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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020 3021
Power Allocation for Intelligent Interference
Exploitation Aided Physical-Layer Security in
OFDM-Based Heterogeneous Cellular Networks
Yuhan Jiang , Yulong Zou , Senior Member, IEEE, Haiyan Guo , Jia Zhu, and Jiahao Gu
Abstract—In this paper, we consider an orthogonal frequency di-
vision multiplexing (OFDM) based heterogeneous cellular network
consisting of a macro cell and a small cell, where a macro-cell base
station (MBS) and a small-cell base station (SBS) communicate
with respective macro-cell user (MU) and small-cell user (SU) with
the existence of a common eavesdropper across different OFDM
subcarriers. In order to make full use of the mutual interference be-
tween MBS and SBS against eavesdropping, an artificially designed
signal is emitted at MBS to cancel out the interference received
at MU as well as to interfere with the common eavesdropper
at each subcarriers. For the purpose of further improving the
secrecy performance, a sum secrecy rate (SSR) of OFDM-based
heterogeneous cellular networks is maximized by optimizing the
power allocation between MBS and SBS across different OFDM
subcarriers when the eavesdropper owns the global instantaneous
channel state information (ICSI), thus called ICSI based SSR
maximization (ICSI-SSRM). As for the case when the ICSI of
wiretap channels is unknown, we propose a statistical CSI based
SSR maximization (SCSI-SSRM) scheme, where the statistical
characteristics of channels from MBS and SBS to eavesdropper
are employed to optimally allocate powers of MBS and SBS across
different subcarriers under the constraint of MBS’s total transmit
power. The formulated ICSI-SSRM and SCSI-SSRM problems are
all non-convex due to form of the difference between two-convex
(D.C.) functions. Thus, we utilize the D.C. approximation approach
to respectively convert original optimization problems into convex
problems. Moreover, iterative optimal power allocation algorithms
for ICSI-SSRM and SCSI-SSRM schemes are also presented to
obtain their respective SSR values. Simulation results illustrate that
Manuscript received June 7, 2019; revised September 10, 2019 and November
25, 2019; accepted January 2, 2020. Date of publication January 14, 2020; date of
current version March 12, 2020. This work was supported in part by the National
Natural Science Foundation of China under Grants 61631020, 61671253, and
91738201, in part by the Natural Science Foundation of Jiangsu Province under
Grant BK20171446, in part by the Key Project of Natural Science Research of
Higher Education Institutions of Jiangsu Province under Grant 18KJB510031,
in part by the Postgraduate Research & Practice Innovation Program of Jiangsu
Province under Grant KYCX19_0892, and in part by the Open Research Foun-
dation of Key Laboratory of Dynamic Cognitive System of Electromagnetic
Spectrum Space (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Industry and
Information Technology under Grant KF20181910. The review of this article
was coordinated by Dr. J. Liu. (Corresponding author: Yulong Zou.)
Y. Jiang, Y. Zou, J. Zhu, and J. Gu are with the School of Telecom-
munications and Information Engineering, Nanjing University of Posts and
Telecommunications,Nanjing 210003, China (e-mail: 15262769115@163.com;
yulong.zou@njupt.edu.cn; jiazhu@njupt.edu.cn; Q16010125@njupt.edu.cn).
H. Guo is with the School of Telecommunications and Information Engineer-
ing, Nanjing University of Posts and Telecommunications, Nanjing 210003,
China, and also with the Key Laboratory of Dynamic Cognitive System of
Electromagnetic Spectrum Space (Nanjing Univ. Aeronaut. Astronaut.), Min-
istry of Industry and Information Technology, Nanjing 210003, China (e-mail:
guohy@njupt.edu.cn).
Digital Object Identifier 10.1109/TVT.2020.2966637
the ICSI-SSRM and SCSI-SSRM algorithms can converge to their
optimal values, which confirms the correctness and validation of
the proposed algorithms. In addition, numerical results are also
given to show that the ICSI-SSRM and SCSI-SSRM schemes out-
perform conventional power allocation methods in terms of their
SSR performance.
Index Terms—Heterogeneous cellular networks, power
allocation, interference, physical-layer security.
I. INTRODUCTION
NOWADAYS, with the emergence of various wireless com-
munication devices [1], [2], such as mobile phones, tablet
computers, smart watches and so on, the demand for radio
spectrum resources is increasing explosively. Thus, it is of
great importance to improve the spectral efficiency [3]–[5].
Heterogeneous cellular network is considered as an effective
means of taking full advantages of radio spectrum resources and
boosting the network capacity [6], [7]. Specifically, the spectrum
resources can be simultaneously accessed by both the macro-cell
user (MU) and small-cell user (SU) in heterogeneous cellular
networks to achieve a higher spectral efficiency [8], [9]. Besides,
in order to meet the high speed data rates, orthogonal frequency
division multiplexing (OFDM) technology has been employed
in heterogeneous cellular networks [10], [11]. However, since a
macro cell shares the same spectrum resources with a small cell
at each subcarriers, a mutual interference among them degrades
the performance of OFDM-based heterogeneous cellular net-
works. Therefore, it is important to investigate power allocation
and interference management to control and limit such mutual
interferences [12]–[15]. More specifically, in heterogeneous cel-
lular networks, the interference caused by each mobile terminals
was controlled below a predefined threshold by designing a
stochastic geometry based power allocation mechanism [16].
Later on, for the purpose of degrading the inter-cell interference
received at the offloaded users caused by macro-cell base stations
(MBSs), the authors of [17] proposed a scheme combing reverse
frequency allocation with user association.
Besides, although the opening nature of wireless communica-
tions brings a lot of convenience to our lives, it is also vulnerable
to eavesdropping attacks. For example, an eavesdropper may
overhear the confidential information transmitted over hetero-
geneous cellular networks [18], [19]. Thus, extensive research
efforts have been devoted to defend against eavesdropping and
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3022 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
further enhance the secrecy performance of wireless communi-
cations, including beamforming (BF) [20], cooperative relays
[21], artificial noise (AN) [22], cooperative jamming [23], [24]
and so on. To be specific, in [20], a joint BF and time allocation
scheme was proposed to maximize the sum rates of the device-to-
device (D2D) users in a time-division duplex D2D cellular net-
work by taking into account the quality-of-service requirement
of cognitive users. The secrecy capacity was improved in [21] by
employing relay nodes to assist the transmission from source to
destination, where outage probability and intercept probability
of both single-relay selection and multi-relay selection schemes
were analyzed. Additionally, the authors of [22] injected AN
signals to confuse the eavesdropper in a multiple-input-single-
output (MISO) multicast system with available eavesdropper’s
statistical channel state information (CSI), and applied BF to
guarantee that AN signals would not cause the interference to le-
gitimate users. Moreover, [23] proposed a cooperative jamming
scheme to defend against randomly distributed eavesdroppers
and designed jammer placement algorithms to obtain the optimal
number of jammers. In order to obtain secure transmission in
MISO wiretap channels, the authors of [24] jointly utilized the
BF, AN and friendly jammering technologies to maximize the
secrecy rate, where full CSI and channel distribution information
of eavesdropper were considered.
Meanwhile, considerable attentions have been paid to the
physical-layer security (PLS) of heterogeneous spectrum-
sharing networks [25]–[31]. More specifically, the closed-from
expressions of outage probability for D2D communication en-
abled multi-channel cellular networks were derived in [25].
Moreover, the D2D technology was employed in LTE-Advanced
networks to improve energy efficiency, delay, throughput [26]
and quality of experience [27] as well as load balancing ef-
ficiency [28]. The PLS of a multi-tier heterogeneous cellular
network having random distributed base stations, users and
eavesdroppers was studied in [29] in terms of connection proba-
bility and secrecy probability. Also, the authors of [30] employed
friendly jammers and full-duplex users to improve the PLS
of heterogeneous spectrum-sharing networks. More recently,
the author of [31] proposed a so-called interference-canceled
underlay spectrum sharing (IC-USS) scheme to improve the PLS
of heterogeneous cellular networks, where an artificial signal
was designed and emitted at MBS to cancel out the interference
received at MU and to interfere with an eavesdropper. Never-
theless, the ratio of transmit power of the small-cell base station
(SBS) to that of the MBS for IC-USS scheme in [31] was fixed
to analyze the system overall outage probability and intercept
probability as well as secrecy diversity. It is worth mentioning
that the transmit power allocation between MBS and SBS can be
further optimized to enhance the PLS of heterogeneous cellular
networks.
In this paper, for the purpose of enhancing the spectral effi-
ciency, limiting the interference and degrading the eavesdrop-
per, we are motivated to examine an optimization of transmit
power allocation between MBS and SBS across different OFDM
subcarriers to maximize the sum secrecy rate (SSR) of both
macro cell and small cell in an OFDM-based heterogeneous
cellular network, where both the instantaneous and statistical
CSI of eavesdropper are considered. The differences between
this paper and [31] are listed as follows. First, we consider
an OFDM based heterogeneous cellular network in our system
model, which is more complex than [31], where the allocated
power for MBS and SBS was fixed. It is more challenging to
perform the optimal power allocation between MBS and SBS
across different OFDM subcarriers. Second, this paper takes into
account both the instantaneous and statistical CSI of wiretap
links to maximize the SSR of OFDM based heterogeneous
cellular networks. The main contributions of this paper can be
summarized as follows.
rWe consider an OFDM based heterogeneous cellular net-
work, where a specially-designed signal is emitted at MBS
to cancel out the interference caused by SBS for any
OFDM subcarrier. To maximize the SSR of both macro cell
and small cell in an OFDM-based heterogeneous cellular
network, we propose an instantaneous CSI (ICSI) based
SSR maximization (ICSI-SSRM) scheme by optimizing
the power allocation between MBS and SBS across dif-
ferent OFDM subcarriers. As for the case when the ICSI
of eavesdropper is unknown, a statistical CSI (SCSI) based
SSR maximization (SCSI-SSRM) strategy is also analyzed
in OFDM based heterogeneous cellular networks.
rDue to the fact that our proposed ICSI-SSRM and SCSI-
SSRM problems are non-convex, we firstly apply the
difference of two-convex functions (D.C.) approximation
method to transform the original problems into convex
problems. Then iterative power allocation algorithms are
proposed to obtain the corresponding optimal solutions for
ICSI-SSRM and SCSI-SSRM schemes.
rNumerical simulations are carried out to show the conver-
gence performance of our proposed iterative ICSI-SSRM
and SCSI-SSRM algorithms. It is also shown that proposed
ICSI-SSRM and SCSI-SSRM schemes obtain a better
secrecy performance than conventional power allocation
approaches.
The rest of this paper is organized as follows. In Section II, we
describe the system model and formulate ICSI-SSRM and SCSI-
SSRM problems in OFDM-based heterogeneous cellular net-
works. Next, Section III respectively gives the solutions of our
formulated ICSI-SSRM and SCSI-SSRM problems and presents
corresponding iterative optimal power allocation algorithms,
followed by Section IV, where numerical simulation results are
given to show the advantage of the proposed ICSI-SSRM and
SCSI-SSRM schemes. Finally, a brief summary of our results is
provided in Section V.
A list of notations and representations used in this paper is
presented in Table I.
II. SYSTEM MODEL AND PROBLEM FORMULATION
In this section, we present the system model of an orthogonal
frequency division multiplexing (OFDM) based heterogeneous
cellular network, where the interference received at macro-cell
user (MU) is canceled out at each subcarrier. Then, we formu-
late instantaneous channel state information (ICSI) based sum
secrecy rate maximization (ICSI-SSRM) and statistical channel
state information (SCSI) based sum secrecy rate maximization
(SCSI-SSRM) schemes in OFDM-based heterogeneous cellular
networks.
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3023
TAB LE I
NOTATIONS AND REPRESENTATIONS
Fig. 1. AnOFDM-based heterogeneous cellular network comprised of a macro
cell and a small cell in the presence of an eavesdropper.
A. System Model
As shown in Fig. 1, we consider an OFDM-based heteroge-
neous cellular network consisting of a macro-cell network and
a small-cell network. There are Nsubcarriers in each OFDM
symbol. For any OFDM subcarrier, a macro-cell base station
(MBS) uses the same spectrum with a small-cell base station
(SBS) to communicate with respective macro-cell user (MU) and
small-cell user (SU) in the face of a common eavesdropper (E).
Each node in this paper is equipped with a single antenna. MBS
and SBS are connected to a core network through fiber cable to
exchange information. It is noted that the focus of this paper is
to maximize the sum secrecy rate (SSR) of both macro cell and
small cell by optimizing the power allocation of MBS and SBS
across different OFDM subcarriers in heterogeneous cellular
networks, considering the instantaneous and statistical channel
state information (CSI) of eavesdropper. Our proposed iterative
power allocation algorithm can be used for some more complex
scenarios. For example, each node in our system model is
equipped with multiple antennas. According to [32] and [33], we
may consider the use of the transmit antenna selection at MBS
and SBS as well as the maximum ratio combining at MU, SU
and E along with a similar iterative power allocation algorithm
to address the multi-antenna scenarios. Moreover, although only
one macro cell and small cell are considered in our system model,
it can be extended to a general large-scale heterogeneous cellular
network having massive macro cells and small cells with the aid
of base station pairing and grouping. In such cases, we divide the
whole spectrum into multiple orthogonal sub-bands, which are
then allocated to different MBS-SBS pairs [31]. Additionally,
we may consider both the large-scale path loss and small-scale
Rayleigh fading in modeling wireless channels, and investigate
the impact of transmission distances on the SSR performance
of our proposed ICSI-SSRM and SCSI-SSRM schemes, which
may be considered for our future work.
In order to defend against the interference caused by SBS as
well as to interfere with a common eavesdropper, an artificially
designed signal xm,n is emitted at MBS on subcarrier n. Thus,
the transmit signals of MBS and SBS at the nth subcarrier can
be respectively expressed by
xMBS,n =PM,n −¯
Pm,nxM,n +xm,n,(1)
xSBS,n =PS,nwS,n xS,n,(2)
where PM,n denotes the sum of the transmit power of xM,n
and xm,n, and ¯
Pm,n is the average transmit power of artificially
designed signal xm,n on subcarrier n. The remaining power
PM,n −¯
Pm,n is used to transmit signal xM,n at the nth sub-
carrier, where PM,n ≥0 and 0 ≤¯
Pm,n ≤PM,n. Note that the
average transmit power of xm,n is used in (1) instead of the
instantaneous power, which is due to the fact that the instanta-
neous transmit power Pm,n may exceed the total transmit power
of PM,n, and further result in that the transmit power of MBS
for the desired signal xM,n is less than zero [31]. xS,n and PS,n
are the transmit signal and power of SBS at the nth subcarrier,
wS,n is a weight coefficient of the SBS’s signal on subcarrier
n. Hence, the received signal at MU on subcarrier ncan be
given by
ym,n =hMm,n PM,n −¯
Pm,nxM,n +xm,n
+hSm,nPS,n wS,nxS,n +nm,n
=PM,n −¯
Pm,nhMm,nxM,n
+hMm,nxm,n +PS,n hSm,nwS,nxS,n +nm,n,
(3)
where hMm,n and hSm,n represent the fading coefficients of
MBS-MU and SBS-MU channel at the nth subcarrier, respec-
tively. nm,n ∼CN(0,σ
2
m,n)is additive white Gaussian noise
(AWGN) at MU on subcarrier n. For the purpose of cancelling
out the interference at MU caused by SBS, the artificially de-
signed signal xm,n and the weight coefficient wS,n at the nth
subcarrier should satisfy
hMm,nxm,n +PS,nhSm,nwS,nxS,n =0,(4)
due to the fact that MBS and SBS are connected by a core
network, so that xS,n and PS,n can be easily obtained at MBS.
What’s more, MBS can acquire the CSI of hSm,n and hMm,n
through various channel estimation methods [34]. Thus, we can
achieve a solution of the artificially designed signal xm,n and
the weight coefficient wS,n at the nth subcarrier as
[xm,n,w
S,n]= 1
σMm,n
×−
PS,n |hSm,n|e−jθMm,nxS,n ,|hMm,n|e−jθSm,n
,(5)
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3024 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
where σ2
Mm,n =E(|hMm,n|2)denotes the channel variance of
MBS-MU on subcarrier n.θMm,n and θSm,n are the channel
phases of MBS-MU and SBS-MU at the nth subcarrier. Then,
the instantaneous and average transmit powers of xm,n on
subcarrier ncan be given by
Pm,n,¯
Pm,n=|hSm,n|2
σ2
Mm,n
PS,n,σ2
Sm,n
σ2
Mm,n
PS,n,(6)
where σ2
Sm,n =E(|hSm,n|2)is the variance of channel from
SBS to MU at the nth subcarrier. According to the range of
0≤¯
Pm,n ≤PM,n, we can achieve
0≤σ2
Sm,n
σ2
Mm,n
PS,n ≤PM,n.(7)
Substituting (4) into (3), we can express the received signal at
MU on subcarrier nas
ym,n =PM,n −¯
Pm,nhMm,nxM,n +nm,n.(8)
According to the Shannon’s capacity formula, the channel ca-
pacity of MBS-MU channel at the nth subcarrier can be written
as
CMm,n =log
2(1+γMm,n),(9)
where
γMm,n =PM,n −σ2
Sm,nPS,n /σ2
Mm,n|hMm,n|2
σ2
m,n
.(10)
Similarly, the received signal of SU on subcarrier nis given by
ys,n =hMs,n PM,n −¯
Pm,nxM,n +xm,n
+hSs,nPS,n wS,nxS,n +ns,n,(11)
where hSs,n and hMs,n represent the fading coefficients of SBS-
SU and MBS-SU channel at the nth subcarrier, respectively, and
ns,n ∼CN(0,σ
2
s,n)is the AWGN received at SU on subcarrier
n. Thus, the channel capacity of SBS-SU channel at the nth
subcarrier can be expressed by
CSs,n =log
2(1+γSs,n),(12)
where
γSs,n
=
PS,n |hSs,n|2|hMm,n|2σ2
Mm,n
PM,n+(|hSm,n|2−σ2
Sm,n)PS,n σ2
Mm,n|hMs,n|2+σ2
s,n
.
(13)
B. ICSI-SSRM Scheme
In this section, we consider an ICSI-SSRM scheme, where the
ICSI of wiretap links is assumed to be known. According to [35]
and [36], we can exploit the channel estimation technologies to
achieve the ICSI of an active eavesdropper. For example, the
ICSI of a legitimate user can be obtained through some channel
estimation methods. However, the legitimate user may be hacked
by a Trojan horse and then becomes an eavesdropper. In this case,
the ICSI of such an eavesdropper is the ICSI of a compromised
legitimate user. Thus, the received signal at eavesdropper on
subcarrier ncan be given by
ye,n =hMe,n PM,n −¯
Pm,nxM,n +xm,n
+hSe,nPS,n wS,nxS,n +ne,n,(14)
where hMe,n and hSe,n are the fading coefficients of MBS-
E and SBS-E channel at the nth subcarrier, respectively, and
ne,n ∼CN(0,σ
2
e,n)is the AWGN at E on subcarrier n.
Indeed, the eavesdropper may achieve more useful infor-
mation to perform successive interference cancellation (SIC)
[37] to sequentially decode its received signal as given by
(14). Meanwhile, the SIC can be also used at SU to obtain a
better performance for the legitimate link. Overall speaking, no
obvious secrecy benefits are expected by applying the SIC at both
E and SU. It is of interest to investigate the impact of SIC on the
secrecy performance of SSRM schemes, which is considered for
further work. Then, we can write the channel capacity of MBS-E
channel at the nth subcarrier as
CMe,n =log
2(1+γMe,n),(15)
where
γMe,n
=PM,n −σ2
Sm,nPS,n σ2
Mm,n|hMe,n|2
PS,n|hMm,n|2|hSe,n|2+|hSm,n|2|hMe,n|2
σ2
Mm,n+σ2
e,n
.
(16)
Meanwhile, the channel capacity of SBS-E channel on subcarrier
ncan be given by
CSe,n =log
2(1+γSe,n),(17)
where
γSe,n
=
PS,n |hSe,n|2|hMm,n|2σ2
Mm,n
PM,n +|hSm,n|2−σ2
Sm,n
PS,nσ2
Mm,n|hMe,n|2+σ2
e,n
.
(18)
The ICSI-SSRM problem can be formulated as
max
PM,n,PS,n
N
n=1
CMm,n −CMe,n +CSs,n −CSe,n
s.t. C1:0≤σ2
Sm,n
σ2
Mm,n
PS,n ≤PM,n
C2:
N
n=1
PM,n =Ptot
M,(19)
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3025
where Ptot
Mis total transmit power of MBS. By substituting (10),
(13), (16) and (18) into (19), the optimization problem can be
simplified as
max
PM,n,PS,n
N
n=1
f1(PM,n,P
S,n)−f2(PM,n,P
S,n)
s.t. C1−C2,(20)
where f1(PM,n,P
S,n)and f2(PM,n,P
S,n)are presented at (21)
and (22) shown at the bottom of this page, respectively.
C. SCSI-SSRM Scheme
For the case that the ICSI of eavesdropper is unavailable, we
propose the eavesdropper’s SCSI based SSRM scheme (denoted
by SCSI-SSRM scheme for short) in this section. We assume that
the fading coefficients of MBS-E and SBS-E channels at the nth
subcarrier are independent complex Gaussian random variables
with zero mean and variances σ2
Me,n and σ2
Se,n, respectively,
i.e., hMe,n ∼CN(0,σ
2
Me,n)and hSe,n ∼CN(0,σ
2
Se,n). Thus,
we express the SCSI-SEEM problem as
max
PM,n,PS,n
N
n=1
E[CMm,n −CMe,n +CSs,n −CSe,n]
s.t. C1−C2,(23)
Then, we focus on solving the following optimization problem,
that is
max
PM,n,PS,n
N
n=1
CMm,n +CSs,n −E[CMe,n]−E[CSe,n]
s.t. C1−C2,(24)
where
E[CMe,n]=log
2[1+E(γMe,n)] = log2
×1+(PM,n −σ2
Sm,nPS,n /σ2
Mm,n)σ2
Me,n
PS,n
(|hMm,n|2σ2
Se,n +|hSm,n|2σ2
Me,n)/σ 2
Mm,n+σ2
e,n,
(25)
and
E[CSe,n]=log
2[1+E(γSe,n)] = log2
×⎡
⎣1+PS,n σ2
Se,n|hMm,n|2/σ 2
Mm,n
PM,n +|hSm,n|2−σ2
Sm,nPS,n/σ 2
Mm,n
σ2
Me,n+σ2
e,n⎤
⎦.
(26)
More details are given in Appendix A.
Substituting (10), (13), (25) and (26) into (24), we have
max
PM,n,PS,n
N
n=1
g1(PM,n,P
S,n)−g2(PM,n,P
S,n)
s.t. C1−C2,(27)
where g1(PM,n,P
S,n)and g2(PM,n,P
S,n)are given at (28) and
(29) shown at the bottom of the next page, respectively.
Lemma: The object functions of optimization problems (20)
and (27) are non-convex.
Proof: Please see Appendix B.
III. SOLUTION OF THE OPTIMIZATION PROBLEM
In this section, we first present the methods to solve the
ICSI-SSRM and SCSI-SSRM problems. Afterwards, their cor-
responding iterative optimal power allocation algorithms are
proposed. Next, we analyze the overall computational com-
plexity of the proposed ICSI-SSRM and SCSI-SSRM algo-
rithms. Finally, we give the convergence proof of the iterative
processes.
A. Solution of the ICSI-SSRM Scheme
This subsection introduces the method to solve the non-
convex ICSI-SSRM problem. Since the optimization problem
(20) is a form of the difference between two-convex (D.C.)
functions, we apply D.C. approximation method [38] to ap-
proximate f2(PM,n,P
S,n)into a linear function. Then, let-
ting f2(˜
PM,n,˜
PS,n)is a feasible solution of f2(PM,n,P
S,n)
and according to the first-order Taylor series expansion of
f1(PM,n,P
S,n)=log21+PM,n−σ2
Sm,nPS,n /σ2
Mm,n|hMm,n|2
σ2
m,n +log2PS,n(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2)
σ2
Mm,n
+σ2
e,n
+log
2PM,n|hMs,n|2+PS,n|hSs,n|2|hMm,n|2+|hMs,n|2|hSm,n|2−|hMs,n|2σ2
Sm,n
σ2
Mm,n
+σ2
s,n
+log
2PM,n|hMe,n|2+PS,n|hMe,n|2|hSm,n|2−σ2
Sm,n
σ2
Mm,n
+σ2
e,n(21)
f2(PM,n,P
S,n)=2log2PM,n|hMe,n|2+PS,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n
σ2
Mm,n
+σ2
e,n
+log
2PM,n|hMs,n|2+PS,n|hMs,n|2|hSm,n|2−σ2
Sm,n
σ2
Mm,n
+σ2
s,n(22)
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3026 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
Algorithm 1: Iterative Optimal Power Allocation Algorithm
for ICSI-SSRM Scheme.
1: Initialization:kmax,ε,(P0
M,n,P0
S,n)=(0,0),f0=0
and k=0.
2: Repeat:
3: Solve (32) with (Pk
M,n,Pk
S,n)to obtain the optimal
solution.
4: Update
fk+1=N
n=1f1(Pk+1
M,n,Pk+1
S,n )−f2(Pk+1
M,n,Pk+1
S,n ).
5: k=k+1.
6: Until:|fk−fk−1|≤εor k≥kmax
7: Output:P∗
M,n =Pk
M,n and P∗
S,n =Pk
S,n.
f2(PM,n,P
S,n), we can achieve (30). Combining the problem
(20) and the formula (30) shown at the bottom of this page, we
can obtain an approximate optimization problem (31) shown at
the bottom of the next page. Thus, assuming that (˜
Pk
M,n,˜
Pk
S,n)
and (˜
Pk+1
M,n,˜
Pk+1
S,n )are the optimal solutions to (31) at iterations k
and k+1, respectively, the problem (20) can be solved through
the iterative procedure (32) shown at the bottom of the next page.
Afterwards, one can observe that (31) is convex. Therefore, it is
simple and straightforward to solve the problem (31) by using
existing convex software tools, e.g., CVX [39].
Moreover, an iterative power allocation algorithm is pre-
sented in Algorithm 1 to achieve optimal solutions of our
formulated ICSI-SSRM problem. Based on the given value
(Pk
M,n,Pk
S,n), we solve problem (32) to obtain the optimal
power allocation solution (Pk+1
M,n,Pk+1
S,n ). When all the up-
dated data nearly keeps unchanged or the number of iterations
approaches to the maximum value, the iteration stops; otherwise,
another round of iteration starts. What’s more, the computa-
tional complexity of the proposed ICSI-SSRM scheme depends
on the number of iterations, variable size and the number of
constraints. Given the convergence tolerance ε, we can write
the iterations excluding convex programming as o(log(fup/ε))
wherein
fup =Ptot
Mmax |hMm,n|2
min σ2
m,nln 2
+Ptot
Smax |hSs,n|2|hMm,n|2
min σ2
s,nσ2
Mm,nln 2.(33)
There are 2 Nscalar variables in problem (32), which needs
at most o((2N)3.5log(1/ε)) calculations [40]. Therefore, the
overall computational complexity of the proposed ICSI-SSRM
scheme [41] can be roughly given by
o(2N)3.5log(fup/ε)log(1/ε).(34)
B. Solution of the SCSI-SSRM Scheme
In this subsection, we obtain the optimal solutions of the
SCSI-SSRM problem. Similar as the ICSI-SSRM problem,
denoting (ˆ
PM,n,ˆ
PS,n)is a feasible solution of optimization
problem (27), the D.C. approximation method [38] is ex-
ploited to transform the SCSI-SSRM problem into a convex one
(35), which can be solved by CVX [39]. Thus, assuming that
(ˆ
Pk
M,n,ˆ
Pk
S,n)and (ˆ
Pk+1
M,n,ˆ
Pk+1
S,n )are optimal solutions of (35)
shown at the bottom of the next page, we are able to achieve
the optimal solutions of (27) through the following iterative
g1(PM,n,P
S,n)=log
21+(PM,n −σ2
Sm,nPS,n /σ2
Mm,n)|hMm,n|2
σ2
m,n +log
2PS,n(σ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2)
σ2
Mm,n
+σ2
e,n
+log
2PM,n|hMs,n|2+PS,n(|hSs,n|2|hMm,n|2+|hMs,n|2|hSm,n|2−|hMs,n|2σ2
Sm,n)
σ2
Mm,n
+σ2
s,n
+log
2PM,nσ2
Me,n +PS,nσ2
Me,n(|hSm,n|2−σ2
Sm,n)
σ2
Mm,n
+σ2
e,n(28)
g2(PM,n,P
S,n)=2log2PM,nσ2
Me,n +PS,nσ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2−σ2
Me,nσ2
Sm,n
σ2
Mm,n
+σ2
e,n
+log
2PM,n|hMs,n|2+PS,n|hMs,n|2|hSm,n|2−σ2
Sm,n
σ2
Mm,n
+σ2
s,n(29)
f2(PM,n,P
S,n)≤f2(˜
PM,n,˜
PS,n)+ (PM,n −˜
PM,n)|hMs,n|2+(PS,n −˜
PS,n)|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n
[˜
PM,n|hMs,n|2+˜
PS,n|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n +σ2
s,n]ln2
+2[(PM,n −˜
PM,n)|hMe,n|2+(PS,n −˜
PS,n)(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n]
[˜
PM,n|hMe,n|2+˜
PS,n(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n +σ2
e,n]ln2(30)
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3027
Algorithm 2: Iterative Optimal Power Allocation Algorithm
for SCSI-SSRM Scheme.
1: Initialization:kmax,ε,(P0
M,n,P0
S,n)=(0,0),g0=0
and k=0.
2: Repeat:
3: Solve (36) with (Pk
M,n,Pk
S,n)to obtain the optimal
solution.
4: Update
gk+1=N
n=1g1(Pk+1
M,n,Pk+1
S,n )−g2(Pk+1
M,n,Pk+1
S,n ).
5: k=k+1.
6: Until:|gk−gk−1|≤εor k≥kmax
7: Output:P∗
M,n =Pk
M,n and P∗
S,n =Pk
S,n.
procedure (36) shown at the bottom of the next page. Then,
we present the iterative optimal power allocation algorithm for
SCSI-SSRM scheme in Algorithm 2.
Finally, following [41], we roughly express the overall com-
putational complexity of the proposed SCSI-SSRM scheme as
o(2N)3.5log(gup/ε)log(1/ε),(37)
where
gup =Ptot
Mmax |hMm,n|2
min σ2
m,nln 2+Ptot
Smax |hSs,n |2|hMm,n|2
min σ2
s,nσ2
Mm,nln 2.
(38)
Proof: Please see Appendix C for the convergence proof of
the iterative processes.
IV. SIMULATION RESULTS
In this section, we present numerical simulations to evalu-
ate the secrecy performances of the proposed ICSI-SSRM and
SCSI-SSRM schemes. In our simulations, all channels between
two nodes are modelled as Rayleigh fading. Also, we consider
E(|hSs,n|2)=1, E(|hMs,n|2)=0.1, E(|hSm,n|2)=σ2
Sm,n =
0.1, E(|hMm,n|2)=σ2
Mm,n =1, E(|hMe,n|2)=σ2
Me,n =1,
E(|hSe,n|2)=σ2
Se,n =1 and σ2
m,n =σ2
s,n =σ2
e,n =0dBm.
Fig. 2 shows the convergence behaviour of the proposed
ICSI-SSRM and SCSI-SSRM algorithms versus the num-
ber of iterations with N=10 and Ptot
M=25 dBm. It can
be observed that as the number of iterations increases, the
sum secrecy rates of both ICSI-SSRM and SCSI-SSRM
schemes first increase, and then converge to their corre-
sponding secrecy rate floors. This verifies that the proposed
max
PM,n,PS,n
N
n=1
f1
(PM,n,P
S,n)−f2˜
PM,n,˜
PS,n−PM,n−˜
PM,n|hMs,n|2+PS, n −˜
PS,n
|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
˜
PM,n|hMs,n|2+˜
PS,n|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n+σ2
s,nln 2
−2[(PM,n −˜
PM,n)|hMe,n|2+(PS,n −˜
PS,n)(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n]
˜
PM,n|hMe,n|2+˜
PS,n(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n +σ2
e,nln 2
s.t. C1−C2(31)
(˜
Pk+1
M,n,˜
Pk+1
S,n )=
arg max
PM,n,P S,n
N
n=1
f1
PM,n,P
S,n−f2(˜
Pk
M,n,˜
Pk
S,n)−PM,n−˜
Pk
M,n
|hMs,n|2+PS,n −˜
Pk
S,n
|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
[˜
Pk
M,n|hMs,n|2+˜
Pk
S,n|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n+σ2
s,n]ln2
−
2PM,n−˜
Pk
M,n|hMe,n|2+PS,n −˜
Pk
S,n|hSe,n|2
|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ 2
Mm,n
˜
Pk
M,n|hMe,n|2+˜
Pk
S,n(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n +σ2
e,nln 2
s.t. C1−C2(32)
max
PM,n,PS,n
N
n=1
g1
PM,n,P
S,n−g2ˆ
PM,n,ˆ
PS,n−PM,n−ˆ
PM,n|hMs,n|2+(PS,n−ˆ
PS,n)|hMs,n|2
|hSm,n|2−σ2
Sm,n
/σ2
Mm,n
ˆ
PM,n|hMs,n|2+ˆ
PS,n|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n +σ2
s,nln 2
−
2(PM,n −ˆ
PM,n)σ2
Me,n +(PS,n −ˆ
PS,n)(σ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2−σ2
Me,nσ2
Sm,n)/σ2
Mm,n
ˆ
PM,nσ2
Me,n +ˆ
PS,nσ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2−σ2
Me,nσ2
Sm,n/σ2
Mm,n +σ2
e,nln 2
s.t. C1−C2(35)
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3028 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
Fig. 2. Covergence behaviour of the proposed ICSI-SSRM and SCSI-SSRM
algorithms versus the number of iterations with N=10 and Ptot
M=25 dBm.
ICSI-SSRM and SCSI-SSRM algorithms have good conver-
gence performance.
In Fig. 3, we present the sum secrecy rate versus the transmit
power of MBS Ptot
Mfor ICSI-SSRM, SCSI-SSRM, ICSI based
equal power allocation (ICSI-EPA) [42] and interference-limited
underlay spectrum sharing (IL-USS) [31] schemes in terms of
the number of subcarriers, N=10. In ICSI-EPA and IL-USS
schemes, the powers of MBS’s OFDM subcarriers are equalled
allocated with a given transmit power of MBS Ptot
M, and the
corresponding fixed powers are allocated for different OFDM
subcarriers of SBS, i.e., PM,n/PS,n =0.6. As we see, the
secrecy performance of proposed ICSI-SSRM, SCSI-SSRM and
IL-USS schemes improves as the transmit power of MBS Ptot
M
increases from 10 dBm to 30 dBm. This is because that increas-
ing the transmit power of MBS results in more interference
received at MU, SU and E. Meanwhile, since that the fading
gains of E(|hMe,n|2)=E(|hSe,n|2)=1 are higher than the
fading gains of E(|hMs,n|2)=E(|hSm,n|2)=0.1, more inter-
ference would be received at E than MU and SU. Therefore, the
sum secrecy rate performance of ICSI-SSRM, SCSI-SSRM and
IL-USS schemes is improved with an increasing transmit power
of MBS Ptot
M. Moreover, as the transmit power of MBS Ptot
M
increases beyond 30 dBm, the sum secrecy rate performance of
ICSI-SSRM and SCSI-SSRM schemes continues to improve,
Fig. 3. Sum secrecy rate versus the transmit power of MBS Ptot
Mfor ICSI-
SSRM, SCSI-SSRM, ICSI-EPA and IL-USS schemes in terms of the number of
subcarriers, N=10.
whereas the IL-USS scheme converges to a sum secrecy rate
floor. This is due to the fact that by increasing the transmit
power of MBS Ptot
M, it results in a significant amount of mutual
interference received at MU and SU in the IL-USS scheme.
Thus, no improvement is obtained in the IL-USS scheme for
a sufficiently high level of the transmit power. However, in
ICSI-SSRM and SCSI-SSRM schemes, the SBS-MU interfer-
ence is cancelled out by using a specially-designed signal at
MBS, leading to a continued improvement of the sum secrecy
rate with an increasing transmit power Ptot
M. Additionally, the
proposed ICSI-SSRM and SCSI-SSRM schemes outperform
the ICSI-EPA scheme in term of sum secrecy rate, which is
due to the fact that our ICSI-SSRM and SCSI-SSRM schemes
are proposed by optimizing power allocation of MBS and SBS
across different OFDM subcarriers. Fig. 3 further demonstrates
that the ICSI-SSRM scheme achieves a better sum secrecy rate
performance than SCSI-SSRM strategy.
Fig. 4 illustrates the sum secrecy rate versus the number of
subcarriers Nfor ICSI-SSRM, SCSI-SSRM, ICSI-EPA and
IL-USS schemes in terms of the transmit power of MBS,
Ptot
M=20 dBm. As observed, the proposed ICSI-SSRM and
SCSI-SSRM schemes outperform the ICSI-EPA and IL-USS
ˆ
Pk+1
M,n,ˆ
Pk+1
S,n =arg max
PM,n,PS,n
N
n=1
g1
PM,n,P
S,n−g2ˆ
Pk
M,n,ˆ
Pk
S,n
−PM,n−ˆ
Pk
M,n|hMs,n|2+PS,n −ˆ
Pk
S,n|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
ˆ
Pk
M,n|hMs,n|2+ˆ
Pk
S,n|hMs,n|2(|hSm,n|2−σ2
Sm,n)/σ2
Mm,n+σ2
s,nln 2
−2[(PM,n −ˆ
Pk
M,n)σ2
Me,n +(PS,n −ˆ
Pk
S,n)(σ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2−σ2
Me,nσ2
Sm,n)/σ2
Mm,n]
[ˆ
Pk
M,nσ2
Me,n +ˆ
Pk
S,n(σ2
Se,n|hMm,n|2+σ2
Me,n|hSm,n|2−σ2
Me,nσ2
Sm,n)/σ2
Mm,n +σ2
e,n]ln2
s.t. C1−C2(36)
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3029
Fig. 4. Sum secrecy rate versus the number of subcarriers Nfor ICSI-SSRM,
SCSI-SSRM, ICSI-EPA and IL-USS schemes in terms of the transmit power of
MBS, Ptot
M=20 dBm.
Fig. 5. Sum secrecy rate of a multi-cell heterogeneous cellular network versus
the number of small cells Mfor ICSI-SSRM, SCSI-SSRM, ICSI-EPA and IL-
USS schemes with the transmit power of MBS, Ptot
M=20 dBm, and the number
of subcarriers, N=10.
methods in terms of sum secrecy rate, this further confirms the
security advantage of proposed ICSI-SSRM and SCSI-SSRM
schemes. Moreover, with an increasing number of subcarri-
ers N, the sum secrecy rates of ICSI-SSRM, SCSI-SSRM,
ICSI-EPA and IL-USS schemes significantly increase, which
demonstrates that it is benefit to SSR by increasing the number of
subcarriers N.
Fig. 5 plots the sum secrecy rate of a multi-cell heteroge-
neous cellular network versus the number of small cells Mfor
ICSI-SSRM, SCSI-SSRM, ICSI-EPA and IL-USS schemes with
the transmit power of MBS, Ptot
M=20 dBm, and the number
of subcarriers, N=10. Here, we consider a large-scale het-
erogeneous cellular network with a macro cell and Msmall
cells, where each small cell consists of a SBS and a SU. Firstly,
a small cell with the best CSI of main link is selected to
communicate with its associated user at each subcarrier. Thus,
the best small cell selection criterion at nth subcarrier is given by
arg maxm∈M|hSmsm,n|2. Then, we employ Algorithms 1 and 2
to solve the ICSI-SSRM and SCSI-SSRM problems in a large-
scale heterogeneous cellular network, respectively. As shown
in Fig. 5, the sum secrecy rate of the proposed ICSI-SSRM,
SCSI-SSRM, ICSI-EPA and IL-USS schemes is significantly
improved as the number of small cells Mcontinues increasing.
Furthermore, the proposed ICSI-SSRM strategy obtains a better
sum secrecy rate performance than SCSI-SSRM, ICSI-EPA and
IL-USS methods, which verifies the advantage of our proposed
ICSI-SSRM scheme.
V. C ONCLUSION
In this paper, we studied the PLS of an OFDM-based heteroge-
neous cellular network consisting of a macro cell and a small cell
with the the existence of a common eavesdropper. An artificially
designed signal was emitted at MBS to offset the interference
caused by SBS and degrade the wiretap of eavesdropper. More-
over, in order to maximize the sum secrecy rate of both macro
cell and small cell in an OFDM-based heterogeneous cellular
network, we examined the optimization of power allocation
between MBS and SBS across different OFDM subcarriers
through considering the instantaneous and statistical CSI of
eavesdropper. Since the proposed ICSI-SSRM and SCSI-SSRM
problems are non-convex, we respectively transformed them
into convex problems by employing the D.C. approach, and
then presented corresponding iterative power allocation algo-
rithms to obtain optimal solutions of the proposed ICSI-SSRM
and SCSI-SSRM schemes. Finally, numerical results showed
that the proposed ICSI-SSRM and SCSI-SSRM schemes ob-
tain a higher secrecy rate than conventional power allocation
schemes.
APPENDIX A
DERIVATION OF (25) AND (26)
According to [35], the lower bound of objective problem in
(23) can be expressed as
max
PM,n,PS,n
N
n=1
CMm,n +CSs,n −E[CMe,n]−E[CSe,n]
s.t. C1−C2,(A.1)
according to Jensen’s inequality, we achieve
E[CMe,n]=E[log2(1+γMe,n)] ≤log2[1+E(γMe,n)],(A.2)
and
E[CSe,n]=E[log2(1+γSe,n)] ≤log2[1+E(γSe,n)],(A.3)
where E(γMe,n)and E(γSe,n)are given at (A.4) and (A.5)
shown at the top of the next page, respectively. Then, following
[35], when the variances of |hSe,n|2and |hMe,n|2are small, the
E(γMe,n)and E(γSe,n)can be approximated into (A.6) shown
at the top of the next page, and
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3030 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
E(γMe,n)=E(PM,n −σ2
Sm,nPS,n /σ2
Mm,n)|hMe,n|2
PS,n(|hMm,n|2|hSe,n|2+|hSm,n|2|hMe,n|2)/σ2
Mm,n +σ2
e,n
=EPM,n −σ2
Sm,nPS,n /σ2
Mm,n|hMe,n|2E1
PS,n(|hMm,n|2|hSe,n|2+|hSm,n|2|hMe,n|2)/σ2
Mm,n +σ2
e,n
=PM,n −σ2
Sm,nPS,n /σ2
Mm,nσ2
Me,n E1
PS,n(|hMm,n|2|hSe,n|2+|hSm,n|2|hMe,n|2)/σ2
Mm,n +σ2
e,n (A.4)
E(γSe,n)=EPS,n |hSe,n|2|hMm,n|2/σ2
Mm,n
[PM,n +|hSm,n|2−σ2
Sm,nPS,n /σ2
Mm,n]|hMe,n|2+σ2
e,n
=EPS,n|hSe,n|2|hMm,n|2/σ2
Mm,nE⎧
⎨
⎩
1
PM,n +|hSm,n|2−σ2
Sm,nPS,n /σ2
Mm,n|hMe,n|2+σ2
e,n ⎫
⎬
⎭
=PS,nσ2
Se,n|hMm,n|2/σ2
Mm,n E⎧
⎨
⎩
1
PM,n +|hSm,n|2−σ2
Sm,nPS,n /σ2
Mm,nσ2
Me,n +σ2
e,n ⎫
⎬
⎭
(A.5)
E(γMe,n)≈(PM,n−σ2
Sm,nPS,n /σ2
Mm,n)σ2
Me,n
PS,n|hMm,n|2E[|hSe,n|2]+|hSm,n|2E[|hMe,n|2]/σ2
Mm,n+σ2
e,n
=PM,n −σ2
Sm,nPS,n /σ2
Mm,nσ2
Me,n
PS,n|hMm,n|2σ2
Se,n +|hSm,n|2σ2
Me,n/σ2
Mm,n +σ2
e,n
(A.6)
E(γSe,n)≈
PS,n|hSe,n|2|hMm,n|2/σ2
Mm,n
PM,n +(|hSm,n|2−σ2
Sm,n)PS,n /σ2
Mm,nE|hMe,n|2+σ2
e,n
=PS,nσ2
Se,n|hMm,n|2/σ2
Mm,n
PM,n +(|hSm,n|2−σ2
Sm,n)PS,n /σ2
Mm,nσ2
Me,n+σ2
e,n
.
(A.7)
APPENDIX B
PROOF OF LEMMA
It is clear that the object functions in (20) and (27) are positive
linear combinations of logarithm functions h(x, y)=ln(a1x+
b1y+c1)−ln(a2x+b2y+c2), where a1,a2,b1,b2,c1and c2
are constants, xand yare nonnegative variables. Following [43],
the concavity and convexity of a two-dimensional function relies
on concave-convex characteristic of its restriction to any line.
Thus, we can achieve
h(x)=h(x, y)|y=αx+β
=ln[a1x+b1(αx +β)+c1]−ln [a2x+b2(αx +β)+c2]
=ln[(a1+b1α)x+b1β+c1]−ln [(a2+b2α)x+b2β+c2],
(B.1)
Then, first and second order derivatives of (B.1) can respectively
expressed as
h(x)= a1+b1α
(a1+b1α)x+b1β+c1
−a2+b2α
(a2+b2α)x+b2β+c2
,
(B.2)
and
h(x)
=−(a1+b1α)2
[(a1+b1α)x+b1β+c1]2+(a2+b2α)2
[(a2+b2α)x+b2β+c2]2,
(B.3)
from which, the positive and negative characteristics of h(x)
depend on specific values of a1,a2,b1,b2,c1,c2,α,βand x,
which means that h(x)is non-convex. We can conclude that
h(x, y)is non-convex, namely, the object functions in (20) and
(27) are non-convex.
APPENDIX C
PROOF OF CONVERGENCE
It can be observed that the principle of iterative optimal power
allocation algorithms for ICSI-SSRM and SCSI-SSRM schemes
are same, thus we only need to prove the convergence of the
ICSI-SSRM algorithm. From (30), we have the inequation (C.1).
Then, following the iterative procedure in (32), we obtain the
formula (C.2). Combining (C.1) and (C.2), we further achieve
(C.3). From (C.3), we obvious that as the iterative numbers
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3031
f2˜
Pk+1
M,n,˜
Pk+1
S,n
≤f2˜
Pk
M,n,˜
Pk
S,n+˜
Pk+1
M,n −˜
Pk
M,n|hMs,n|2+˜
Pk+1
S,n −˜
Pk
S,n|hMs,n|2|hSm,n|2−σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMs,n|2+˜
Pk
S,n|hMs,n|2|hSm,n|2−σ2
Sm,n/σ2
Mm,n +σ2
s,nln 2
+
2˜
Pk+1
M,n −˜
Pk
M,n|hMe,n|2+˜
Pk+1
S,n −˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMe,n|2+˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n +σ2
e,nln 2
(C.1)
N
n=1
f1
˜
Pk+1
M,n,˜
Pk+1
S,n −f2
˜
Pk
M,n,˜
Pk
S,n
−˜
Pk+1
M,n−˜
Pk
M,n|hMs,n|2+˜
Pk+1
S,n −˜
Pk
S,n|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMs,n|2+˜
Pk
S,n|hMs,n|2|hSm,n|2−σ2
Sm,n/σ2
Mm,n +σ2
s,nln 2
−
2(˜
Pk+1
M,n −˜
Pk
M,n)|hMe,n|2+(˜
Pk+1
S,n −˜
Pk
S,n)|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMe,n|2+˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n +σ2
e,nln 2
=max
PM,n,PS,n
N
n=1
f1(PM,n,P
S,n)−f2
˜
Pk
M,n,˜
Pk
S,n
−PM,n −˜
Pk
M,n|hMs,n|2+PS,n −˜
Pk
S,n|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMs,n|2+˜
Pk
S,n|hMs,n|2|hSm,n|2−σ2
Sm,n/σ2
Mm,n+σ2
s,n
ln 2
−
2PM,n −˜
Pk
M,n|hMe,n|2+PS,n −˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMe,n|2+˜
Pk
S,n(|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n)/σ2
Mm,n +σ2
e,nln 2
≥
N
n=1
f1˜
Pk
M,n,˜
Pk
S,n−f2˜
Pk
M,n,˜
Pk
S,n(C.2)
N
n=1
f1˜
Pk+1
M,n,˜
Pk+1
S,n −f2˜
Pk+1
M,n,˜
Pk+1
S,n
≥
N
n=1
f1
˜
Pk+1
M,n,˜
Pk+1
S,n −f2˜
Pk
M,n,˜
Pk
S,n−˜
Pk+1
M,n−˜
Pk
M,n|hMs,n|2+˜
Pk+1
S,n −˜
Pk
S,n
|hMs,n|2
|hSm,n|2−σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMs,n|2+˜
Pk
S,n
|hMs,n|2|hSm,n|2−σ2
Sm,n/σ2
Mm,n +σ2
s,nln 2
−
2˜
Pk+1
M,n−˜
Pk
M,n|hMe,n|2+˜
Pk+1
S,n −˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n
˜
Pk
M,n|hMe,n|2+˜
Pk
S,n|hSe,n|2|hMm,n|2+|hMe,n|2|hSm,n|2−|hMe,n|2σ2
Sm,n/σ2
Mm,n +σ2
e,nln 2
≥
N
n=1
f1˜
Pk
M,n,˜
Pk
S,n−f2˜
Pk
M,n,˜
Pk
S,n(C.3)
N
n=1
CMm,n −CMe,n +CSs,n −CSe,n
≤
N
n=1
log21+PM,n −σ2
Sm,nPS,n /σ2
Mm,n|hMm,n|2
σ2
m,n
+log
21+PS,n|hSs,n|2|hMm,n|2/σ2
Mm,n
PM,n +(|hSm,n|2−σ2
Sm,n)PS,n /σ2
Mm,n|hMs,n|2+σ2
s,n
≤
N
n=1PM,n −σ2
Sm,nPS,n /σ2
Mm,n|hMm,n|2
σ2
m,n ln 2+PS,n|hSs,n|2|hMm,n|2/σ2
Mm,n
PM,n +(|hSm,n|2−σ2
Sm,n)PS,n /σ2
Mm,n|hMs,n|2+σ2
s,nln 2
≤
N
n=1
PM,n|hMm,n|2
σ2
m,n ln 2+PS,n|hSs,n|2|hMm,n|2/σ2
Mm,n
σ2
s,n ln 2
≤Ptot
Mmax |hMm,n|2
min(σ2
m,n)ln2+Ptot
Smax |hSs,n|2|hMm,n|2
minσ2
s,nσ2
Mm,nln 2(C.4)
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3032 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 3, MARCH 2020
increase, the proposed iterative procedure is monotonically non-
decreasing. In addition, due to the fact that N
n=1PM,n =Ptot
M,
N
n=1PS,n =Ptot
Sand for ∀x>−1, log2(1+x)≤x/ln 2as
well as 0 ≤σ2
Sm,nPS,n /σ2
Mm,n ≤PM,n, the upper bound of
the object function (20) can be given by (C.4). Then, combining
(C.3) and (C.4), we can ensure that the iterative procedure will
convergence to the optimal solutions of (20).
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JIANG et al.: POWER ALLOCATION FOR INTELLIGENT INTERFERENCE EXPLOITATION AIDED PHYSICAL-LAYER SECURITY 3033
Yuhan Jiang received the B.Eng. degree in commu-
nication engineering from Nantong University, Nan-
tong, China, in July 2016. She is currently working
toward the Ph.D. degree in signal and information
processing with the Nanjing University of Posts and
Telecommunications, Nanjing, China. Her research
interests include cognitive radio, physical-layer se-
curity, and green communications.
Yul on g Zo u (Senior Member, IEEE) received the
B.Eng. degree in information engineering from the
Nanjing University of Posts and Telecommunications
(NUPT), Nanjing, China, in July 2006, the Ph.D.
degree in electrical engineering from the Stevens
Institute of Technology, Hoboken, NJ, USA, in May
2012, and the Ph.D. degree in signal and information
processing from NUPT in July 2012. He is currently
a Full Professor and Doctoral Supervisor with NUPT.
He was the recipient of the 9th IEEE Communications
Society Asia-Pacific Best Young Researcher in 2014
and was a co-recipient of the Best Paper Award at the 80th IEEE Vehicular
Technology Conference in 2014. He was an Editor of the IEEE COMMUNICA-
TIONS SURVEYS &TUTORIALS, IEEE COMMUNICATIONS LETTERS,EURASIP
Journal on Advances in Signal Processing,IET Communications,andChina
Communications. In addition, he was a TPC Member for various IEEE sponsored
conferences, e.g., IEEE ICC/GLOBECOM/WCNC/VTC/ICCC, etc.
Haiyan Guo received the B.Eng. and Ph.D. degrees
in signal and information processing from the Nan-
jing University of Posts and Telecommunications
(NUPT), Nanjing, China, in 2005 and 2011, respec-
tively. From 2013 to 2014, she was a Postdoctoral
Research Fellow with Southeast University. She is
currently an Assistant Professor with NUPT. Her
research interests include physical-layer security, en-
ergy harvesting, and speech signal processing.
Jia Zhu received the B.Eng. degree in computer
science and technology from the Hohai University,
Nanjing, China, in July 2005, and the Ph.D. de-
gree in signal and information processing from the
Nanjing University of Posts and Telecommunications
(NUPT), Nanjing, China, in April 2010. She is cur-
rently a Full Professor with NUPT.From June 2010 to
June 2012, she was a Postdoctoral Research Fellow
with the Stevens Institute of Technology, Hoboken,
NJ, USA. Since November 2012, she has been a
Full-Time Faculty Member with the Telecommuni-
cation and Information School, NUPT. Her general research interests include
the cognitive radio, physical-layer security, and communications theory.
Jiahao Gu is currently working toward the B.Eng. de-
gree in communication engineering with the Nanjing
University of Posts and Telecommunications, Nan-
jing, China. His research interests include cognitive
radio, physical-layer security, and machine learning
in communications.
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