. Wang , I. Lee , Joint optimization of AN-aided beamforming
and power splitting designs for MISO secrecy channel with SWIPT, in: Proc.IEEE ICC, 2016, pp. 1–6 .
[19] B. Li , Z. Fei , Z. Chu , Y. Zhang , Secure Transmission for Heterogeneous CellularNetworks with Wireless Information and Power Transfer, IEEE Systems J. PP
(99) (2017) 1–12 .
20] Z. Zhu, Z. Chu, F. Zhou, H. Niu, Z. Wang, I. Lee, Secure beamforming designs forsecrecy MIMO SWIPT systems, IEEE Wireless Commun. Lett. (2018) in press,
[online:] http://ieeexplore.ieee.org/document/8169119/ . [21] Z. Zhu , Z. Chu , Z. Wang , I. Lee , Outage constrained robust beamforming for se-
cure broadcasting systems with energy harvesting, IEEE Trans. Wireless Com-mun. 15 (11) (2016) 7610–7620 .
22] B. Li , Z. Fei , Z. Chu , Optimal transmit beamforming for secure SWIPT in a
two-tier hetnet, IEEE Commun. Lett. 21 (11) (2017) 2476–2479 . 23] Z. Zhu, S. Huang, Z. Chu, F. Zhou, D. Zhang, I. Lee, Robust designs of beam-
forming and power splitting for distributed antenna systems with wireless en-ergy harvesting, IEEE Syst. J. (2018) in press, [online:] http://ieeexplore.ieee.
org/document/8283591/ . 24] Z. Zhu , Z. Chu , N. Wang , S. Huang , Z. Wang , I. Lee , Beamforming and power
splitting designs for AN-aided secure multi-user MIMO SWIPT systems, IEEE
Trans. Inf. Forensics Security 12 (12) (2017) 2861–2874 . 25] D. Wang , R. Zhang , X. Cheng , Z. Quan , L. Yang , Joint power allocation and split-
ting (JoPAS) for swipt in doubly selective vehicular channels, IEEE Trans. GreenCommun. Netw. 1 (4) (2017) 494–502 .
26] A. Khisti , G.W. Wornell , Secure transmission with multiple antennas II: the MI-MOME wiretap channel, IEEE Trans. Inform. Theory 56 (11) (2010) 5515–5532 .
[27] Q. Li , W.K. Ma , Spatially selective artificial-noise aided transmit optimization
for MISO multi-eves secrecy rate maximization, IEEE Trans. Signal Process. 61(10) (2013) 2704–2717 .
28] Z. Chu , K. Cumanan , Z. Ding , M. Johnston , S.L. Goff, Secrecy rate optimizationsfor a MIMO secrecy channel with a cooperative jammer, IEEE Trans. Veh. Tech-
nol. 64 (5) (2015) 1833–1847 . 29] L. Liu , R. Zhang , K.C. Chua , Secrecy wireless information and power transfer
with MISO beamforming, IEEE Trans. Signal Process. 62 (7) (2014) 1850–1863 . 30] M. Khandaker , K. Wong , Masked beamforming in the presence of energy-har-
vesting eavesdroppers, IEEE Trans. Inf. Forensics Sec. 10 (1) (2015) 40–54 .
[31] S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan , Linear Matrix Inequalities inSystem and Control Theory, SIAM Stud. Appl. Math., Philadelphia PA, 1994 .
32] R.A. Horn , C.R. Johnson , Matrix Analysis, Cambridge University Press, NewYork, 1985 .
68 Z. Zhu et al. / Computer Networks 137 (2018) 61–68
in 2010, and received the Ph.D. degree from Zhengzhou University, China, in 2017. Cur-
hengzhou University, China. His research interests include information theory and signal ireless network, physical layer security, wireless cooperative networks, internet of things,
and energy harvesting communication systems.
utomatic Control from Harbin Shipbuilding Engineering Institute, Harbin, China, in 1986
utomatic Control Theory and Application from Xi’an Jiaotong University, Xi’an, China, in zhou University, Zhengzhou, China, as a lecturer in the Department of Electronics. From
he was promoted to professor in the Department of Communication Engineering. Prof. within embedded systems, signal processing and communication theory.
lectrical and Electronic Engineering, Newcastle University, U.K., in 2016. He was with the
London, U.K., from 2016 to 2017. He is currently with the 5G Innovation Center, Institute research interests include physical layer security, wireless cooperative networks, wireless
theory.
seda University, Tokyo, Japan (2013–2017), M.S. degree with honor from Central China he is an Assistant Professor with the Zhengzhou University, Zhengzhou, China, He is also
ry, Department of Electrical and Computer Engineering, Seoul National University, Seoul,
te Electrical Power System with Renewable Energy Sources, North China Electric Power Technology Laboratory, National Chung Hsing University (2012). He has engaged in two
working co-funded by the EU FP-7, Horizon 2020, Japanese Monbushou and NICT. He has uch as IEEE ICC, WCNC, VTC, CCNC, Healthcom . His research interests include 5G, internet
and signal processing.
trol and instrumentation engineering from Seoul National University, Korea, in 1995 and atics and the Ph.D. degree in electrical and computer engineering from the University of
pectively. From 1997 and 20 0 0, he was with the Department of Electronics Engineering, and an Academic Full-time Instructor. From 2005 to 2007, he was with Qualcomm Inc.,
14, he was with the School of Information and Communication, Korea University, Seoul, een with the Seoul National University (SNU), where he is currently a Professor with the
search interests include wireless communications, statistical signal processing, estimation
y. Dr. Shim was the recipient of the M. E. Van Valkenburg Research Award from the ECE Young Engineer Award from IEIE (2010), and Irwin Jacobs Award from Qualcomm and
g for Communications and Networking (SPCOM) Technical Committee of the IEEE Signal e IEEE Transactions on Signal Processing, IEEE Wireless Communications Letters, Journal
he IEEE Journal on Selected Areas in Communications (JSAC).
Zhengyu Zhu received B.S. degree from Henan University
rently, He is with the School of Information Engineering, Zprocessing for wireless communications such as MIMO w
vehicle communications, convex optimization techniques,
Zhongyong Wang received his B.S. and M.S. degrees in A
and 1988, respectively, and received his Ph.D. degree in A1998. Since 1988, Zhongyong Wang has been with Zheng
1999 to 2002, he was an associate professor, and in 2002Wang’s general fields of interest cover numerous aspects
Zheng Chu received the Ph.D. degree from the School of E
Faculty of Science and Technology, Middlesex University, of Communication Systems, University of Surrey, U.K. His
power transfer, convex optimization techniques, and game
Di Zhang received his Ph.D. degree with honor from WaNormal University, Wuhan, China (2010–2013). Currently,
a Senior Researcher with the Information System Laborato
Korea. He visited the National Key Laboratory of AlternaUniversity (2015–2017), and the Advanced Communication
international projects in wireless communications and netserved as the TPC member of several IEEE conferences, s
of things, vehicle communications, green communications
Byonghyo Shim received the B.S. and M.S. degrees in con1997, respectively. He received the M.S. degree in mathem
Illinois at Urbana-Champaign, USA, in 2004 and 2005, resKorean Air Force Academy as an Officer (First Lieutenant)
San Diego, CA, USA, as a Staff Engineer. From 2007 to 20as an Associate Professor. Since September 2014, he has b
Department of Electrical and Computer Engineering. His re
and detection, compressed sensing, and information theorDepartment of the University of Illinois (2005), Hadong
KICS (2016). He is an elected member of Signal ProcessinProcessing Society. He has been an Associate Editor of th
of Communications and Networks, and a Guest Editor of t
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