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Secure Transmissions in Millimeter Wave Systems

February 2017
IEEE Transactions on Communications PP(99):1-1

February 2017
PP(99):1-1

DOI:10.1109/TCOMM.2017.2672661

Authors:

Xi'an Jiaotong University

Exploiting millimeter wave is an effective way to meet the data traffic demand in the 5G wireless communication system. In this paper, we study secure transmissions under slow fading channels with multipath propagation in millimeter wave systems. Concerning the new propagation characteristics of millimeter wave, we investigate three transmission schemes, namely maximum ratio transmitting (MRT) beamforming, artificial noise (AN) beamforming and partial MRT (PMRT) beamforming. We evaluate the secrecy performance by analyzing both the secrecy outage probability (SOP) and the secrecy throughput for each scheme. Particularly, for the AN scheme, we derive a closed-form expression for the optimal power allocation ratio of the information signal power to the total transmit power that minimizes the SOP, as well as obtain an explicit solution on the optimal transmission parameters that maximize the secrecy throughput. By comparing the secrecy performances achieved by different strategies, we demonstrate that the secrecy performance of the millimeter wave system is significantly influenced by the relationship between the legitimate user’s and the eavesdropper’s spatially resolvable paths, which is different from the wireless systems with statistically independent channel models. In the absence of the common path between the legitimate user and the eavesdropper, MRT beamforming is the best scheme. In the presence of common paths, AN beamforming and PMRT beamforming show their respective superiorities depending on the transmit power and the number of common paths. Numerical results are provided to verify our theoretical analysis.

Description of the spatially resolvable paths.

…

Secrecy throughput versus ∆ϕ, with Nt = 100, P = 15dBm, r D = 100m and ϵ = 0.1.

…

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Transactions on Communications

Secure Transmissions in Millimeter Wave Systems

Ying Ju, Hui-Ming Wang, Senior Member, IEEE, Tong-Xing Zheng, Member, IEEE, and Qinye Yin

Abstract—Exploiting millimeter wave is an effective way to

meet the data trafﬁc demand in the 5G wireless communication

system. In this paper, we study secure transmissions under slow

fading channels with multipath propagation in millimeter wave

systems. Concerning the new propagation characteristics of mil-

limeter wave, we investigate three transmission schemes, namely

maximum ratio transmitting (MRT) beamforming, artiﬁcial noise

(AN) beamforming and partial MRT (PMRT) beamforming.

We evaluate the secrecy performance by analyzing both the

secrecy outage probability (SOP) and the secrecy throughput

for each scheme. Particularly, for the AN scheme, we derive a

closed-form expression for the optimal power allocation ratio of

the information signal power to the total transmit power that

minimizes the SOP, as well as obtain an explicit solution on

the optimal transmission parameters that maximize the secrecy

throughput. By comparing the secrecy performances achieved by

different strategies, we demonstrate that the secrecy performance

of the millimeter wave system is signiﬁcantly inﬂuenced by the

relationship between the legitimate user’s and the eavesdropper’s

spatially resolvable paths, which is different from the wireless

systems with statistically independent channel models. In the

absence of the common path between the legitimate user and

the eavesdropper, MRT beamforming is the best scheme. In

the presence of common paths, AN beamforming and PMRT

beamforming show their respective superiorities depending on

the transmit power and the number of common paths. Numerical

results are provided to verify our theoretical analysis.

Index Terms—Physical layer security, millimeter wave, multi-

path, secrecy outage, secrecy throughput, artiﬁcial noise.

I. INT ROD UC TI ON

WITH the rapid and continuous development of the

wireless communication technology, enormous amount

of conﬁdential messages will be transmitted through wireless

systems. Nevertheless, the radio characteristics of electromag-

netic wave and the open feature of the wireless channel make

the design of secure communication challenging. Physical

layer security, exploiting the wireless channel characteristics to

maximize the difference between the legitimate user’s channel

This work was partially supported by the National High-Tech Research and

Development Program of China under Grant 2015AA01A708, the National

Natural Science Foundation of China under Grants 61671364 and 61172093,

the Author of National Excellent Doctoral Dissertation of China under

Grant 201340, the New Century Excellent Talents Support Fund of China

under Grant NCET-13-0458, the Young Talent Support Fund of Science

and Technology of Shaanxi Province under Grant 2015KJXX-01, and the

Specialized Research Fund for the Doctoral Program of Higher Education

of China under Grant 20130201130003. The associate editor coordinating

the review of this paper and approving it for publication was C.-X. Wang.

(Corresponding author: Hui-Ming Wang.)

Y. Ju is with the MOE Key Laboratory for Intelligent Networks and

Network Security, School of Electronic and Information Engineering, Xi’an

Jiaotong University, Xi’an 710049, China, and also with Shaanxi Monitor-

ing Station, State Radio Monitoring Center, Xi’an 710200, China (e-mail:

juyingtju@163.com).

H.-M. Wang, T.-X. Zheng and Q. Yin are with the MOE Key Laboratory for

Intelligent Networks and Network Security, School of Electronic and Infor-

mation Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail:

xjbswhm@gmail.com; txzheng@stu.xjtu.edu.cn; qyyin@mail.xjtu.edu.cn).

and the eavesdropper’s channel, provides a powerful tool to

improve the secrecy performance of wireless communication

systems [1], [2]. In recent years, multiple-antenna technique

is considered as an efﬁcient way to enhance the physical

layer security [3]-[7]. By adopting multiple-antenna technique,

various studies have deduced and calculated secrecy capacity

from the perspective of information theory. In these early

studies, a signiﬁcant assumption is that the eavesdropper’s

channel state information (CSI) is accessible to the transmitter.

When the eavesdropper’s instantaneous CSI is not available at

the transmitter in practice, artiﬁcial noise (AN) beamforming

has been proposed in [8] where the transmitter emits the infor-

mation bearing signal together with AN to interfere with the

eavesdropper. The power allocation between the information

signal and the AN is studied both under the fast fading channel

[9], [10] and the slow fading channel [11], [12]. Under the

slow fading channel, transmission schemes are designed to

reduce secrecy outage probability (SOP) and increase secrecy

throughput. In [11], the analytical power allocation that mini-

mizes the SOP is obtained in the scenario where the legitimate

user’s channel is available. In [12], the code rate and power

allocation are optimized to maximize the secrecy throughput in

both the non-adaptive and adaptive schemes under a given SOP

constraint. We should point out that, the design and analysis

of physical layer security schemes rely heavily on the wireless

channel. However, all the aforementioned works are only valid

for the channel which has rich scattering in the frequency band

below 3 GHz.

The explosive growth in demand for data trafﬁc calls

for signiﬁcant increases in the capacity of wireless systems.

Millimeter wave communication is a particularly promising

approach for meeting this challenge because of the huge

amounts of available spectrum possessed by millimeter wave

[13], [14]. An increasing number of recent literatures show

their interests in millimeter wave [15], [16]. Millimeter wave

channel models have been studied based on their propaga-

tion characteristics theoretically [17] and experimentally [18],

where the ray cluster model is demonstrated as the most

suitable model for the millimeter wave propagation environ-

ment. Adopting the ray cluster model, many beamforming

strategies are designed for millimeter wave systems in [19]-

[24]. Speciﬁcally, a joint spatial division and multiplexing

(JSDM) strategy is proposed for a millimeter wave multiuser

system in [19]. The beamforming schemes in millimeter wave

cellular systems are investigated in [20], [21]. Furthermore, a

hybrid RF/baseband transmission scheme is proposed in [22]

to reduce the design and implementation complexity, and the

scheme is further simpliﬁed in [23], [24]. The propagation

characteristics of millimeter wave illustrated in these studies

are different from the traditional wireless communications with

spectral band below 3 GHz, which can be summarized as

Transactions on Communications

follows:

1) Scattering and multipaths in the millimeter wave band

are sparse. The scattering environment makes many of the

traditional statistically independent fading distributions inac-

curate for the millimeter wave channel. Channels under the

millimeter wave band are not independent and identically

distributed (i.i.d.) Rayleigh but rather correlated fading.

2) Due to the short wavelength inherent characteristic of

millimeter wave, more antennas can be equipped in a limited

space. Large antenna array provides a high beamforming gain

which in turn overcomes the huge path loss caused by the

increase in frequency, as well as improves the directionality

and spatial resolution [25]-[27].

Concerning speciﬁc propagation features of millimeter

wave, physical layer security in millimeter wave systems

attracts new interests [28]-[31]. Speciﬁcally, in [29], a low-

complexity directional modulation technique, namely antenna

subset modulation (ASM), is proposed by exploiting the

potential of large antenna arrays to guarantee the security.

It is concluded that ASM achieves a narrow beamwidth in

the desired direction and a high symbol error rate (SER) in

undesired directions. In [30], secrecy throughputs are analyzed

from the perspectives of delay-tolerant transmission and delay-

limited transmission, and analog beamforming using phase

shifters is utilized at the millimeter wave base station to

reduce the system cost. Secrecy performance of noise-limited

and AN assisted millimeter wave cellular networks with the

stochastic geometry framework is analyzed in [31]. However,

neither a systematic secrecy transmission scheme has been

proposed, nor the achievable secrecy performance has been

analyzed in these works. To the best of our knowledge,

no previous work has provided secure transmission schemes

and comprehensive secrecy performance analysis under a ray

cluster channel model that characterizes multipath propagation

for a millimeter wave system. So far, how to safeguard the

physical layer security of a millimeter wave system is still an

open problem, which motivates our work.

A. Our Work and Contributions

In this paper, we investigate the secure transmissions under

slow fading channels in a millimeter wave system. We assume

that an eavesdropper intercepts the communication from the

transmitter to the legitimate destination and the eavesdropper’s

instantaneous CSI is not known at the transmitter. In our

previous conference papers [32], [33], we discuss how to apply

the AN scheme to millimeter wave systems. Building on our

prior works, we investigate three secure transmission schemes

by evaluating both the SOP and the secrecy throughput, and

give more insightful and comprehensive analysis in this paper.

Our contributions are summarized as follows:

1) A discrete angular domain channel model considering

spatially resolvable paths is established to perform theoretical

design and analysis of transmission schemes for millimeter

wave systems, where the channel is constituted by the spatially

resolvable paths and represented by the spatially orthogonal

basis. Furthermore, we ﬁnd that the secrecy performance of

millimeter wave system is signiﬁcantly inﬂuenced by the

relationship between the destination’s and the eavesdropper’s

spatially resolvable paths, which is unlike those wireless

systems with statistically independent channel models.

2) Concerning the channel condition of the millimeter wave

system, we investigate three transmission methods. We ﬁrst

analyze the new secrecy properties of the maximum ratio trans-

mitting (MRT) beamforming for the millimeter wave system.

Then we propose two secure transmission schemes, namely

AN beamforming and partial MRT (PMRT) beamforming. For

the AN scheme, we design a new form of AN generation.

For the PMRT scheme, conﬁdential signals are emitted by

a narrow beam which keeps away from the eavesdropper’s

resolvable paths. We analyze the secrecy performance of the

AN beamforming by deriving a closed-form SOP and an

accurate integral-form secrecy throughput. We further obtain

the power allocation ratio of the information signal power to

the total transmit power that minimizes the SOP or maximizes

the secrecy throughput. For the PMRT beamforming, we

derive a closed-form secrecy throughput to evaluate its secrecy

performance.

3) We illustrate that the MRT beamforming is the best

scheme in terms of achieving the minimum SOP and the

maximum secrecy throughput when there is no common path

between the destination and the eavesdropper. For the case

where common paths exist, the AN scheme has the best

secrecy performance among the three schemes when either

the transmit power is low or the number of common paths are

large, otherwise the PMRT scheme shows its superiority.

B. Organization and Notations

This paper is organized as follows. In section II, we establish

the channel model for the millimeter wave system and describe

the related security problem. In section III, we propose three

secure transmission schemes. In section IV and V, we analyze

the secrecy performance, including the SOP and the secrecy

throughput, achieved by AN beamforming, MRT beamforming

and PMRT beamforming. We further obtain the optimal power

allocation that minimizes the SOP or maximizes the secrecy

throughput for the AN scheme. In section VI, we provide

numerical results to verify our theoretical analysis. In section

VII, we conclude our paper.

We use the following notations in this paper: bold up-

percase (lowercase) letters denote matrices (vectors). (·)∗,

(·)T,(·)H,| · |,∥ · ∥,P{·} and EA{·} denote conjugate,

transpose, conjugate transpose, absolute value, Euclidean nor-

m, probability, and mathematical expectation with respect

to A, respectively. CN(µ, σ2),Exp(λ)and Gamma(N, λ)

denote circularly symmetric complex Gaussian distribution

with mean µand variance σ2, exponential distribution with

parameter λ, and gamma distribution with parameters Nand

λ, respectively. CM×Ndenotes the space of all M×Nma-

trices with complex-valued elements. RMand Z+denote M-

dimensional real number domain and positive integer domain,

respectively. log(·),lg(·)and ln(·)denote base-2, base-10

and natural logarithms, respectively. fu(·),Fu(·)and F−1

u(·)

denote probability distribution function (PDF), cumulative

distribution function (CDF) of uand inverse function of Fu(·),

Transactions on Communications

respectively. The intersection and difference between two sets

Ω1and Ω2are denoted by Ω1∩Ω2and Ω1\Ω2, respectively.

Ei(−x) = ∞

e−t

tdt with x > 0.

II. SY ST EM MO DE L

We consider a millimeter wave system where the con-

ﬁdential information transmission from a transmitter to a

destination is intercepted by an eavesdropper. The transmitter

has Ntantennas, while the destination and the eavesdropper

are equipped with one antenna1, respectively.

A. Channel Model

With the sparse scattering and multipaths, the millimeter

wave channel can be represented by a ray cluster based spatial

channel model, where the channel is constituted by Ncclusters

and each cluster contains Nrpaths [18]-[20], [22]-[24]. Thus

the channel can be described as

h=Ntβ

NcNr

lc

glc,lra(Θlc,lr)H,(1)

where βis the average path loss between the transmitter and

the receiver, glc,lris the complex gain of the lth

rpath in the

lth

ccluster, a(Θlc,lr)is the normalized array response (steering

vector) at the azimuth angle of departure (AOD) of θlc,lr, and

Θlc,lr

,sin(θlc,lr). When an uniform linear array (ULA) is

adopted, the normalized array response can be given by

a(Θ) = 1

√Nt

[1, e−j2πd

λΘ, e−j22πd

λΘ,·· · , e−j(Nt−1) 2πd

λΘ]T,

(2)

where dis the antenna spacing, λis the wavelength, and

generally d=λ/2. We assume the channel contains one

cluster in this paper according to the experimental results in

[18], [34]. Because in the millimeter wave system, transmit

power is most probably concentrated on one speciﬁc cluster.

B. Discrete Angular Domain Channel Model

As discussed above, by characterizing individual multipaths,

ray cluster channel model extremely conforms to the practical

physical propagation environment, and is identiﬁed as the

physical channel model of millimeter wave. However, we need

to establish a mathematical model for the theoretical analysis

purpose. Then the discrete angular domain channel model

which considers spatially resolvable paths shows up [15], [35].

The angular domain resolvability is determined by the

length of the transmit antenna array M=Ntd

λ, due to the

ﬁnite angular resolution characteristic of the array-size-limited

system. As proved in [35], paths whose Θdiffer by less than

Mare not resolvable by the array. Thus the basic idea of

the discrete angular domain channel model is to sample the

angular domain at a ﬁxed spacing of 1

Mat the transmitter and

1We consider a single receive antenna for tractability. In practice, multiple

receive antennas are equipped and they will form a receive beam, which is

equivalent to a directional single antenna. This will not inﬂuence the analysis

performed in the paper. Similar assumption has also been adopted by [19],

[29], [30], etc.

to represent the channel by the spatially orthogonal basis [15],

[35], [36]. The orthogonal basis can be deﬁned as

U,[a(Ψ1),a(Ψ2),·· · ,a(ΨN t)],(3)

where Ψi,1

M(i−1−Nt−1

2)for i= 1,2,·· · , Nt. Each

column of Uis an array response vector that represents a

physical angle θwith θ= arcsin Ψ. We can easily ﬁnd that

there is a one-to-one mapping between Ψ∈(−1,1) and the

AOD θ∈[−π/2, π/2]. The orthogonal basis provides a very

simple but approximate decomposition of the total transmitted

signal into the multipath transmitted along different physical

directions up to a resolution of 1

M. We represent the ith

channel gain in terms of comprehensive effect of all paths

whose Θis within a window of width 1

Maround Ψi. Thus

the discrete angular domain channel model can be described

h=Ntβ

LgUH,(4)

where g= [g1, g2,·· · , gN t]is the complex gain vector. We

assume all paths’ AODs are distributed within the angular

range [θmin, θmax ], where θmin ≤θmax ∈[−π/2, π/2]. If

Ψi∈[sin(θmin),sin(θmax )], the ith column of U(the ith

orthogonal basis vector) represents a spatially resolvable path.

Due to the limited scattering feature of the millimeter wave

system, only a few of the Ntorthogonal basis vectors represent

spatially resolvable paths. Lis denoted as the number of

spatially resolvable paths with L < Nt, and can be calculated

by L=⌊Msin(θmax) + Nt+1

2⌋−⌈Msin(θmin) + Nt+1

2⌉+ 1.

Following the channel models in [18, section III E] and [37,

section III D], since each resolvable path contains several

practical paths, if Ψi∈[sin(θmin),sin(θmax )], we assume that

the ith complex gain giis a complex Gaussian coefﬁcient with

zero mean and unit variance, i.e., gi∼ CN(0,1); otherwise,

gi= 0.

We assume that the instantaneous CSI of the destination

is perfectly known at the transmitter [8]-[12]. We deﬁne a

suspicious area where the eavesdropper’s paths are possibly

distributed in. It means that the paths’ AODs of the eaves-

dropper are within the angular range Asus ,[θE,min , θE,max],

with θE,min ≤θE,max ∈[−π/2, π/2]. Since the eavesdropper

and its surrounding obstacles may not physically change their

positions for a long period, we treat AODs as unchanged value

within several channel coherent times, and the information

of suspicious area is known at the transmitter. However,

the complex gain of each path changes rapidly. Thus the

instantaneous information of gEis assumed to be unknown,

whereas its distribution is available.

According to (4), we describe channels of the destination

and the eavesdropper as hD=NtβD

LDgDUHand hE=

NtβE

LEgEUH, where βDand βEare the path loss, gDand

gEdenote the complex gains, LDand LEare numbers of

spatially resolvable paths through the destination’s channel the

eavesdropper’s channel. Obviously, LD< Ntand LE< Nt.

As shown in Fig. 1, we deﬁne the set ΩD,{IDi|IDi ∈

Z+, IDi ∈[1, Nt], ID1< ID2<··· < ID LD}, where IDi is

an index of the basis vector which represents a destination’s

resolvable path. Deﬁne the set ΩE,{IEi|IE i ∈Z+, IEi ∈

Transactions on Communications

Transmitter

Destination

Eavesdropper

(a) LC= 0

Transmitter

Eavesdropper

Destination

(b) LC= 0

Fig. 1. Description of the spatially resolvable paths.

[1, Nt], IE1< IE2<·· · < IELE}, where IEi is an index of

the basis vector which represents an eavesdropper’s resolvable

path. The set ΩC,ΩD∩ΩEdescribes the common paths of

the destination and the eavesdropper, and LCis the number

of common paths. The set ΩA,ΩE\ΩCincludes all the

elements in ΩEbut not in ΩCand the set ΩP,ΩD\ΩC

includes all the elements in ΩDbut not in ΩC.

We deﬁne the function S(B,Ω) ,[bI1,bI2,·· · ,bIK],

where B,[b1,b2,·· · ,bN], and Ω,{Ii|Ii∈Z+, Ii∈

[1, N ], I1< I2<··· < IK, K ≤N}. The function S

generates a matrix whose columns are selected from B. Deﬁne

gD,S(gD,ΩD)∈C1×LD,˜

gE,S(gE,ΩE)∈C1×LE,

UD,S(U,ΩD)∈CNt×LD,˜

UE,S(U,ΩE)∈CNt×LE,

gD,(C),S(gD,ΩC)∈C1×LC,gD,(P),S(gD,ΩP)∈

C1×(LD−LC),gE,(C),S(gE,ΩC)∈C1×LCand gE,(A),

S(gE,ΩA)∈C1×(LE−LC). Thus we can rewrite hD=

NtβD

LD˜

gD˜

Dand hE=NtβE

LE˜

gE˜

C. Problem Description

The capacities of the destination’s channel and the eaves-

dropper’s channel can be respectively given by CD= log(1 +

ξD)and CE= log(1 + ξE), with ξDand ξEdenoting the

received signal-to-interference-plus-noise ratios (SINRs). By

utilizing the well-known Wyner’s wiretap encoding scheme,

Rt,Rsand Re,Rt−Rsare deﬁned as codeword rate,

secrecy rate and rate redundancy, where Reis exploited to

offer secrecy against eavesdropping.

The secure information can not be correctly recovered by

the destination when CD< Rt. Besides, once CEexceeds

Re, perfect secrecy is destroyed and a secrecy outage occurs.

To avoid the above two undesirable situations, we adopt an

adaptive on-off transmission scheme proposed in [12], where

the transmitter decides when to radiate signals based on the

instantaneous CSI of the destination. Throughout the paper, for

notational brevity, we deﬁne γ,∥˜

gD∥2as the overall channel

gain of the destination, γC,∥gD,(C)∥2and γP,∥gD,(P)∥2.

Obviously, γ=γC+γP. Deﬁne γ◦,(γC, γP)∈R2as the

instantaneous gains of the common and non-common paths of

the destination. Deﬁne Υ, the transmission region, as the set

of those γ◦satisfying the transmission constraint. Since the

channel gain γ◦varies from time to time, the transmitter emits

signals only when γ◦∈Υ; otherwise, the transmitter keeps

silence. Deﬁne the SOP for a given γ◦as

Pso =P{CE> Rt−Rs|γ◦},∀γ◦∈Υ.(5)

Secrecy throughput measures the effective average transmis-

sion rate of the conﬁdential message, which is deﬁned as

τ=Eγ◦[Rs(γ◦)] ,(6)

where Rs(γ◦) = 0 for γ◦/∈Υ.

III. TRA NS MI SS IO N SCH EM ES

In this section, we ﬁrst analyze the secrecy performance of

the MRT beamforming in the millimeter wave system as a

benchmark. Next, by considering the channel features of mil-

limeter wave, we propose two transmission schemes, namely

AN beamforming and PMRT beamforming, to improve the

secrecy performance of the MRT beamforming for the case

where the destination and the eavesdropper have common

resolvable paths.

A. MRT Beamforming

The MRT beamforming strategy is a simple but effective

transmission method. Although it is studied by lots of the

researchers, we will study the new security properties that it

presents in the millimeter wave system. The transmitter sends

one data stream, i.e, Ns= 1. The signals received at the

destination and the eavesdropper are

yMRT

D=√PhDw1s+nD,(7)

yMRT

E=√PhEw1s+nE,(8)

where w1=hH

D/∥hD∥is the beamforming vector, Pis the

total transmit power, sis the information bearing signal with

E[|s|2] = 1,nDand nEare i.i.d. additive white Gaussian

noise with zero-mean and variance σ2

n, i.e., nD∼ CN (0, σ2

and nE∼ CN(0, σ2

n). Then the SNRs of the destination and

the eavesdropper can be respectively described as

ξMRT

D=P∥hD∥2

σ2

=P βDNt

σ2

nLD∥gDUH∥2=P βDNt

σ2

nLD∥˜

gD∥2,

(9)

ξMRT

E=P|hEhH

D|2

σ2

n∥hD∥2=P βENt

σ2

nLE

|gEUHUgH

D|2

∥gDUH∥2

=P βENt|gE,(C)gH

D,(C)|2

σ2

nLE∥˜

gD∥2.(10)

Transactions on Communications

Only if i∈ΩD∩ΩE, i.e., i∈ΩC,gEi g∗

Di = 0. Thus we have

gEgH

D=gE,(C)gH

D,(C).

From the above two equations, several observations can be

obtained.

1) In the situation that LC= 0, i.e., the destination

and the eavesdropper have no common path, array steer-

ing vectors in ˜

UDand ˜

UEare orthogonal. hEhH

NtβE

LENtβD

LD˜

gE˜

E˜

UD˜

D= 0 leads to ξMRT

E= 0 and

CMRT

E= 0, such that Pso(γ◦) = 0. Therefore, when LC= 0,

the secrecy outage never occurs.

2) From the deﬁnitions of gEand gH

D, they are uncor-

related. gE,(C)is a vector whose elements are all selected

from gE, and gH

D,(C)is a vector whose elements are all

selected from gH

D. Therefore, gE,(C)and gH

D,(C)are un-

correlated. Moreover, as gE,(C)and gH

D,(C)are Gaussian

distribution vectors, we have that gE,(C)and gH

D,(C)are

independent. Since each element of gE,(C)follows a Gaus-

sian distribution with zero mean and unit variance, which

is independent of the unit-norm vector gH

D,(C)

∥gD,(C)∥, we have

that |gE,(C)

D,(C)

∥gD,(C)∥|2∼Exp(1) [27]. Therefore, we ob-

tain EξMRT

E=P βENt∥gD,(C)∥2

σ2

nLE∥˜

gD∥2E|gE,(C)

D,(C)

∥gD,(C)∥|2=

P βENt∥gD,(C)∥2

σ2

nLE∥˜

gD∥2. When LCincreases, ∥gD,(C)∥2at the nu-

merator of EξMRT

Eincreases, which leads to an increase

in EξMRT

E. The secrecy performance becomes worse when

LCincreases.

3) The conclusion implies that the secrecy performance

of millimeter wave system is dramatically inﬂuenced by the

relationship between spatially resolvable paths of the desti-

nation and the eavesdropper, which is unlike those wireless

systems with statistically independent channel models. That is

because array steering vectors are the key constituent part of

the channel formulas.

For the situation of LC= 0, there are two basic ideas

to improve the secrecy performance. One idea is emitting

interference to deteriorate the eavesdropper’s channel. The

other idea is to avoid signal leakage to the eavesdropper’s

channel. Based on those two ideas, we propose two transmis-

sion schemes, namely the AN beamforming and the PMRT

beamforming.

B. AN Beamforming

The idea of AN beamforming is to emit information bearing

signal together with AN in order to confuse the eavesdropper.

AN is transmitted in the null space of the destination’s channel

to guarantee the fact that the destination is not interfered with

AN. Utilizing AN is an effective way to improve secrecy

performance when the eavesdropper’s instantaneous CSI is

unknown at the transmitter. However, the complexity of the

null space calculation which includes singular value decom-

position (SVD) depends on the number of transmit antennas.

Considering the expectation of the 5G millimeter wave system,

there will be hundreds of transmit antennas, which leads to a

high complexity. Compared with the statistically independent

channel, millimeter wave channel has speciﬁc propagation

characteristics, so we propose a new AN generating method in

this paper which is much simpler but effective. In our method,

AN is transmitted to the directions of the eavesdropper’s

resolvable paths excluding the directions of common paths.

The transmitted signal can be given by

x=ηP w1s+(1 −η)P

LE−LC

W2z,(11)

where W2=S(U,ΩA) = [w2,1,w2,2,·· · ,w2,(LE−LC)]∈

CNt×(LE−LC)is the AN beamforming matrix, z∈

C(LE−LC)×1is the AN bearing signal with E[zzH] =

ILE−LC,ηis the power allocation ratio of the information

signal power to the total transmit power with 0≤η≤1. From

the deﬁnition of W2, we ﬁnd that the generating method of

the AN beamforming matrix is simple as we only select some

columns from U. Since ΩA= ΩE\ΩC, we have hDW2=0.

Therefore, utilizing speciﬁc characteristics of the millimeter

wave channel is beneﬁcial for reducing the complexity of the

design and application for AN. It should be noted that the

case η= 1 is equivalent to the MRT beamforming where the

transmitter does not transmit AN but only information bearing

signal with the total transmit power P. Signals received by the

destination and the eavesdropper can be described as

yAN

D=ηP hDw1s+(1 −η)P

LE−LC

hDW2z+nD,(12)

yAN

E=ηP hEw1s+(1 −η)P

LE−LC

hEW2z+nE.(13)

Then the SINRs of the destination and the eavesdropper can

be respectively formulated as

ξAN

D=ηP ∥hD∥2

σ2

=ηP βDNtγ

σ2

nLD

,(14)

ξAN

E=ηP |hEw1|2

(1−η)P

LE−LC∥hEW2∥2+σ2

ηP βENt

LE∥˜

gD∥2|gEUHUgH

D|2

(1−η)P βENt

(LE−LC)LE∥gEUHW2∥2+σ2

ηP βENt

LE∥˜

gD∥2|gE,(C)gH

D,(C)|2

(1−η)P βENt

(LE−LC)LE∥gE,(A)∥2+σ2

ηP βENtγC

σ2

nLEγ|gE,(C)

gD,(C)H

∥gD,(C)∥|2

(1−η)P βENt

σ2

n(LE−LC)LE∥gE,(A)∥2+ 1 .(15)

By denoting gEUHW2=χA,1, χA,2,·· · , χA,(LE−LC), we

have χA,j =Nt

i=1 gEia(Ψi)Hw2,j . Since W2=S(U,ΩA)

and Uis a unitary matrix, we get gEUHW2=gE,(A).

AN transmission effectively interferes with the eavesdrop-

per, but decreases the power utilized for data transmission

and reduces the signal power at the destination. Therefore, the

power allocation ratio ηis critical to ensure a good secrecy

performance. Thus we will study the optimal power allocation

that minimizes the SOP or maximizes the secrecy throughput

in section IV.

Transactions on Communications

C. PMRT Beamforming

For the MRT scheme, the transmitting beams steer in

all directions of the destination’s resolvable paths, which

contain LCpaths to the eavesdropper in the situation that

LC= 0. That means the eavesdropper also receives the

conﬁdential signal. We propose a narrow-beam transmission

scheme, which is called partial MRT (PMRT), aiming at

the above problem to improve the secrecy performance. The

PMRT scheme transmits signals only in partial directions

of the destination’s resolvable paths excluding the directions

of common paths. The PMRT beamforming matrix w3=

(gD,(P)UH

(P))H/∥gD,(P)UH

(P)∥, where U(P)=S(U,ΩP) =

uP,1,uP,2,··· ,uP,(LD−LC)∈CNt×(LD−LC). Signals re-

ceived by the destination and the eavesdropper are yP

√PhDw3s+nDand yP

E=√PhEw3s+nE, respectively.

Then the SINRs of the destination and the eavesdropper can

be respectively described as

ξP

D=P βDNt

σ2

nLD

|gDUHU(P)gH

D,(P)|2

gD,(P)UH

(P)U(P)gH

D,(P)

=P βDNt

σ2

nLD

γP,(16)

ξP

E=P βENt

σ2

nLE

|˜

gE˜

EU(P)gH

D,(P)|2

gD,(P)UH

(P)U(P)gH

D,(P)

= 0.(17)

Denoting gDUHU(P)=χP,1, χP,2,··· , χP,(LD−LC), we

have χP,j =Nt

i=1 gDia(Ψi)HuP ,j . Since U(P)=S(U,ΩP),

we get gDUHU(P)=gD,(P). From ˜

UE=S(U,ΩE)and

ΩE∩ΩP= Ø, we have ˜

EU(P)=0.

There is a special case LD=LE=LCwhich means

that all the destination’s and eavesdropper’s resolvable paths

overlap. For the case LE=LC, i.e., ΩE= ΩC,W2= Ø and

no AN is emitted in the AN scheme. It is the same as the MRT

scheme and all the power is allocated to the transmission of

information bearing signal, i.e., η= 1. For the case LD=LC,

i.e., ΩD= ΩC,w3= Ø in the PMRT scheme. Since LCis

large, the eavesdropper receives a large amount of conﬁdential

messages, hence both the AN scheme and the PMRT scheme

do not work any more. However, in practice, this extreme

case is hard to occur due to the following two reasons. 1)

Since the reﬂection and scattering in practical propagation

environment are complicated, signals transmitted to receivers

at different locations encounter various reﬂection objects and

go through different paths. Even in the same direction, the

AODs of receivers may be different. 2) Furthermore, in the

5G millimeter wave system, when the number of transmit

antennas becomes large, the spacing 1

Mgets small and the

spatial horizon is divided exquisitely. Thus little difference

of paths between the destination and the eavesdropper can be

found. Therefore it is reasonable for us to assume LE−LC>0

or LD−LC>0in our study. For the situation LD=LCand

LE−LC>0, we can utilize the AN scheme to guarantee the

secure transmission. Whereas for the situation LE=LCand

LD−LC>0, we can exploit the PMRT scheme to improve

the secrecy performance. For the situation LD−LC>0and

LE−LC>0, both two schemes work.

IV. SEC RE CY PE RF OR MA NC E OF AN BE AM FO RM IN G AN D

MRT BEAMFORMING

In this section, we investigate the secrecy performance

of AN beamforming. We ﬁrst analyze the secrecy outage

performance by deriving a closed-form SOP and design the

optimal power allocation η◦to minimize the SOP. Then we

maximize the secrecy throughput under a given SOP constraint

and obtain the optimal power allocation ratio η∗. In addition,

we analyze the secrecy performance of MRT beamforming as

a special case of AN beamforming when the power allocation

ratio η= 1.

A. SOP Minimization and Optimal Power Allocation

We ﬁrst derive the CDF of ξAN

Ein (15). Deﬁne u,

|gE,(C)

D,(C)

∥gD,(C)∥|2, we have u∼Exp(1). Deﬁne v,

∥gE,(A)∥2, we have v∼Gamma(LE−LC,1). Since ΩC∩

ΩA= Ø,uand vare independent to each other. Moreover,

we deﬁne a(γ◦),P βENtγC

σ2

nLE(γC+γP),b,P βENt

σ2

n(LE−LC)LEand

c(γ◦),P βDNt(γC+γP)

σ2

nLD. For notational brevity, we omit γ◦

from a(γ◦)and c(γ◦), and treat them as functions of γ◦by

default. The CDF of ξAN

Ecan be given by

FAN

ξE(x) = Pηau

(1 −η)bv + 1 < x

=Pu < (1 −η)bxv +x

ηa = 1 −Eve−(1−η)bx

ηa v−x

ηa 

= 1 −e−x

ηa ∞

vLE−LC−1

Γ(LE−LC)e−[1+ (1−η)bx

ηa ]vdv

(a)

= 1 −e−x

ηa 1 + (1 −η)bx

ηa −(LE−LC)

(18)

where (a)holds for the integration formula [38, 3.326.2].

Given that the instantaneous CSI of the destination is avail-

able at the transmitter, we set Rtequal to CDand minimize

the SOP under each destination’s channel realization. Based on

the on-off transmission scheme, to get a better secrecy perfor-

mance, CDshould exceed Rsin order to guarantee a positive

Reagainst the eavesdropper, i.e., only if CD> Rs, the

transmitter radiates signals, otherwise, transmission should be

suspended. Since ξAN

D=ηc, we obtain that η > ηmin ,T−1

where T,2Rs. From (18), the SOP deﬁned in (5) can be

expressed as

Pso(γ◦),P{CE> CD−Rs|γ◦}

=PξAN

E>ξAN

D−(T−1)

T

= exp −ηc −(T−1)

ηaT 

×1 + (1 −η)b[ηc −(T−1)]

ηaT −(LE−LC)

(19)

We derive the following properties from the above equation:

1) Pso monotonically decreases with P. Since

dPso

dP =−T−1

ηT a2da

dP +(1−η)γ

γCT δ

dP Pso, where

δ= 1 + (1−η)b[ηc−(T−1)]

ηaT >0, and da

dP >0,dc

dP >0,

Transactions on Communications

we have dPso

dP <0. It implies that secrecy outages are more

likely to occur in low transmit power scenarios.

2) Pso monotonically decreases with βD,

while increases with βE. On one hand, since

dPso

dβD=−1

aT +(1−η)γ

γCT δ Pso dc

dβDand dc

dβD>0, we have

dPso

dβD<0. On the other hand, since dPso

dβE=ηc−(T−1)

ηT a2Pso da

dβE

and da

dβE>0, we obtain dPso

dβE>0. As βdecreases with

the increase of the distance between the receiver and the

transmitter, we ﬁnd either a closer destination or a farther

eavesdropper will be beneﬁcial for decreasing Pso.

Then the problem of the SOP minimization can be formu-

lated as

min

ηPso(γ◦),

s.t. ηmin < η ≤1.

(20)

The minimum of Pso(γ◦)can only be achieved at the

boundary η= 1 or those zero-crossing points of the ﬁrst-

order derivative of Pso(γ◦). The derivative of Pso(γ◦)can be

given by

dPso

dη =bc(LE−LC)η−3

aT exp −ηc −(T−1)

ηaT 

×1 + (1 −η)b[ηc −(T−1)]

ηaT −(LE−LC)−1

×η3+ε1η2+ε2η+ε3,

(21)

where ε1=T−1

aT (LE−LC),ε2=−(T−1)[aT +b(c+T−1)]

aT bc(LE−LC)−T−1

and ε3=(T−1)2

aT c(LE−LC). Denote K(η) = η3+ε1η2+ε2η+

ε3. We ﬁnd the sign of dPso

dη follows that of K(η). In other

words, to investigate the monotonicity of Pso on η, we need

to examine the sign of K(η). For notational brevity, we deﬁne

¯a,P βENt

σ2

nLE=γC+γP

γCaand ¯c,P βDNt

σ2

nLD=1

γC+γPc. In the

following theorem, we provide the solution to problem (20).

Theorem 1: The optimal η◦that minimizes the SOP is

η◦=









Ø, γ ≤T−1

¯c,

1,T−1

¯c< γ ≤(¯a+ 1)(T−1)

¯a¯c,

η⋆,otherwise,

(22)

where η⋆=3

−q

2+p3

27 +q2

4+3

−q

2−p3

27 +q2

4−ε1

with p=ε2−ε2

3,q=ε3−ε1ε2

3+2ε3

27 , and η◦= Ø means

that the transmission is suspended.

Proof: Please see Appendix A.

Theorem 1 indicates that when γis small which corresponds

to a poor quality of the destination’s channel, the transmitter

either suspends the transmission or transmits information bear-

ing signals with full power. When γbecomes large enough,

it is wise to emit AN to decrease the SOP. The resulting

minimum Pso(γ◦)is obtained by substituting η◦into (19).

Since we minimize the SOP under each destination’s channel

realization, the overall SOP is consquently minimized.

B. Secrecy Throughput Maximization and Optimal Power Al-

location

In this subsection, we maximize the secrecy throughput

under a SOP constraint through a dynamic transmission pa-

rameter scheme, which means values of Rs,Rtand ηare

chosen dynamically for each destination’s channel realization.

From the deﬁnition in (6), the secrecy throughput will be

maximized if we maximize the secrecy rate Rs(γ◦)for each

γ◦. Therefore, the optimization problem can be formulated as

max

η,Rt

Rs(γ◦),

s.t. 0< Rs(γ◦)< Rt(γ◦)≤CD,(23a)

Pso(γ◦)≤ϵ, (23b)

0≤η≤1,(23c)

where ϵ∈[0,1] is a pre-set SOP threshold, (23a)-(23c) show

the constraints for reliable transmission, secrecy outage and

power allocation, respectively.

Lemma 1: The optimization problem in (23) is equivalent

max

ηRs(γ◦) = log 1 + ηc

1 + ηκ(η),

s.t. 0≤η≤1, c > κ(η),

(24)

where κ(η),F−1

ξE(1−ϵ)

η,c > κ(η)is the transmission

constraint of the on-off transmission scheme, which means

that the transmitter emits signals only when this constraint is

satisﬁed.

Proof: Please see Appendix B.

The deﬁnition of κ(η)yields FAN

ξE(ηκ(η)) = 1 −ϵ, which

is equivalent to

Q1(κ) = 0,(25)

where Q1(κ),e−κ(η)

a1 + (1−η)bκ(η)

a−(LE−LC)−ϵ.

Lemma 2: κ(η)is a monotonically increasing and convex

function of ηin the range η∈[0,1].

Proof: Please see Appendix C.

Although κis an implicit function of η, we can calculate

κefﬁciently by utilizing Lamma 2. We simply observe κ≥0

from the deﬁnition of κ. Lamma 2 shows that the maximum

κcan be get when η= 1, which is κmax =−aln ϵaccording

to (25). Given an arbitrary η,Q1(κ)monotonically decreases

with κ. Combined with this and Q1(0) = 1 −ϵ > 0,

Q1(κmax) = ϵ[1 −(1 −η)bln ϵ]−(LE−LC)−ϵ≤0, we derive

that Q1has the unique zero-crossing point. Therefore, for a

given η, we can calculate κthat satisﬁes (25) by utilizing the

bisection method within the range [0, κmax]instead of a one-

dimensional exhaustive search. Then we give the implemen-

tation steps of the bisection method. We start with an interval

[κl, κu]known to contain the solution of κ, and the initial

values of κland κuare 0and κmax respectively. We calculate

Q1(κ)at its midpoint κm= (κl+κu)/2, to determine whether

the solution is in the lower or upper half of the interval, and

update the interval accordingly, i.e., if Q1(κm)<0, we set

κu=κm; if Q1(κm)>0, we set κl=κm. This produces

a new interval, which also contains the solution of κ, but has

Transactions on Communications

half the width of the initial interval. This is repeated until the

width of the interval is small enough.

Theorem 2: Given c > κ(η),Rsis a concave function of

η. The optimal η∗that maximizes Rsis given by

η∗=





1,c

1 + c+[1 + (LE−LC)b]aln ϵ

1−aln ϵ>0,

η⋆,otherwise,

(26)

where η⋆is the unique root of the following equation

dRs

dη =1

ln 2 c

1 + ηc −κ+ηdκ

dη

1 + ηκ = 0,(27)

with dκ

dη deﬁned in (37).

Proof: Please see Appendix D.

We can efﬁciently search the optimal η⋆by exploiting the

bisection method due to the concave characteristic of Rswith

respect to η.

Corollary 1: The optimal η⋆monotonically increases with

respect to βD,ϵand γP, and monotonically decreases with

recpect to βE.

Proof: Please see Appendix E.

Corollary 1 indicates that in order to promote the secrecy

rate, more power should be: 1) allocated to the information

signal under a better quality of the destination’s channel (a

larger βD) or a higher proportion of common paths’ power to

the total destination’s channel gain (a larger γP), 2) allocated

to the AN under a better quality of the eavesdropper’s channel

(a larger βE) or a stronger SOP constraint (a smaller ϵ).

We obtain the maximum secrecy rate R∗

s(γ◦)after get-

ting the optimal power allocation ratio η∗. The transmis-

sion region deﬁned in subsection II-C can be expressed as

Υ = {γ◦|c > κ}. The transmitter examines the the constraint

γ◦∈Υfor each instantaneous channel realization of the

destination to decide whether starting communication or not,

i.e., the transmitter emits signals with R∗

s(γ◦)only when

γ◦∈Υwhich guarantees a positive Rs; otherwise, the

transmitter keeps silence and we set Rs(γ◦) = 0. Evidently,

if the optimal η∗that maximizes Rs(γ◦)does not meet the

constraint, any other ηcan not satisfy it either. So we can only

check the transmission constraint by substituting η∗. Since

ΩC∩ΩP= Ø, we ﬁnd that γC∼Gamma(LC,1) and

γP∼Gamma(LD−LC,1) are independent to each other.

Together with (6), the maximum secrecy throughput of AN

beamforming can be given by

τ∗= Υ

R∗

s(γ◦)fγP(x)fγC(y)dxdy, (28)

where fγC(x) = xLC−1

Γ(LC)e−xand fγP(x) = xLD−LC−1

Γ(LD−LC)e−xare

the PDFs of γCand γP, respectively.

C. Secrecy Performance of MRT Beamforming

Since MRT beamforming is a special case of AN beamform-

ing with η= 1, we can easily analyze the secrecy performance

of MRT beamforming from the results of AN beamforming

and derive several more concise results.

By substituting η= 1 into (19), we obtain the SOP of MRT

beamforming Pso(γ◦) = exp −c−(T−1)

aT . According to (24),

since κ=−aln ϵwhen η= 1, the maximum Rs(γ◦)can be

given by

R∗

s(γ◦) = log 1 + c

1−aln ϵ= log (γC+γP)[1 + ¯c(γC+γP)]

γP+ (1 −¯aln ϵ)γC

(29)

with the transmission region Υ = {γ◦|γP>−γC+

−¯aln ϵ

¯c√γC}.

Corollary 2: The maximum secrecy throughput of MRT

beamforming can be given by

τ∗=

LD−LC−1



m=0

Γ(LD−LC−m)∞

fγC(y)e−ς

×ςLD−LC−1−m[Q3(µ1) + Q3(µ2)−Q3(µ3) + µ4]dy,

(30)

where ς=−γC+−¯aln ϵ

¯c√γC,µ1=1

y+ς,µ2=

¯c

¯cy+¯cς +1 ,µ3=1

(1−¯aln ϵ)y+ς,µ4= log (y+ς)(¯cy +¯cς+1)

(1−¯aln ϵ)y+ς

and Q3(x) = 1

ln 2 m

n=1 1

(m−n)! [(−1)m−n−1

xm−ne1

xEi(−1

x) +

m−n

k=1 (k−1)!(−1

x)m−n−k].

Proof: Please see Appendix F.

We need to mention that when LC= 0,CMRT

E= 0,

we have Pso(γ◦)=0for the MRT beamforming, hence the

outage constraint Pso(γ◦)≤ϵalways holds and the maximum

R∗

s(γ◦) = Rt=CMRT

D. For the MISO channel, the MRT

beamforming can achieve the largest receive SNR ξDat the

destination with the given transmit power P. Any other scheme

has a lower received SNR and hence its reliable rate must be

less than CMRT

D. Thus τ=Eγ◦[Rs(γ◦)] achieved by the

MRT scheme reaches the maximum achievable value. In a

word, the MRT beamforming is the best scheme in terms of

achieving the maximum secrecy throughput under the scenario

of LC= 0.

V. SE CR EC Y PER FO RM AN CE O F PMRT BEAMFORMING

In this section, we analyze the SOP and the secrecy through-

put of the PMRT beamforming. Since ξP

E= 0 and CP

E= 0,

Pso(γ◦)deﬁned in (5) equals to 0. We observe that secrecy

outage never occurs when PMRT beamforming is adopted,

which is a signiﬁcant property of the PMRT scheme.

Since the SOP constraint Pso(γ◦)≤ϵalways holds, the

maximum achievable value of Rs(γ◦)is formulated as

R∗

s(γ◦) = Rt=CP

D= log(1 + ¯cγP).(31)

The maximum secrecy throughput is given by

τ∗=∞

R∗

s(γ◦)fγP(x)dx

=∞

log(1 + ¯cx)xLD−LC−1

Γ(LD−LC)e−xdx

ln 2

LD−LC−1



n=1

(LD−LC−1−n)!

×(−1)LD−LC−n

¯cLD−LC−1−ne1

¯cEi(−1

¯c)

LD−LC−1−n



k=1

(k−1)!(−1

¯c)LD−LC−1−n−k.

(32)

Transactions on Communications

The above equation holds for the integration formula [38,

4.337.5]. We observe that τ∗monotonically increases with

¯c, hence τ∗monotonically increases with P,Ntand βD. It

implies that increasing transmit power, increasing the trans-

mitter’s antennas or decreasing the distance between the

transmitter and the destination are beneﬁcial for increasing

the secrecy throughput.

At the low-SNR regime as P→0, we have ¯c→0. Since

lim

y→01+y=ey, the maximum secrecy throughput can be given

τ∗=1

ln 2 ∞

¯cx xLD−LC−1

Γ(LD−LC)e−xdx =1

ln 2 ¯c(LD−LC).

(33)

We easily observe that τ∗monotonically decreases with

respect to LC. Although we derive this property at the low

SNR regime, we ﬁnd the property is also correct when SNR

becomes higher from the numerical results. It is because that as

the number of common paths LCdecreases, the beamforming

matrix matches with more destination’s resolvable paths and

the destination’s capacity CDincreases, hence the secrecy

throughput increases.

VI. NU ME RI CA L RES ULTS

In this section, numerical results are presented to verify our

theoretical analysis. The location coordinates of the transmitter

and the destination are (0,0) and (rD,0), respectively. The

transmitter is equipped with a 100-antenna ULA, where the

antenna spacing dis set to be half wavelength. We assume

the angular spread of each cluster is σϕ= 20◦[18], [19],

and the cluster’s central AOD of the destination is ϕD= 0◦.

Therefore the AODs for paths transmitted to the destination

are within the angular range [−10◦,10◦]. Considering an

eavesdropper at a distance rE= 100m from the transmitter,

when the eavesdropper moves, LCvaries. According to the

experimental results obtained in [18], the path loss is modeled

as β= 10−1

10 [ρ1+ρ210 lg(r)], where ris the distance in meters,

ρ1= 61.4and ρ2= 2 are the measurement results for 28 GHz

frequency. The noise power σ2

n=−50 dBm.

A. Secrecy Performance of AN Beamforming

Fig. 2 describes SOP versus the number of common paths

LCfor different P’s. We see that Pso signiﬁcantly reduces

as LCdecreases or Pincreases. It is because that as LC

becomes larger, more conﬁdential information is leaked to the

eavesdropper’s channel. We also ﬁnd that AN beamforming

has obvious superiority over MRT beamforming in terms of

achieving lower SOP. Therefore, AN transmission is beneﬁcial

to security. The results of Monte-Carlo simulations match well

with the analytical values.

Fig. 3 illustrates the optimal power allocation that minimize

Pso(γ◦)versus Pfor different Rs’s. “Searched η◦” refers to

the results obtained by exhaustively searching the minimum

of (19) and “theoretical η◦” corresponds to the root of the

cubic equation in (22). It is easy to see that the theoretical η◦

matches well with the searched η◦. Evidently, η◦becomes

lower with an increase in Por a decrease in Rs. The

1 3 5 7 9 11 13 15 17 19

10−5

10−4

10−3

10−2

10−1

100

Secrecy Outage Probability

P= 0dBm,analytica l

P= 0dBm,simulation

P= 5dBm,analytica l

P= 5dBm,simulation

MRT

Fig. 2. SOP versus LCfor different P’s, with Nt= 100,Rs= 5bit/s/Hz,

LD= 20 and rD= 100m.

0 5 10 15 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

P(dBm)

η° that Minimizes the SOP

theoretical η◦

searched η◦

Rs= 5

Rs= 3

Rs= 4

Fig. 3. Optimal power allocation ratio η◦that minimizes the SOP versus P

for different Rs’s, with Nt= 100,LC= 11,LD= 20 and rD= 100m.

−10 −5 0 5 10 15 20

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P(dBm)

η* that Maximizes the Secrecy Throughput

LC= 6

LC= 11

LC= 16

Fig. 4. Optimal power allocation ratio η∗that maximizes the secrecy

throughput versus Pfor different LC’s, with Nt= 100,rD= 100m,

LD= 20 and ϵ= 0.01.

underlying reason is that to support a higher Rs, more power

should be allocated to the information bearing signal.

Fig. 4 shows the optimal η∗that maximizes the secrecy

throughput versus Pfor different LC’s. At the low transmit

power region, η∗keeps 1, which reveals that full power should

Transactions on Communications

1 3 5 7 9 11 13 15 17 19

0.2

0.3

0.4

0.5

0.6

0.7

0.8

η* that Maximizes the Secrecy Throughput

ǫ= 0.1

ǫ= 0.01

ǫ= 0.001

Fig. 5. Optimal power allocation ratio η∗that maximizes the secrecy

throughput versus LCfor different ϵ’s, with Nt= 100,P= 15dBm,

LD= 20 and rD= 100m.

−10 −5 0 5 10 15 20

P(dBm)

Secrecy Throughput

MRT

PMRT

Fig. 6. Secrecy throughput versus P, with Nt= 100,rD= 100m, LD=

20,LC= 16 and ϵ= 0.01.

be allocated to information signals to guarantee a reliable

link to the destination. Then η∗drops with the increase of

P, which implies that more power is permitted for the AN

transmission to confuse the eavesdropper on the premise that

the outage constraint is satisﬁed. In addition, as LCincreases,

η∗decreases. Since the eavesdropper receives more power of

conﬁdential signals in the larger LCscenario, we should shift

more power to AN transmission in order to interfere with the

eavesdropper.

Fig. 5 presents the optimal η∗that maximizes the secrecy

throughput versus LCfor different outage threshold ϵ’s. As

shown in the ﬁgure, η∗decreases as ϵdecreases, which

indicates that a larger fraction of power should be allocated

to AN in order to confuse the eavesdropper and achieve a

tolerable SOP under a more rigorous SOP constraint.

B. Comparison of Transmission Schemes

Fig. 6 describes the secrecy throughput versus P. Obvious-

ly, by increasing transmit power P, the secrecy throughput

increases. Furthermore, we obtain an important observation

that to achieve higher secrecy throughput, the PMRT scheme

1 3 5 7 9 11 13 15 17 19

Secrecy Throughput

MRT,rD= 100m

MRT,rD= 150m

AN,rD= 100m

AN,rD= 150m

PMRT,rD= 100m

PMRT,rD= 150m

Fig. 7. Secrecy throughput versus LCfor different rD’s, with Nt= 100,

P= 15dBm, LD= 20 and ϵ= 0.1.

is a better choice than the AN scheme at the high transmit

power regime, whereas the AN scheme shows its superiority

over the PMRT scheme. The underlying reason is that at the

low SNR regime, CDis small, hence CDis the dominant

factor contributing to the secrecy throughput. For the AN

scheme, most of the transmit power or even the full power

should be allocated to the information bearing signals in

order to increase CD. Since information bearing signals of

AN beamforming cover all directions of the destination’s

paths while those of PMRT beamforming only cover partial

directions of the destination’s paths, the destination’s capacity

of AN beamforming is larger than that of PMRT beamforming.

Therefore AN beamforming is better. At the high SNR regime,

for the AN scheme, the eavesdropper receives a large amount

of the conﬁdential message’s power, so we should allocate

most of the power to AN to confuse the eavesdropper and only

a little power is allocated to the information bearing signals to

support CD. For PMRT beamforming, full power is utilized

to transmit the conﬁdential signals which leads to a large CD.

Therefore PMRT beamforming is better.

In addition, Fig. 6 shows that as a special case of AN

beamforming, MRT beamforming presents a comparable per-

formance to AN beamforming under the low transmit power

scenario. However, with the increase of the transmit power,

the superiority of AN beamforming becomes more obvious.

Fig. 7 plots the secrecy throughput as a function of LC

for different rD’s. Secrecy throughput becomes higher with

the decrease of rD, which conﬁrms the fact that increasing

βDis helpful to enhance the secrecy throughput performance.

Meanwhile, when LCdecreases, since the beamforming ma-

trix matches with more destination’s resolvable paths in the

PMRT scheme and the eavesdropper receives fewer conﬁ-

dential messages in the AN scheme, the secrecy throughput

becomes higher.

Besides, we obtain an important observation about the supe-

riorities among the three schemes when LCvaries from Fig. 7.

On one hand, under large LCscenarios, AN beamforming has

the best performance among the three schemes. The underlying

reason is that, in order to keep away from the directions of the

Transactions on Communications

5 10 15 20

∆φ(◦)

Secrecy Throughput

ASM[27]

MRT

PMRT

Fig. 8. Secrecy throughput versus ∆ϕ, with Nt= 100,P= 15dBm,

rD= 100m and ϵ= 0.1.

eavesdropper’s resolvable paths in the large LCcase, signals

of PMRT beamforming are emitted in very few directions

of the destination’s resolvable paths which leads to a poor

match with the destination’s channel. However, information

bearing signals of AN beamforming cover all directions of

the destination’s paths to reach a high capacity CD. Although

the eavesdropper receives more information, it is disturbed

by the AN. On the other hand, under small LCscenarios,

PMRT beamforming has the best performance among the three

schemes. It is because that PMRT beamforming matches with

most directions of the destination’s paths which leads to a

large CD, meanwhile the eavesdropper can not intercept any

information.

Fig. 8 presents the secrecy throughput versus ∆ϕto com-

pare secrecy performances between transmission schemes in-

vestigated in this paper and the ASM scheme proposed in

[27], where ∆ϕ=ϕE−ϕDis the angular difference between

the cluster’s central AOD of the eavesdropper and that of the

destination. We set the number of antennas in each subset

equal to 30 for the ASM scheme. Obviously, transmission

schemes analyzed in this paper have better performances in

terms of achieving higher secrecy throughput than the ASM

scheme.

VII. CON CL US IO N

This paper provided the secure transmission scheme design

and comprehensive performance analysis under slow fading

channels considering multipath propagation for millimeter

wave systems. In consideration of the speciﬁc propagation

features of the millimeter wave, discrete angular domain chan-

nel model was proposed considering spatially resolvable paths

from the perspective of analysis and design of the millimeter

wave system. In the absence of the common path between

the destination and the eavesdropper, the MRT beamforming

was demonstrated as the best scheme. In the presence of

common paths, two transmission schemes were proposed to

improve the secrecy performance. The closed-form SOP was

obtained for both schemes. Furthermore, the secrecy through-

put was analyzed by deriving an accurate integral expression

for the AN scheme and a closed-form formula for the PMRT

scheme, respectively. For the AN beamforming, The optimal

power allocation ratio was derived to achieve the objective of

minimizing the SOP or maximizing the secrecy throughput.

It can be demonstrated from the numerical results that the

secrecy performance of the AN scheme is better than the

PMRT scheme when the transmit power is low or the number

of common paths is large, whereas the PMRT scheme shows

its superiority over the AN scheme.

APP EN DI X A

PROO F OF TH EO RE M 1

We have that the transmitter only emits signals when η >

ηmin =T−1

c. If T−1

c≥1, i.e., γ≤T−1

¯c, no feasible η∈

[0,1] satisﬁes η > ηmin and the transmission is suspended.

If T−1

c<1, the transmitter emits signals in the range of

η∈(ηmin,1]. Next, we derive the optimal value of ηthat

minimizes Pso(γ◦).

We ﬁrst prove the convexity of K(η)on η∈(ηmin,1]. From

the expression of K(η), we have d2K(η)

dη2= 6η+ 2ε1>0, i.e.,

K(η)is a convex function of η. Then we determine the sign

of K(η). The values of K(η)at the boundaries η=ηmin

and η= 1 are K(ηmin) = η2

min(ηmin −1) −1

b(LE−LC)and

K(1) = b(LE−LC)[c−(T−1)]−(T−1)

bc(LE−LC). Obviously, K(ηmin)<0

always holds. Then we discuss the optimal value of ηfor the

following two cases.

1) When K(1) ≤0, since K(η)is convex in the range

η∈(ηmin,1],K(η)and dPso

dη are always negative. Hence

Pso monotonically decreases with η, and the minimum Pso is

achieved at η= 1,with the corresponding condition obtained

from K(1) ≤0, which is T−1

¯c< γ ≤(¯a+1)(T−1)

¯a¯c.

2) When K(1) >0, it means K(η)and dPso

dη become ﬁrst

negative and then positive as ηincreases from ηmin to 1, i.e.,

Pso ﬁrst decreases and then increases with η, and the optimal

value of ηis the unique root of the cubic equation K(η) = 0.

Solving this equation using Cardano’s formula yields η⋆.

Combining the above two cases completes the proof.

APP EN DI X B

PROO F OF LE MM A 1

With the deﬁnition of Pso in (5), we rewritten (23b) as

Pso(γ◦) = 1 −FAN

ξE(2Rt−Rs−1) ≤ϵ. (34)

Since FAN

ξE(x)is a monotonically increasing function, (34)

is equivalent to 2Rt−Rs−1≥F−1

ξE(1 −ϵ). Deﬁning κ(η),

F−1

ξE(1−ϵ)

η, constraint in (23b) can be expressed as

Rs≤Rt−log(1 + ηκ(η)).(35)

From (23a), in order to obtain a higher Rs, we set Rtequal

to its maximum value, which is CAN

D= log(1+ηc). According

to (35), the maximum achievable value of Rscan be given by

Rs(γ◦) = [log(1 + ηc)−log(1 + ηκ(η))]+.(36)

To achieve a positive secrecy rate, γ◦needs to satisfy the

constraint c > κ(η), which means that the transmitter does

not start communication unless this constraint is satisﬁed.

Therefore, the optimization problem in (23) can be rewritten

as (24).

Transactions on Communications

APP EN DI X C

PROO F OF LE MM A 2

Exploiting the derivative rule for implicit functions, we

obtain the ﬁrst-order derivative of κ(η)

dκ

dη =−∂Q1/∂η

∂Q1/∂κ =ab(LE−LC)κ

b(1 −η)κ+ab(LE−LC)(1 −η) + a.

(37)

Since a > 0,b > 0,c > 0,LE−LC>0and 1−η≥0,

we have dκ(η)

dη >0. Then the second-order derivative of κ(η)

can be given by

d2κ

dη2=1

κdκ

dη 2

ab2(LE−LC)κκ+a(LE−LC)−(1 −η)dκ

dη 

[b(1 −η)κ+ab(LE−LC)(1 −η) + a]2.

(38)

Substituting (37) into (38), we obtain

κ+a(LE−LC)−(1 −η)dκ

dη =a(LE−LC)

+b(1 −η)κ2+aκ

b(1 −η)κ+ab(LE−LC)(1 −η) + a>0.

(39)

Thus we can derive that

d2κ

dη2>1

κdκ

dη 2

>0.(40)

With dκ

dη >0and d2κ

dη2>0, we complete the proof.

APP EN DI X D

PROO F OF TH EO RE M 2

The ﬁrst-order and second-order derivatives of Rswith

respect to ηcan be described respectively as

dRs

dη =1

ln 2 c

1 + ηc −κ+ηdκ

dη

1 + ηκ ,(41)

d2Rs

dη2=−1

ln 2 c2

(1 + ηc)2+1

(1 + ηκ)2

×(1 + ηκ)2dκ

dη +ηd2κ

dη2−κ+ηdκ

dη 2

(b)

<−1

ln 2 c2

(1 + ηc)2−κ2

(1 + ηκ)2

=−1

ln 2 c

1 + ηc +κ

1 + ηκ c−κ

(1 + ηc)(1 + ηκ)

(c)

<0,

(42)

where dκ

dη and d2κ

dη2are given by (37) and (38) in Appendix C,

(b)is derived by utilizing (40), (c)holds for c > κ. Thus we

have proven that Rsis a concave function.

Now we investigate the optimal power allocation ratio η∗

that maximizes Rs. From the ﬁrst-order derivative formula of

Rsin (41), we obtain

dRs

dη |η=0 =1

ln 2 (c−κ)>0,(43)

dRs

dη |η=1 =1

ln 2 c

1 + c+[1 + (LE−LC)b]aln ϵ

1−aln ϵ.

(44)

Rsmonotonically increases through η= 0 according to

(43). Due to the concave property of Rs, when dRs

dη |η=1 >0,

the maximum Rsis achieved at η= 1; otherwise, the maxi-

mum Rsis derived at the unique η⋆which is the zero-crossing

point of dRs

dη . Therefore, the optimal η∗that maximizes Rscan

be given in (26).

APP EN DI X E

PROO F OF CO ROLLARY 1

Substituting (37) into dRs

dη = 0, we can derive that

b(1 −η)κ2+ [abc(LE−LC)η2+ab(LE−LC)

+a−bc(1 −η)]κ−abc(LE−LC)(1 −η)−ac = 0.

(45)

Denote the left side of the equation as Q2, we can obtain

the following formulas

∂Q2

∂η =z1

dκ

dη +z2>0,(46)

∂Q2

∂a =bc(LE−LC)η2κ+b(LE−LC)κ+κ

−bc(LE−LC)(1 −η)−c

(d)

a(1 −η)κ(c−κ)>0,(47)

∂Q2

∂b = (1 −η)κ2+ac(LE−LC)η2κ−c(1 −η)κ

+a(LE−LC)κ−ac(LE−LC)(1 −η)

(e)

b(c−κ)>0,(48)

∂Q2

∂c =ab(LE−LC)η2κ−b(1 −η)κ

−ab(LE−LC)(1 −η)−a

(f)

c[−b(1 −η)κ2−ab(LE−LC)κ−aκ]<0,(49)

where z1= [2b(1−η)κ+abc(LE−LC)η2−bc(1−η)+ab(LE−

LC)+a],z2=−bκ2+bcκ+2abc(LE−LC)ηκ+abc(LE−LC)

and dκ

dη >0. Substituting (45) into z1, we can obtain that

z1=b(1 −η)κ+1

κ[abc(LE−LC)(1 −η) + ac]>0.z2>0

holds for c > κ.(d),(e)and (f)are derived from substituting

(45).

1) γP: Exploiting derivative rule for implicit function-

s with the equation Q2= 0.dη

dγP=−∂Q2/∂γP

∂Q2/∂η =

−z1dκ

dγP+∂Q2

∂a

dγP+∂Q2

∂c

dγP

∂Q2/∂η . Obviously, da

dγP<0,dc

dγP>0,

and we have dκ

da >0from (25). Thus we obtain dη

dγP>0

which implies the optimal η⋆monotonically increases with

respect to γP.

2) βD:dη

dβD=−∂Q2/∂βD

∂Q2/∂η =−

∂Q2

∂c

dβD

∂Q2/∂η , where dc

dβD>

0. Thus we obtain dη

dβD>0which implies the optimal η⋆

monotonically increases with respect to βD.

3) βE:dη

dβE=−∂Q2/∂βE

∂Q2/∂η =−z1dκ

dβE+∂Q2

∂a

dβE+∂Q2

∂b

dβE

∂Q2/∂η ,

where da

dβE>0,db

dβE>0and we have dκ

dβE>0from

Transactions on Communications

(25). Thus we obtain dη

dβE<0which implies the optimal

η⋆monotonically decreases with respect to βE.

4) ϵ:dη

dϵ =−∂Q2/∂ϵ

∂Q2/∂η =−z1dκ

dϵ

∂Q2/∂ η , and we have dκ

dϵ <0

from (25). Thus we obtain dη

dϵ >0which implies the optimal

η⋆monotonically increases with respect to ϵ.

APP EN DI X F

PROO F OF CO ROLLARY 2

By denoting ς=−γC+−¯aln ϵ

¯c√γCand substituting (29)

into (28), we derive the maximum secrecy throughput of MRT

beamforming

τ∗=∞

0∞

R∗

s(γ◦)fγP(x)fγC(y)dxdy

(g)

=∞

0∞

Γ(LD−LC)log (¯

x+y+ς)[¯

c(¯

x+y+ς) + 1]

¯x+ς+ (1 −¯aln ϵ)y

×(¯x+ς)LD−LC−1e−(¯x+ς)fγC(y)d¯xdy

=∞

e−ςfγC(y)

Γ(LD−LC)

LD−LC−1



m=0 LD−LC−1

mςLD−LC−1−m

∞

0log(1 + 1

y+ς¯x) + log(1 + ¯c

¯cy + ¯cς + 1 ¯x)

−log(1 + 1

(1 −¯aln ϵ)y+ς¯x) + log (y+ς)(¯cy + ¯cς + 1)

(1 −¯aln ϵ)y+ς

×¯xme−¯xd¯xdy,

(50)

where (g)holds for the transformation ¯x=x−ς. According

to [38, 4.337.5], the ﬁnal result shown in (30) is obtained.

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Academic Press, 2007.

Ying Ju received the B.S. and M.S. degrees in

the School of Electronic Information Engineering

from Tianjin University, Tianjin, China, in 2008

and 2010, respectively. She is currently pursuing

the Ph.D. degree in the School of Electronic and

Information Engineering at Xi’an Jiaotong Univer-

sity, Xi’an, China. She is also an engineer with the

Department of Shaanxi Monitoring Station, State

Radio Monitoring Center, Xi’an, China. Her research

interests include physical layer security of wireless

communications, millimeter wave communication

systems, and stochastic geometry.

Hui-Ming Wang (S’07-M’10-SM’16) received the

B.S. and Ph.D. degrees, both with ﬁrst class honors

in Electrical Engineering from Xi’an Jiaotong Uni-

versity, Xi’an, China, in 2004 and 2010, respectively.

He is currently a Full Professor with the Department

of Information and Communications Engineering,

Xi’an Jiaotong University, and also with the Ministry

of Education Key Lab for Intelligent Networks and

Network Security, China. From 2007 to 2008, and

2009 to 2010, he was a Visiting Scholar at the

Department of Electrical and Computer Engineering,

University of Delaware, USA. His research interests include cooperative

communication systems, physical-layer security of wireless communications,

MIMO and space-timing coding.

Dr. Wang received the National Excellent Doctoral Dissertation Award in

China in 2012, a Best Paper Award of International Conference on Wireless

Communications and Signal Processing, 2011, and a Best Paper Award of

IEEE/CIC International Conference on Communications in China, 2014. He

is currently an Associate Editor for the IEEE ACCESS. He also served as a

Symposium Chair of Wireless Communications and Networking in ChinaCom

2015, a Technical Program Committee Chair of the Workshop on physical

layer security in IEEE Globecom 2016, and TPC members of various IEEE

sponsored conferences, including the IEEE Globecom, ICC, WCNC, VTC,

and PIMRC, etc. He is a co-author of the book “Physical Layer Security in

Random Cellular Networks” published by Springer in 2016.

Tong-Xing Zheng (S’14-M’16) received the B.S.

and Ph.D. degrees in the School of Electronic and

Information Engineering from Xi’an Jiaotong Uni-

versity, Xi’an, China, in 2010 and 2016, respectively.

He is currently a Lecturer with the Department

of Information and Communications Engineering,

Xi’an Jiaotong University, and also with the Ministry

of Education Key Lab for Intelligent Networks and

Network Security, China.

He has co-authored the book Physical Layer Secu-

rity in Random Cellular Networks (Springer, 2016).

His current research interests include the physical-layer security of wireless

communications, heterogeneous cellular networks, full-duplex communica-

tions, cooperative communication systems, and stochastic geometry.

Transactions on Communications

Qinye Yin received the B.S., M.S., and Ph.D. de-

grees in communication and electronic systems from

Xi’an Jiaotong University, Xi’an, China, in 1982,

1985, and 1989, respectively.

He is currently a Professor of Information En-

gineering Institute, Xi’an Jiaotong University. His

research interests focus on the joint time-frequency

analysis and synthesis, the theory and applications of

wireless sensor networks, multiple antenna MIMO

broadband communication systems (including smart

antenna systems), parameter estimation, and array

signal processing.

Enhancing Security in Millimeter Wave SWIPT Networks

Preprint

Full-text available

Jun 2024

Rui Zhu

Millimeter wave (mmWave) communication encounters a major issue of extremely high power consumption. To address this problem, the simultaneous wireless information and power transfer (SWIPT) could be a promising technology. The mmWave frequencies are more appropriate for the SWIPT comparing to current low-frequency wireless transmissions, since mmWave base stations (BSs) can pack with large antenna arrays to achieve significant array gains and high-speed short-distance transmissions. Unfortunately, the implementation of SWIPT in the wireless communication may lead to an expanded defencelessness against the eavesdropping due to high transmission power and data spillage. It is conventionally believed that narrow beam offers inherent information-theoretic security against the eavesdropping, because only the eavesdroppers, which rely on the line-of-sight path between the legitimate transmitter and receiver, can receive strong enough signals. However, some mmWave experiments have shown that even by using highly directional mmWaves, the reflection signals caused by objects in the environment can be beneficial to the eavesdroppers. This paper studies the security performance in general mmWave SWIPT networks, and investigates the probability of successful eavesdropping under different attack models. Analytical expressions of eavesdropping success probability (ESP) of both independent and colluding eavesdroppers are derived by incorporating the random reflection paths in the environment. Theoretical analysis and simulation results reveal the effects of some key parameters on the ESP, such as the time switching strategy in SWIPT, densities of mmWave BSs, and carriers frequencies, etc. Based on the numerical and simulation results, some design suggestions of mmWave SWIPT are provided to defend against eavesdropping attacks and achieve secure communication in practice.

On the physical layer security capabilities of reconfigurable intelligent surface empowered wireless systems

Preprint

Full-text available

Aug 2023

In this paper, we investigate the physical layer security capabilities of reconfigurable intelligent surface (RIS) empowered wireless systems. In more detail, we consider a general system model, in which the links between the transmitter (TX) and the RIS as well as the links between the RIS and the legitimate receiver are modeled as mixture Gamma (MG) random variables (RVs). Moreover, the link between the TX and eavesdropper is also modeled as a MG RV. Building upon this system model, we derive the probability of zero-secrecy capacity as well as the probability of information leakage. Finally, we extract the average secrecy rate for both cases of TX having full and partial channel state information knowledge.

Absolute Security in Terahertz Wireless Links

Article

Full-text available

Jul 2023

Security against eavesdropping is one of the key concerns in the design of any communication system. Many common considerations of the security of a wireless communication channel rely on comparing the signal level measured by Bob (the intended receiver) to that accessible to Eve (a single eavesdropper). Frameworks such as Wyner's wiretap model ensure the security of a link, in an average sense, when Bob's signal-to-noise ratio (SNR) exceeds Eve's. Unfortunately, because these guarantees rely on the noise realizations at Eve, statistically, Eve can still occasionally succeed in decoding information. The goal of achieving exactly zero probability of intercept over an engineered region of the broadcast sector, which we term absolute security, remains elusive. Here, we describe the first architecture for a wireless link with a single eavesdropper, that provides absolute security. I.e., a cryptographic deterministic and non-probabilistic security approach that does not rely on statistical assumptions about noise, shared secure key, or Eve's computational power. Our approach relies on the inherent properties of broadband and high-gain antennas, and is therefore ideally suited for implementation in millimeter-wave and terahertz wireless systems, where such antennas will generally be employed. We exploit spatial minima of the antenna pattern at different frequencies, the union of which defines a wide region where Eve is guaranteed to fail regardless of her computational capabilities, and regardless of the noise in the channels. Unlike conventional zero-forcing beam forming methods, we show that, for realistic assumptions about the antenna configuration and power budget, this absolute security guarantee can be achieved over most possible eavesdropper locations. Since we use relatively simple frequency-multiplexed coding, together with the underlying physics of a diffracting aperture, this idea is broadly applicable in many contexts.

Interplay between Physical Layer Security and Blockchain Technology for 5G and Beyond: A Comprehensive Survey

Preprint

Full-text available

Mar 2023

p>Fifth-generation and beyond (5G and xG) wireless networks are envisioned to meet the requirements of vertical applications like high traffic throughput, ultra-massive connectivity, extremely low latency, and high quality of service. Disruptive technologies, such as massive multiple-input multiple-output, millimeter wave, and multiple access are being deployed to meet these requirements. However, their deployment poses several challenges, including a lack of network transparency, management decentralization, and reliability. Moreover, the heterogeneity of future networks raises security concerns, e.g., confidentiality, privacy, and trustworthiness. Indeed, due to the emergence of novel paradigms, e.g., quantum computing, traditional security approaches are no longer sufficient to protect over-the-air communications. Hence, 5G/xG networks must consider smart security techniques to operate seamlessly and efficiently. Within this context, physical layer security (PLS) and blockchain represent promising solutions to complement existing methods. By exploiting the characteristics of wireless links, PLS can enhance the security of communications, while blockchain may enable networks' decentralization, integrity, and trustworthiness. Motivated by these advancements, we provide an in-depth review of the existing PLS and blockchain literature. Then, for the first time in the literature, we present a framework to integrate PLS with blockchain in 5G/xG systems. We first provide a thorough discussion about the potential of PLS and blockchain for 5G/xG systems. Then, we present our vision of a cross-layer architecture that leverages PLS and blockchain. Through a case study, we demonstrate the high potential of cross-layer design to improve the security of vehicular networks. Finally, we identify related challenges and shed light on future research directions.</p

On Secure mmWave RSMA Systems

Article

May 2024

Millimeter-wave (mmWave) communication is one of the effective technologies for the next generation of wireless communications due to the enormous amount of available spectrum resources. Rate splitting multiple access (RSMA) is a powerful multiple access, interference management, and multiuser strategy for designing future wireless networks. In this work, a multiple-input-single-output mmWave RSMA system is considered wherein a base station serves two users in the presence of a passive eavesdropper. Different eavesdropping scenarios are considered corresponding to the overlapped resolvable paths between the main and the wiretap channels under the considered transmission schemes. The analytical expressions for the secrecy outage probability (SOP) are derived respectively through the Gaussian–Chebyshev quadrature method. Monte Carlo simulation results are presented to validate the correctness of the derived analytical expressions and demonstrate the effects of system parameters on the SOP of the considered mmWave RSMA systems.

NOMA-Assisted Secure Offloading for Vehicular Edge Computing Networks With Asynchronous Deep Reinforcement Learning

Article

Jan 2023

Mobile edge computing (MEC) offers promising solutions for various delay-sensitive vehicular applications by providing high-speed computing services for a large number of user vehicles simultaneously. In this paper, we investigate non-orthogonal multiple access (NOMA) assisted secure offloading for vehicular edge computing (VEC) networks in the presence of multiple malicious eavesdropper vehicles. To secure the wireless offloading from the user vehicles to the MEC server at the base station, the physical layer security (PLS) technology is leveraged, where a group of jammer vehicles is scheduled to form a NOMA cluster with each user vehicle for providing jamming signals to the eavesdropper vehicles while not interfering with the legitimate offloading of the user vehicle. We formulate a joint optimization of the transmit power, the computation resource allocation and the selection of jammer vehicles in each NOMA cluster, with the objective of minimizing the system energy consumption while subjecting to the computation delay constraint. Due to the dynamic characteristics of the wireless fading channel and the high mobility of the vehicles, the joint optimization is formulated as a Markov decision process (MDP). Therefore, we propose an asynchronous advantage actor-critic (A3C) learning algorithm-based energy-efficiency secure offloading (EESO) scheme to solve the MDP problem. Simulation results demonstrate that the agent adopting the A3C-based EESO scheme can rapidly adapt to the highly dynamic VEC networks and improve the system energy efficiency on the premise of ensuring offloading information security and low computation delay.

M3A: Multipath Multicarrier Misinformation to Adversaries

Conference Paper

Oct 2023

Wireless channels are vulnerable to eavesdroppers due to their broadcast nature. One approach to thwart an eavesdropper (Eve) is to decrease her SNR, e.g., by reducing the signal in her direction. Unfortunately, such methods are vulnerable to (1) a highly directional Eve that can increase her received signal strength and (2) Eve that is close to the receiver, Bob, or close to the transmitter, Alice. In this paper, we design and experimentally evaluate Multipath Multicarrier Misinformation to Adversaries (M3A), a system for Alice to send data to Bob while simultaneously sending misinformation to Eve. Our approach does not require knowledge of Eve’s channel or location and, with multipath channels, randomly transforms Eve’s symbols even if Eve is located one wavelength-scale distance from Bob (approximately 10 cm) or if Eve is located between Alice and Bob in their direct path (Eve is approximately 1/3 closer to Alice). In particular, our approach is to move each of Eve’s received symbols (over time and across subcarriers), to an independently random transformation as compared to Bob, without Alice or Bob knowing Eve’s location or channel. We realize this by modulating Alice’s per-subcarrier beamforming weights with an i.i.d. random binary sequence, as if Alice had a separate antenna array for each subcarrier, and could randomly turn antennas in each array on and off. We implement M3A on a real-time Massive MIMO testbed and show that M3A can increase Eve’s bit error rate more than two hundredfold compared to beamforming, even if she is positioned approximately a wavelength away, whether above, below, or beside Bob. Finally, to ensure reliability at Bob, we show that with M3A, Bob’s bit error rate is approximately an order of magnitude lower than achieved with prior work.

Physical Layer Security in Full-Duplex Millimeter Wave Communication Systems

Article

Jan 2023

In this paper, we investigate physical layer security in full-duplex (FD) millimeter-wave (mmWave) communication system, where an FD receiver generates the jamming signal at the destination to protect the confidential message. Secrecy rate and secrecy throughput are selected as metrics to characterize the secrecy performance. We analyze and derive closed-form expressions for secrecy metrics for both cases with the availability of global and partial channel state information (CSI), respectively. Specifically, we jointly design beamforming at the source and destination to enhance the secrecy performance to the greatest extent possible. With joint optimization of the power allocation ratio, between the source and destination, and the secrecy outage probability constraint, we can further obtain the maximum secrecy rate and secrecy throughput. This study determines that the optimal hybrid beamforming matrix for the jamming signal is a rank-1 matrix. Simulation results illustrate that our designed secrecy transmission scheme with FD jamming receiver outperforms conventional half-duplex (HD) methods even when residual self-interference (SI) is considered. Asaresult of adequately designing the beamforming of the jamming signal, the secrecy of FD mmWave system is no longer constrained by SI in the multi-antenna case. Furthermore, our results also find that there always exists an optimal pair of the power allocation ratio and secrecy outage probability constraint to maximize the secrecy throughput given a fixed transmit power

RIS-Aided Secure Millimeter-Wave Communication Under RF-Chain Impairments

Article

Jan 2023

The effects of hardware impairments (HWIs) on the secrecy performance of a reconfigurable intelligent surface (RIS)-assisted millimeter wave system are investigated, where a multi-antenna base station (BS) transmits confidential messages to a single-antenna mobile user (MU) in the presence of a single-antenna passive eavesdropper (Eve). Artificial noise (AN)-aided transmission by the BS is proposed for improving the achievable secrecy rate. As the first step, we construct a system model in the absence of HWIs. For this case, we present optimal solutions for the signal and AN powers, the beamforming design at the BS, and the phase shifts of the RIS elements. Then closed-form expressions are derived for the cumulative distribution functions of the signal-to-noise-ratios experienced at the legitimate and eavesdropping nodes. Finally, a compact solution is presented for the ergodic secrecy rate (ESR) performance. At the next step, we extend our designs and analysis by considering the HWIs of the radio-frequency (RF) modules of the BS, MU and Eve. Our results highlight the detrimental impact of HWIs on the achievable ESR. Finally, we find that the ESR can be further increased by beneficially distributing the tolerable HWIs between the transmission and reception RF chains.

Random Beam Switching: A Physical Layer Key Generation Approach to Safeguard mmWave Electronic Devices

Article

Aug 2023

Extracting secret keys from millimeter wave (mmWave) wireless channels fast and efficiently for securing communications between mmWave electronic devices is a challenge due to the limitations of static environments. In this paper, we propose a random beam switching (RBS) based physical layer key generation (PLKG) scheme in the mmWave systems. Utilizing the sparsity characteristics of mmWave channels between electronic devices, we apply virtual angles of effective-beams and activated-beams as the random source. Through channel detection, we establish an RBS space between the transmitter and receiver. Then they randomly select beams from the RBS space and transmit reference signals to generate consistent keys. Furthermore, by using information theory, we analyze the effectiveness, reliability and security performance of RBS scheme theoretically. Specifically, we derive the theoretical expression of key generation rate (KGR) and then obtain its upper bound. We also prove that the key mismatch ratio (KMR) approaches zero in the high signal-to-noise ratio (SNR) region. Then we demonstrate that the eavesdropper cannot obtain any information about the activated-beams. Numerical results are provided to verify our theoretical analysis. We demonstrate that the RBS scheme can provide sufficient secret keys even in static environments while achieving good secrecy performance to safeguard electronic devices.

Secrecy Throughput Maximization for Millimeter Wave Systems with Artificial Noise

Conference Paper

Full-text available

Sep 2016

In this paper, we study the secrecy throughput in millimeter wave systems under slow fading channels considering multipath propagation. For the specific propagation characteristics of millimeter wave, we provide transmission scheme designs and a comprehensive secrecy performance analysis. Specifically, we maximize the secrecy throughput under a secrecy outage probability (SOP) constraint through a dynamic parameter transmission scheme, and provide the optimal solution to transmission parameters, including the codeword rate and the power allocation ratio of the information signal power to the total transmit power. We find that the secrecy performance of the millimeter wave system under investigation is significantly influenced by the relationship between spatially resolvable paths of the legitimate user and those of the eavesdropper, which differs from those wireless systems with statistically independent channel. Numerical results are provided to verify our theoretical analysis.

Secure Transmission with Artificial Noise in Millimeter Wave Systems

Conference Paper

Full-text available

Apr 2016

The use of millimeter wave is an effective way to meet the data traffic demand of the 5G wireless communication system. For the new propagation characteristics of millimeter wave, in this paper, we study the secure transmission with artificial noise under slow fading channels considering multipath propagation in millimeter wave systems. Firstly, when partial eavesdropper's channel state information is known at the transmitter, an artificial noise transmission strategy which depends on directions of the destination's and the eavesdropper's propagation paths is proposed. Then we analyze the secrecy outage probability (SOP) through an on-off transmission scheme. Furthermore, we minimize the SOP subject to a secrecy rate constraint and derive a closed-form optimal power allocation between the information bearing signal and artificial noise. Numerical results are provided to show the superiority of the proposed scheme.

Secure MISO Wiretap Channels With Multiantenna Passive Eavesdropper: Artificial Noise vs. Artificial Fast Fading

Article

Full-text available

Jan 2015

The artificial noise (AN) scheme is an efficient strategy for enhancing the secrecy rate of a multiple-input– single-output channel in the presence of a passive eavesdropper, whose channel state information is unavailable. Recently, a randomized beamforming scheme has been proposed for deteriorating the eavesdropper’s bit-error-rate performance via corrupting its receiving signal by time-varying multiplicative noise. However, the secrecy rate of such a scheme has not been well addressed yet. In this paper, we name it the artificial fast fading (AFF) scheme and provide a comprehensive secrecy rate analysis for it. We show that with this scheme, the eavesdropper will face a noncoherent Ricean fading single-input–multiple-output channel. Although the closed-form secrecy rate is difficult to obtain, we derive an exact expression for the single-antenna-eavesdropper case and a lower bound for the multiantenna-eavesdropper case, both of which can be numerically calculated conveniently. Furthermore, we compare the AFF scheme with the AN scheme and show that their respective superiorities to each other depend on the number of antennas that the transmitter and the eavesdropper possessed, i.e., when the eavesdropper has more antennas than the transmitter does, the AFF scheme achieves a larger secrecy rate; otherwise, the AN scheme outperforms. Motivated by this observation, we propose a hybrid AN-AFF scheme and investigate the power allocation problem, which achieves better secrecy performance further.

Safeguarding 5G Wireless Communication Networks Using Physical Layer Security

Article

Full-text available

Apr 2015

The fifth generation (5G) network will serve as a key enabler in meeting the continuously increasing demands for future wireless applications, including an ultra-high data rate, an ultrawide radio coverage, an ultra-large number of devices, and an ultra-low latency. This article examines security, a pivotal issue in the 5G network where wireless transmissions are inherently vulnerable to security breaches. Specifically, we focus on physical layer security, which safeguards data confidentiality by exploiting the intrinsic randomness of the communications medium and reaping the benefits offered by the disruptive technologies to 5G. Among various technologies, the three most promising ones are discussed: heterogenous networks, massive multiple-input multiple-output, and millimeter wave. On the basis of the key principles of each technology, we identify the rich opportunities and the outstanding challenges that security designers must tackle. Such an identification is expected to decisively advance the understanding of future physical layer security.

Physical Layer Security in Millimeter Wave Cellular Networks

Article

Apr 2016

Recent researches show that millimeter wave (mmWave) communications can offer orders of magnitude increases in the cellular capacity. However, the secrecy performance of a mmWave cellular network has not been investigated so far. Leveraging the new path-loss and blockage models for mmWave channels, which are significantly different from the conventional microwave channel, this paper comprehensively studies the network-wide physical layer security performance of the downlink transmission in a mmWave cellular network under a stochastic geometry framework. We first study the secure connectivity probability and the average number of perfect communication links per unit area in a noise-limited mmWave network for both non-colluding and colluding eavesdroppers scenarios, respectively. Then, we evaluate the effect of the artificial noise (AN) on the secrecy performance, and derive the analysis result of average number of perfect communication links per unit area in an interference-limited mmWave network. Numerical results are demonstrated to show the network-wide secrecy performance, and provide interesting insights into how the secrecy performance is influenced by various network parameters: antenna array pattern, base station (BS) intensity, and AN power allocation, etc.

Artificial Noise Assisted Secure Transmission for Distributed Antenna Systems

Article

Aug 2016

This paper studies the artificial noise (AN) assisted secure transmission for a distributed antenna systems (DAS). To avoid a significant overhead caused by full legitimate channel state information (CSI) acquisition, tracking and collection in the central processor, we propose a distributed AN scheme utilizing the large-scale CSI of the legitimate receiver and eavesdropper. Our objective is to maximize the ergodic secrecy rate (ESR) via optimizing the power allocation between the confidential signal and AN for each remote antenna (RA) under the per-antenna power constraint. Specifically, exploiting random matrix theory, we first establish an analytical expression of the achievable ESR, which leads to a non-convex optimization problem with multiple non-convex constraints in the form of high-order fixed-point equations. To handle the intractable constraints, we recast it into a max-min optimization problem, and propose an iterative block coordinate descent (BCD) algorithm to provide a stationary solution. The BCD algorithm is composed of three subproblems, where the first two subproblems are convex with closed-form solutions, and the last one is a convex-concave game whose saddle-point is located by a tailored barrier algorithm. Simulation results validate the effectiveness of the proposed iterative algorithm and show that our scheme not only reduces the system overhead greatly but also maintains a good secrecy performance.

An Introduction to Millimeter-Wave Mobile Broadband Systems

Article

Jun 2011

Almost all mobile communication systems today use spectrum in the range of 300 MHz-3 GHz. In this article, we reason why the wireless community should start looking at the 3-300 GHz spectrum for mobile broadband applications. We discuss propagation and device technology challenges associated with this band as well as its unique advantages for mobile communication. We introduce a millimeter-wave mobile broadband (MMB) system as a candidate next-generation mobile communication system. We demonstrate the feasibility for MMB to achieve gigabit-per-second data rates at a distance up to 1 km in an urban mobile environment. A few key concepts in MMB network architecture such as the MMB base station grid, MMB inter-BS backhaul link, and a hybrid MMB + 4G system are described. We also discuss beamforming techniques and the frame structure of the MMB air interface.

Secure communication in cellular networks: The benefits of millimeter wave mobile broadband

Conference Paper

Jun 2014

This paper proposes millimeter wave (mmWave) mobile broadband for achieving secure communication in downlink cellular network. Analog beamforming with phase shifters is adopted for the mmWave transmission. The secrecy throughput is analyzed based on two different transmission modes, namely delay-tolerant transmission and delay-limited transmission. The impact of large antenna arrays at the mmWave frequencies on the secrecy throughput is examined. Numerical results corroborate our analysis and show that mmWave systems can enable significant secrecy improvement. Moreover, it is indicated that with large antenna arrays, multi-gigabit per second secure link at the mmWave frequencies can be reached in the delay-tolerant transmission mode and the adverse effect of secrecy outage vanishes in the delay-limited transmission mode.

On the feasibility of beamforming in millimeter wave communication systems with multiple antenna arrays

Article

Feb 2015

The use of the millimeter (mm) wave spectrum for next generation (5G) mobile communication has gained significant attention recently. The small carrier wavelengths at mmwave frequencies enable synthesis of compact antenna arrays, providing beamforming gains that compensate the increased propagation losses. In this work, we investigate the feasibility of employing multiple antenna arrays (at the transmitter and/or receiver) to obtain diversity/multiplexing gains, where each of the arrays is capable of beamforming independently. Considering a codebook based beamforming system (the set of possible beamforming directions is fixed a priori, e.g., to facilitate limited feedback), we observe that the complexity of jointly optimizing the beamforming directions across the multiple arrays is highly prohibitive, even for very reasonable system parameters. To overcome this bottleneck, we develop two complementary approaches, premised on the sparse multipath structure of the mmwave channel. Specifically, we reduce the complexity of the joint beamforming optimization problem by restricting attention to a small set of candidate directions, based on: (a) computation of a novel spatial effective power metric, and (b) estimation of the channel's angles of arrival. Our methods enable a drastic reduction of the optimization search space (a factor of 100 reduction), while delivering close to optimal performance, thereby indicating the potential feasibility of achieving diversity and multiplexing gains in mmwave systems.

A Hybrid RF/Baseband Precoding Processor Based on Parallel-Index-Selection Matrix-Inversion-Bypass Simultaneous Orthogonal Matching Pursuit for Millimeter Wave MIMO Systems

Article

Jan 2015

A millimeter wave (mm-wave) communication system provides multi-Gb/s data rates in short-distance transmission. Because millimeter waves have short wavelength, transceivers can be composed of large antenna arrays to alleviate severe signal attenuation. Furthermore, the link performance can be improved by adopting precoding technology in multiple data stream transmission. However, the complexity of radio frequency (RF) chains increases when large antenna arrays are used in mm-wave systems. To reduce the hardware cost, the precoding circuit can be jointly designed in both analog and digital domains to reduce the required number of RF chains. This paper proposes a new method of building the joint RF and baseband precoder that reduces the computation complexity of the original precoder reconstruction algorithm and enables highly parallel hardware architecture. Moreover, the proposed precoder reconstruction algorithm was designed and implemented using TSMC 90-nm UTM CMOS technology. The proposed precoder reconstruction processor supports the transmissions of one to four data streams for 8 × 8 mm-wave multiple-input multiple-output systems. The operating frequency of this chip was 167 MHz, and the power consumption was 243.2 mW when the supply voltage was 1 V. The core area of the postlayout result was about 3.94 mm 2. The proposed processor achieved 4, 4.9, 6.7, and 6.7 M channel matrices per second in four-, three-, two-, and one-stream modes, respectively.

Secure Transmissions in Millimeter Wave Systems

Abstract and Figures

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