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: zheng.chu@surrey.ac.uk (Z. Chu), di_zhang@islab.snu.ac.kr ,

r.di.zhang@ieee.org (D. Zhang), bshim@islab.snu.ac.kr (B. Shim).

g

b

t

t

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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r

l

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w

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m

T

s

T

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m

b

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r

4

p

a

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s

s

b

e

e

a

t

(

v

p

v

a

≥(

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 2

Z. 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

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. �

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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