# Downlink Power Minimization in Intelligent Reconfigurable Surface-Aided
Security Classification Wireless Communications System

Jintao Xing, , Tiejun Lv, , Yashuai Cao, ,
Jie Zeng, , and Pingmu Huang Manuscript received September 1, 2021; revised
March 28, 2022; accepted June 8, 2022. This work was supported by the National
Natural Science Foundation of China (No. 62001264), and the Natural Science
Foundation of Beijing (No. L192025). _(Corresponding author: Tiejun Lv and Jie
Zeng)_.J. Xing, T. Lv and Y. Cao are with the School of Information and
Communication Engineering, Beijing University of Posts and Telecommunications
(BUPT), Beijing 100876, China (e-mail: {jintaoxing, lvtiejun,
yashcao}@bupt.edu.cn).J. Zeng is with the School of Cyberspace Science and
Technology, Beijing Institute of Technology, Beijing 100081, China (e-mail:
zengjie@bit.edu.cn).P. Huang is with the School of Artificial Intelligence,
Beijing University of Posts and Telecommunications (BUPT), Beijing 100876,
China (e-mail: pmhuang@bupt.edu.cn).

###### Abstract

User privacy protection is considered a critical issue in wireless networks,
which drives the demand for various secure information interaction techniques.
In this paper, we introduce an intelligent reflecting surface (IRS)-aided
security classification wireless communication system, which reduces the
transmit power of the base station (BS) by classifying users with different
security requirements. Specifically, we divide the users into confidential
subscribers with secure communication requirements and general communication
users with simple communication requirements. During the communication period,
we guarantee the secure rate of the confidential subscribers while ensuring
the service quality of the general communication users, thereby reducing the
transmit power of the BS. To realize such a secure and green information
transmission, the BS implements a beamforming design on the transmitted signal
superimposed with artificial noise (AN) and then broadcasts it to users with
the assistance of the IRS’s reflection. We develop an alternating optimization
framework to minimize the BS downlink power with respect to the active
beamformers of the BS, the AN vector at the BS, and the reflection phase
shifts of the IRS. A successive convex approximation (SCA) method is proposed
so that the nonconvex beamforming problems can be converted to tractable
convex forms. The simulation results demonstrate that the proposed algorithm
is convergent and can reduce the transmit power by 20% compared to the best
benchmark scheme.

###### Index Terms:

Physical layer security, security classification, secure beamforming,
artificial noise, intelligent reflecting surface, green communications.

##  I Introduction

Information security and user privacy have become increasingly important in
fifth-generation (5G) mobile networks due to the explosive growth of wireless
terminal devices [1]. The inherent exposure of the wireless communication
medium inevitably incurs information leakage, which exacerbates wireless
network security issues such as data uploading, caching, and secure wireless
computing for private data (SWCPD) [2]. Consequently, methods for protecting
the secure delivery of information during transmission have recently drawn
considerable attention. Key encryption technologies have been proposed to
maintain wireless security. However, due to improvements in modern computer
technology, the traditional security solutions that rely heavily on computing
power have become increasingly insecure; it has become easier for
eavesdroppers to decipher the security information using supercomputers.
Therefore, physical layer security (PLS) was developed as a mainstream
wireless technology. The main idea underlying PLS involves utilizing
transmission channel characteristics from the physical level. To capitalize on
the multiplexing gain brought by large-scale multiple-input multiple-output
(MIMO) antennas, various approaches have been developed that employ
beamforming at the base station (BS) and introduce additional artificial noise
(AN) to enhance the PLS [3, 4]. In the context of large-scale MIMO systems,
the beamforming gain attained by high-directional antennas can increase the
desired power for confidential subscribers; hence, the effective information
received by the eavesdroppers can be greatly reduced.

However, installing massive antennas and radio frequency (RF) chains in large-
scale MIMO systems results in excessive hardware costs and signal processing
complexity [5]. On the one hand, that outcome violates the critical design
metric for green communication systems [6]; on the other hand, the high energy
consumption involved in active MIMO restricts the practical deployment of MIMO
secure wireless communications in 5G and beyond. During the transmission
period, using relays to forward signals will lead to large power consumption
overhead. Moreover, employing a malicious relay poses a high risk of
information leakage [7]. These problems urgently need new technology.
Recently, the development of electronic circuits and metamaterials technology
has allowed the intelligent reflecting surface (IRS) to be exploited in
existing wireless networks. The IRS is a plane composed of a large number of
low-cost passive reflective elements. To precisely control the reflection
direction of the incident signals, each element is connected to a smart
controller that can tune its amplitude and phase [8]. As a passive forwarding
node, the deployment of the IRS offers promise to meet low-cost spectrum
efficiency goals [9, 10, 11]. An IRS can easily be placed on a wall, ceiling,
or other area thanks to its light weight and adjustability. The introduction
of the IRS offers increased flexibility and extends the possibilities of
current wireless systems, which differ from the existing active relays.

Motivated by the aforementioned considerations, this paper considers an IRS-
aided secure transmission system in which the passive beamforming technique of
the IRS is integrated with the active beamforming and AN interference
capabilities of the BS. This paper focuses primarily on how to benefit system
performance by adding the new degree of freedom presented by the IRS.

###  I-A Related Works

Using 5G and beyond, the popular Internet of Things (IoT) and machine learning
applications have intensified the need for secure information transmission and
user privacy protections [12, 13, 14, 15]. Requiring only knowledge of the
fundamental radio propagation characteristics, PLS techniques can safeguard
confidential information based on advanced information theoretic methods [16].
Wyner et al. [17] proposed the concept of a wireless wire-tap model in 1975,
revealing that confidential broadcasting can be achieved through precoding
methods that utilize the physical layer differences between the legitimate
users and the eavesdroppers’ channels at the transmitter. When the channel
quality of a legitimate user is stronger than that of an eavesdropper, the
coding methods can be designed to achieve a positive secrecy rate. Later, S.
Zhao et al. [18] extended the secure beamforming scheme to a full-duplex MIMO
untrusted relay system that maximizes the secrecy sum rate (SSR) of the system
and concluded that the untrusted relay needs to be treated as a pure
eavesdropper under low signal-to-noise ratio (SNR) conditions to achieve the
satisfactory system gain. P. Huang et al. [19] investigated the secure
beamforming design in downlink IoT systems. To maximize the SSR, two
optimization schemes were proposed to address scenarios involving both passive
and active eavesdroppers. Superimposing the AN on the transmit signal has been
considered an efficient method for reducing the SNR of passive eavesdroppers.
In [20], the authors explored a novel hierarchical PLS model and proposed an
AN-assisted beamforming scheme to solve the non-convex SSR maximization
problem. S. Hong et al. [21] proposed an efficient algorithm and derived the
optimal TPC matrix, AN covariance matrix by using the Lagrange multiplier
method, and the optimal phase shifts by an efficient MM algorithm in secure
MIMO wireless communication system. Apart from the conventional orthogonal
multiple access (OMA) mode assumed in the above mentioned studies, S. Huang et
al. [22] proposed a minimum-angle difference based user pairing scheme in
mmWave networks by invoking the non-orthogonal multiple access (NOMA)
technique. Their scheme minimized the secrecy outage probability of user
pairs, and enhanced the confidentiality performance by designing a hybrid
beamforming scheme. In terms of passive defense, H. Zhang et al. [23] devised
a different strategy by actively listening to two suspicious communication
links to improve the SSR. Additionally, network coding schemes have been
applied to protect information transmission. In [24], the authors proposed
generating a secure network coding from multipath channels by constructing a
secure network coding system. A secure information transmission problem was
studied and solved by utilizing an adaptive quantification algorithm to
prevent wiretap attacks.

However, when relays are adopted for auxiliary communications, whether the
relays are malicious is generally unknown. When malicious relays are present,
adopting a conventional PLS scheme would degrade the system performance.
Unlike relays, the IRS opens up substantial additional possibilities for
secure transmission due to its passive and portable characteristics [25, 26]
and has been extensively studied for assisting wireless transmission [27, 28].
An IRS-assisted secure wireless communication system was first considered in
[29], which maximized the secrecy rate of the legitimate communication link by
jointly designing the transmit beamformer at the BS and the passive beamformer
of the IRS. In [30], the authors considered maximizing the achievable security
sum rate in IRS-assisted cognitive radio systems. To maximize system
confidentiality, J. Chen et al. [31] formulated a minimum secrecy rate
maximization problem under various practical constraints on the reflecting
coefficients, which captures the nature of phase shifts and amplitudes of the
IRS. In [32], the authors considered an IRS-assisted Gaussian MIMO wire tap
channel scenario and found an interesting trade-off between the quality of
service (QoS) at the receiver and the secrecy rate. In [33], the authors
considered a more challenging scenario where the eavesdropper is configured
with multiple antennas. Specifically, they proposed an alternating
optimization algorithm that can be extended to the IRS reflection pattern with
discrete phase shifts.

The explosive growth of information must be transmitted through wireless
channels, which will inevitably contain a lot of information with high-
security performance requirements. It is unrealistic that all communication
information is roughly transmitted securely and will cause link redundancy and
a considerable waste of resources. Different wireless terminal devices have
different requirements for confidentiality in a practical wireless
communication system. It is particularly critical to ensure information that
involves security and privacy, such as financial transactions or encrypted
calls. For instance, if the wireless terminal device requests some irrelevant
information, such as entertainment media resources or current public news, and
the information does not need to be encrypted. In a wireless application
protocol (WAP), users with different security requirements write their
requests into data packets and send them to the BS [34]. The BS divides the
user into confidential subscribers or general communication users according to
its security request type. The transmission of highly confidential information
for confidential subscribers often requires a higher service priority, so
operators can use different security transmission schemes and implement
different pricing strategies to achieve economic gain. The security
classification scheme can not only effectively reduce the redundancy of the
secure encryption during information transmission but also increase the
operator’s economic benefits.

###  I-B Contributions

Most studies assume that the same secure transmission policies are applied to
all user devices in a cellular system. However, this secure communication
mechanism will lead to redundant operations for some communication users
without security requirements, resulting in additional energy expenditure. In
contrast to existing works, we consider the different security requirements of
users in the network; thus, unnecessary energy consumption may be saved and
green communication realized by performing a security classification for all
users. Specifically, our scheme divides all communication users into two
categories based on their security communications requirements: confidential
subscribers and general communication users. Confidential subscribers consist
of users that need to communicate securely with the BS due to their own
communication confidentiality requirements, or to the existence of a terminal
that may potentially attempt to steal the transmission signals. General
communication users refer to those users who do not require confidential
transmission; only their QoS constraints need to be met during the
communication period. In the considered IRS-aided security classification
wireless communication system, we expect to achieve secure and green
communication goals by developing an alternating optimization framework to
improve the security performance of the legitimate communication users. We aim
to minimize the downlink transmit power of the BS while satisfying users’
different security rate requirements by optimizing the transmit beamforming
vectors at the BS, the injected AN vector at the BS, and the reflection phase
shifts of the IRS. The key contributions of this paper are summarized as
follows.

  * •

We consider a new security classification scheme in an IRS-aided wireless
communication system. By classifying users into confidential subscribers with
secure communication requirements and general communication users with simple
communication requirements, we formulate joint active beamforming, AN
injection and IRS passive beamforming problems to improve the transmit power
utilization.

  * •

The formulated active power minimization problem is difficult to solve since
it is a multivariate optimization problem with multiple nonconvex constraints.
We propose an alternating optimization framework to divide the original
problem into a series of subproblems. Then, we derive the first-order Taylor
approximation expressions of the nontrivial decoupled problems to make them
tractable.

  * •

We reformulate the passive beamforming subproblem into rank-one constrained
linear matrix inequality (LMI) problems to address the unit modulus
constraints; hence, the optimal phase shift vector can be recovered by
invoking the eigen value decomposition (EVD) with Gaussian randomization. In
addition, we analyze the convergence of the proposed algorithm. The simulation
results reveal insights about the optimal deployments of the IRS and
communication users and verify the effectiveness of the proposed algorithm.

The remainder of this paper is organized as follows. In Section II, we present
the IRS-aided security classification wireless communication system. In
Section III, we analyze and reformulate the optimization problem, followed by
the proposed power minimization algorithm. The numerical results and
discussion are provided in Section IV. Finally, Section V concludes this
paper.

_Notations_ : Boldface lower and uppercase letters denote vectors and
matrices, respectively. The Hermitian transpose, Frobenius norm, and the trace
of the matrix $\mathbf{A}$ are denoted as $\mathbf{A}^{H}$,
$\left\|\mathbf{A}\right\|$, and $\mathrm{Tr}(\mathbf{A})$, respectively.
$|\mathbf{A}|$ stands for the determinant of $\mathbf{A}$.
$\mathrm{Diag}\left(\mathbf{a}\right)$ creates a diagonal matrix with the
entries of vector $\mathbf{a}$ on its diagonal.
$\left[\cdot\right]^{+}\triangleq\mathrm{max}\left\\{0,\,\cdot\right\\}$.
$\mathcal{CN}\left(\mu,\sigma^{2}\right)$ denotes a circularly symmetric
complex Gaussian distribution with mean $\mu$ and variance $\sigma^{2}$.

##  II System Model

Fig. 1: An illustration of the considered scenario.

As shown in Fig. 1, we consider an IRS-aided security classification wireless
communication system. The system consists of a BS, an IRS, a confidential
subscriber, a general communication user and an eavesdropper named Alice. The
confidential subscriber needs to request confidential information such as
financial transactions or encrypted calls and has requirements carved into
data packets to transmit to the BS. The BS classifies this user as a
confidential subscriber by identifying the data packets according to the WAP.
Similarly, a user with nonconfidential information such as entertainment
videos or current affairs news is classified as a general communication user.
The eavesdropper named Alice tries to eavesdrop on vital information for the
confidential subscriber. We assume that there are obstacles (such as tall
buildings, hillsides, etc.) between the users and the BS. Therefore, the BS
cannot transmit information directly to users; it can communicate with users
only through the reflection links of the IRS. The eavesdropper is assumed to
be passive, which means that it can receive only the broadcast information due
to the open wireless transmission medium and cannot actively send interference
signals or misroute the transmitted data. The BS is equipped with $M$ transmit
antennas. The IRS unit integrates a large number of low-cost meta-atoms, with
$N_{a}$ elements horizontally and $N_{b}$ elements vertically arranged. The
total number of passive elements of the IRS is given by $N=N_{a}\times N_{b}$.
In the considered system, we assume that the confidential subscriber, the
general communication user, and Alice are each equipped with a single antenna.
All the nodes work in half-duplex mode and all the channels involved in this
paper are assumed to be quasi-static flat-fading. The IRS-aided PLS works
assuming that perfect CSI is available and widely considered [35, 36]. The CSI
between the IRS and devices can be acquired by resorting to classic and high-
precision channel estimation methods such as alternating least squares (ALS)
and vector approximate message passing (VAMP) methods [37, 38].

Let $\mathbf{G}\in\mathbb{C}^{N\times M}$ denote the baseband equivalent
channels between the BS and the IRS, and let $\mathbf{h}_{1}$,
$\mathbf{h}_{2}$ and $\mathbf{h}_{e}$ denote that between the IRS and the
confidential subscriber, the IRS and the general communication user, and the
IRS and Alice, respectively. We define the diagonal reflection phase shift
matrix as $\mathbf{\boldsymbol{\Phi}}=\mathrm{diag}\left(\mathbf{v}\right)$,
where $\mathbf{v}=\left[v_{1},v_{2},\cdots,v_{N}\right]^{T}$,
$v_{n}=e^{j\theta_{n}}$ interprets the unit modulus reflection coefficient
corresponding to the $n$-th IRS element, and $\theta_{n}\in[0,2\pi)$ denotes
the reflection coefficient of the $n$-th element. The symbol notations and
their explanations are listed in Table I.

Table I: PARAMETERS AND THEIR MEANINGS $\mathbf{w}_{1}$ | Beamforming for Confidential Subscriber
---|---
$\mathbf{w}_{2}$ | Beamforming for Communication User
$\mathbf{z}$ | Artificial Noise Vector
$s$ | Transmit Symbol for Users
$P_{t}$ | Total Transmit Power
$\mathbf{G}$ | CSI of BS to IRS
$\mathbf{h}_{1}$ | CSI of BS to Confidential Subscriber
$\mathbf{h}_{2}$ | CSI of BS to Communication User
$\mathbf{h}_{e}$ | CSI of IRS to Alice
$\mathbf{\boldsymbol{\Phi}}$ | Reflection Angle of IRS
$\sigma^{2}$ | Noise Power

The BS broadcasts a superposition of the source data and the AN symbols to the
users through the active beamforming design. The transmit signal at the BS is
expressed as

$\displaystyle\mathbf{x}$
$\displaystyle=\mathbf{w}_{1}s_{1}+\mathbf{w}_{2}s_{2}+\mathbf{z},$
$\displaystyle=\left[\mathbf{w}_{1},\mathbf{w}_{2},\mathbf{z}\right]\cdot\left[\begin{array}[]{c}s_{1}\\\
s_{2}\\\ 1\end{array}\right],$ (4)

where $s_{1}$ and $s_{2}$ indicate the information-bearing signal to the
confidential subscriber and general communication user, respectively. The
corresponding beamforming vectors are denoted as
$\mathbf{w}_{i}\in\mathbb{C}^{M\times 1}$, and $i\in\\{1,2\\}$.
$\mathbf{w}_{1}$ denotes the beamforming vector corresponding to the
confidential subscriber and is also termed as the “confidential beamformer”.
$\mathbf{w}_{2}$ denotes the beamforming vector corresponding to the general
communication user and is also called the “general beamformer”. The considered
signal $s_{i}$ is the unit power, i.e., $\mathbb{E}[|s_{i}|^{2}]=1$. The AN
$\mathbf{z}\in\mathbb{C}^{M\times 1}$ is generated from the distribution of
$\mathrm{\mathcal{CN}\left(0,\mathbf{Z}\right)}$ with $\mathbf{Z}\succeq 0$
being the covariance matrix of the AN vector [19].

The signals received by the confidential subscriber and the general
communication user are denoted by

$y_{c}=\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{1}s_{1}+\mathbf{w}_{2}s_{2}+\mathbf{z}\right)+n_{1},$
(5)

and

$y_{g}=\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\left(\mathbf{w}_{1}s_{1}+\mathbf{w}_{2}s_{2}+\mathbf{z}\right)+n_{2},$
(6)

respectively, where
$n_{k}\sim\mathrm{\mathcal{CN}}\left(0,\sigma_{k}^{2}\right)$ represents
additive white Gaussian noise (AWGN) and $\sigma_{k}^{2}$ is the corresponding
noise variance.

Because Alice is primarily interested in intercepting confidential information
from the subscriber, the signal received by Alice is expressed as111Generally,
eavesdroppers often act as regular communication users in cellular networks
and perform eavesdropping attacks only during a certain task period.

$y_{e}=\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{1}s_{1}+\mathbf{w}_{2}s_{2}+\mathbf{z}\right)+n_{e}.$
(7)

Accordingly, the data rates of the confidential subscriber, the general
communication user and Alice are given by222In the IRS-aided communication
system, the BS and IRS are usually installed on a building tower or floor that
is relatively high above the ground; thus, it is unrealistic for eavesdroppers
to deploy interception equipment at high altitudes. Therefore, Alice receives
only the signals reflected by the IRS, not the modulated signal sent over
direct BS-user links.

$\displaystyle R_{c}$
$\displaystyle=\log_{2}\left(1+\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\right),$
(8) $\displaystyle R_{g}$
$\displaystyle=\log_{2}\left(1+\frac{|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\mathbf{w}_{2}|^{2}}{|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\left(\mathbf{w}_{1}+\mathbf{z}\right)|^{2}+\sigma_{2}^{2}}\right),$
(9)

and

$R_{e}=\log_{2}\left(1+\frac{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}\right),$
(10)

respectively.

According to Wyner’s theory [17], the SSR of the confidential subscriber,
denoted by $R_{sec}$, can be formulated as (11), shown at the top of the next
page, where $\left[x\right]{}^{+}=\max\left\\{x,0\right\\}$.

$\displaystyle R_{sec}$ $\displaystyle=\left[R_{c}-R_{e}\right]{}^{+}$
$\displaystyle\triangleq\left[\log_{2}\left(1+\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\right)-\log_{2}\left(1+\frac{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}\right)\right]^{+},$
(11)

Our goal in this paper is to meet both the communication requirements of the
confidential subscriber and the basic QoS constraints of the general
communication user who lacks security requirements. Mathematically, the
problem is formulated as follows:

$\displaystyle\mathbf{P1:}\qquad$
$\displaystyle\underset{\mathbf{w}_{1},\mathbf{w}_{2},\mathbf{z},\boldsymbol{\Phi}}{\min}\;\;P_{t}$
$\displaystyle s.t.\qquad$ $\displaystyle\mathrm{C1}:R_{sec}\geq\delta_{1},$
$\displaystyle\mathrm{C2}:R_{g}\geq\delta_{2},$ (12)
$\displaystyle\mathrm{C3}:\mathbf{Z}\succeq 0,$
$\displaystyle\mathrm{C4}:\mathbf{\boldsymbol{\Phi}}=\mathrm{diag}\left(\mathbf{v}\right),|v_{n}|^{2}=1,$

where $P_{t}=\|\mathbf{w}_{1}\|^{2}+\|\mathbf{w}_{2}\|^{2}+\|\mathbf{z}\|^{2}$
denotes the total power required at the BS. Constraint C1 indicates that the
security rate of the confidential subscriber should satisfy a minimum security
requirement $\delta_{1}$. Constraint C2 is imposed to satisfy the general
communication user’s minimum communication transmission QoS requirement
$\delta_{2}$ and implies that the confidentiality performance does not need to
be considered for general communication users. Constraint C3 specifies that
the covariance matrix of the AN is a Hermitian matrix and positive
semidefinite. Constraint C4 specifies the reflection phase shifts of the IRS
as a diagonal matrix with $N$ unit modulus entries.

##  III Algorithm Design for Secure IRS-aided Wireless Communication

Problem $\mathbf{P1}$ cannot be directly solved using the traditional convex
optimization tools because it is difficult to optimize multiple optimization
variables simultaneously due to the coupling variables and the non-convexity
of the constraints. To decouple these optimization variables, we develop an
alternating optimization algorithm to optimize the active confidential
beamformer $\mathbf{w}_{1}$ and general beamformer $\mathbf{w}_{2}$ at the BS,
the AN, and the IRS coefficient matrix in an iterative manner, which can
achieve the suboptimal solution of the original problem. Based on the
alternating optimization framework, the original problem can be decomposed
into three subproblems, i.e., the optimization of the confidential beamformer,
the joint optimization of the general beamformer and the design of the
injected AN vector, and the optimization of the IRS phase shifts. By solving
these subproblems in an alternating iterative manner, the overall transmit
power can be minimized to realize secure and green communications.

###  III-A Optimization of the Confidential Beamformer $\mathbf{w}_{1}$

By taking the structural characteristics of the expression constraints C1 and
C2 into account, we observe that $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$ are
multiplicatively coupled in the optimization problem $\mathbf{P1}$. Therefore,
we optimize $\mathbf{w}_{1}$ and $\mathbf{w}_{2}$ separately.

Given the general beamformer $\mathbf{w}_{2}$, the AN vector $\mathbf{z}$ and
the reflection coefficients $\boldsymbol{\Phi}$ of the IRS, only constraints
C1 and C2 are involved in the optimization of $\mathbf{w}_{1}$; consequently,
constraints C3 and C4 can be omitted. Note that C1 and C2 are nonconvex with
respect to $\mathbf{w}_{1}$ when fixing the variables
$\mathbf{w}_{2},\boldsymbol{\Phi}$ and $\mathbf{z}$. To deal with the
nonconvexity, C1 can be transformed as follows:

$\displaystyle\mathrm{C1a}:$ $\displaystyle
R_{sec}=\log_{2}\left(1+\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\right)$
$\displaystyle-\log_{2}\left(1+\frac{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}\right)\geq\delta_{1}$
$\displaystyle=\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}+|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}+|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}$
$\displaystyle\times\frac{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\geq
2^{\delta_{1}}.$ (13)

Problem (10) is a nonconvex quadratically constrained quadratic program
(QCQP). Therefore, we can relax it into a convex problem by using semidefinite
relaxation (SDR). First, we define

$\displaystyle\mathbf{W}_{1}=\mathbf{w}_{1}\mathbf{w}_{1}^{H},$
$\displaystyle\mathbf{W}_{2}=\mathbf{w}_{2}\mathbf{w}_{2}^{H},$
$\displaystyle\mathbf{H}_{k}=\mathbf{G}^{H}\boldsymbol{\Phi}^{H}\mathbf{h}_{k}\mathbf{h}_{k}^{H}\boldsymbol{\Phi}\mathbf{G},$
$\displaystyle\alpha=\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}.$
(14)

Based on the variable substitution, constraint C1a can be transformed into:

$\displaystyle\frac{\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{1}\mathbf{W}_{1}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{1}\mathbf{W}_{2}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{1}\mathbf{Z}\right)+\sigma_{1}^{2}}{\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{e}\mathbf{W}_{1}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{e}\mathbf{W}_{2}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{e}\mathbf{Z}\right)+\sigma_{e}^{2}}\geq
2^{\delta_{1}}\alpha$
$\displaystyle\Leftrightarrow\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{1}\mathbf{W}_{1}\right)-2^{\delta_{1}}\alpha\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{e}\mathbf{W}_{1}\right)+\beta\geq
0,$ (15)

where

$\displaystyle\beta=\mathrm{Tr}\left[\mathbf{H}_{1}\left(\mathbf{W}_{2}+\mathbf{Z}\right)\right]+\sigma_{1}^{2}$
$\displaystyle-2^{\delta_{1}}\alpha\left(\mathrm{Tr}\left[\mathbf{H}_{e}\left(\mathbf{W}_{2}+\mathbf{Z}\right)\right]+\sigma_{e}^{2}\right).$
(16)

Constraint C1a becomes a convex semidefinite program (SDP) with respect to
$\mathbf{W}_{1}$, which is more tractable.

Note that C2 is a nonconvex inequality constraint. Thus, it is likely that by
linearizing the nonconvex inequality with respect to $\mathbf{w}_{1}$, C2 can
be recast to

$\displaystyle\mathrm{C2a}:R_{g}=$
$\displaystyle\log_{2}\left(1+\frac{|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\mathbf{w}_{2}|^{2}}{|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\left(\mathbf{w}_{1}+\mathbf{z}\right)|^{2}+\sigma_{2}^{2}}\right)\geq\delta_{2}$
$\displaystyle\Leftrightarrow$
$\displaystyle\frac{\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{2}\right)}{\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{1}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{Z}\right)+\sigma_{2}^{2}}\geq
2^{\delta_{2}}-1$ (17) $\displaystyle\Leftrightarrow$
$\displaystyle\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{2}\right)-\left(2^{\delta_{2}}-1\right)$
$\displaystyle\left(\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{1}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{Z}\right)+\sigma_{2}^{2}\right)\geq
0.$

Therefore, the new constraint C2a presents a convex linear matrix inequality
(LMI) representation.

With the new constraints C1a and C2a, optimizing $\mathbf{w}_{1}$ in
$\mathbf{P1}$ can be reduced to

$\displaystyle\mathbf{P2:}\quad\underset{\mathbf{W}_{1}}{\min}\;$
$\displaystyle\mathbf{\mathrm{Tr}}\left(\mathbf{W}_{1}\right)$ $\displaystyle
st.\;$
$\displaystyle\mathrm{C1a}:\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{1}\mathbf{W}_{1}\right)-2^{\delta_{1}}\alpha\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{e}\mathbf{W}_{1}\right)+\beta\geq
0,$
$\displaystyle\mathrm{C2a}:\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{2}\right)-\left(2^{\delta_{2}}-1\right)$
(18)
$\displaystyle\left(\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{W}_{1}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{H}_{2}\mathbf{Z}\right)+\sigma_{2}^{2}\right)\geq
0,$ $\displaystyle\mathrm{C5}:\mathbf{W}_{1}\succeq 0,$

and constraint C5 is imposed to guarantee
$\mathbf{W}_{1}=\mathbf{w}_{1}\mathbf{w}_{1}^{H}$. Now, problem $\mathbf{P2}$
is convex in auxiliary matrix $\mathbf{W}_{1}$ and can be solved by CVX. If
the solution $\mathbf{W}_{1}$ satisfies the rank-one constraint, the optimal
beamformer $\mathbf{w}_{1}$ can be recovered from $\mathbf{W}_{1}$ by
performing the classic Cholesky decomposition [39]. However, in general, the
solution obtained by SDR cannot exhibit the rank-one property. We can find the
suboptimal $\mathbf{w}_{1}$ by applying the rank-one approximations of
$\mathbf{W}_{1}$, such as eigenvalue decomposition (EVD) with Gaussian
randomization. To be specific, we decompose $\mathbf{W}_{1}$ as
$\mathbf{W}_{1}=\mathbf{U}_{v}\boldsymbol{\Sigma}_{v}\mathbf{U}_{v}^{H}$,
where $\mathbf{U}_{v}=\left[u_{v,1},...u_{v,M}\right]$ and
$\boldsymbol{\Sigma}_{v}=\mathrm{diag}\left(\lambda_{v,1},...,\lambda_{v,M}\right)$
are a unitary matrix and a diagonal matrix, respectively. We can generate a
vector as
$\mathbf{\overline{w}}_{1}=\mathbf{U}_{v}\boldsymbol{\Sigma}_{v}^{1/2}\boldsymbol{r}_{l}$
where
$\boldsymbol{r}_{l}\sim\mathrm{\mathcal{CN}}\left(0,\boldsymbol{I}_{M}\right)$
and $\boldsymbol{r}_{l}$ is the randomly generated vector satisfying Gaussian
distribution with zero means. Then, we can obtain a suboptimal solution from
multiple approximate solutions. It should be noted that the SDR is an
efficient and widely used convex approximation approach, which can achieve
satisfactory performance and approach the optimal performance [40, 41].

###  III-B Optimization of the Beamformer $\mathbf{w}_{2}$ and the AN
$\mathbf{z}$

Due to the fact that the algebraic expressions involved in the optimization
problem are in the symmetric functions $\mathbf{w}_{2}$ and $\mathbf{z}$, we
can jointly optimize the general beamformer $\mathbf{w}_{2}$ and the AN
$\mathbf{z}$. Given the confidential beamformer $\mathbf{w}_{1}$ and the
reflection phase-shifts $\boldsymbol{\Phi}$ of the IRS, optimizing
$\mathbf{w}_{2}$ and $\mathbf{z}$ involve only constraints C1, C2 and C3;
therefore, C4 can be omitted.

Now, for a given $\mathbf{w}_{1}$ and $\boldsymbol{\Phi}$, we can recast C1 as
follows:

$\displaystyle\mathrm{C1b}:$ $\displaystyle
R_{sec}=\log_{2}\left(1+\frac{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{1}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\right)$
$\displaystyle-\log_{2}\left(1+\frac{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\mathbf{w}_{1}|^{2}}{|\mathbf{h}_{e}^{H}\boldsymbol{\Phi}\mathbf{G}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}\right)\geq\delta_{1}$
(19) $\displaystyle=-N_{1}+N_{2}+N_{3}-N_{4}\geq\delta_{1},$

where

$\displaystyle N_{1}=$
$\displaystyle-\log_{2}\left(\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{Z}\right)\right.$
$\displaystyle\left.+\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{W}_{1}\right)+\sigma_{1}^{2}\right),$
(20) $\displaystyle N_{2}=$
$\displaystyle-\log_{2}\left(\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{Z}\right)+\sigma_{1}^{2}\right),$
(21) $\displaystyle N_{3}=$
$\displaystyle-\log_{2}\left(\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{Z}\right)\right.$
$\displaystyle\left.+\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{W}_{1}\right)+\sigma_{e}^{2}\right),$
(22) $\displaystyle N_{4}=$
$\displaystyle-\log_{2}\left(\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{Z}\right)+\sigma_{e}^{2}\right).$
(23)

Note that $N_{2}$ and $N_{3}$ are in convex form with respect to
$\mathbf{w}_{2}$ and $\mathbf{z}$ in (16), but the terms $-N_{1}$ and $-N_{4}$
are in concave form with respect to $\mathbf{w}_{2}$ and $\mathbf{z}$. Hence,
(16) is nonconvex due to the difference-of-convex form [40]. To address the
nonconvexity, we resort to successive convex approximation (SCA) to construct
a global underestimator for the function $N_{1}$ and $N_{4}$. Their first-
order Taylor approximation expressions, which can be written as discussed in
(24) and (25), are shown at the top of next page.

$\displaystyle N_{1}\left(\mathbf{W}_{2},\mathbf{Z}\right)$ $\displaystyle\geq
N_{1}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\mathbf{W}_{2}}N_{1}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\left(\mathbf{W}_{2}-\mathbf{W}_{2}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\mathbf{Z}}N_{1}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\left(\mathbf{Z}-\mathbf{\mathbf{Z}}^{\left(t\right)}\right)\right)\right),$
(24) $\displaystyle N_{4}\left(\mathbf{W}_{2},\mathbf{Z}\right)$
$\displaystyle\geq
N_{4}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\mathbf{W}_{2}}N_{4}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\left(\mathbf{W}_{2}-\mathbf{W}_{2}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\mathbf{Z}}N_{4}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\left(\mathbf{Z}-\mathbf{\mathbf{Z}}^{\left(t\right)}\right)\right)\right).$
(25)

In (24) and (25),

$\displaystyle\nabla_{\mathbf{W}_{2}}N_{1}\left(\mathbf{W}_{2},\mathbf{Z}\right)=\nabla_{\mathbf{Z}}N_{1}\left(\mathbf{W}_{2},\mathbf{Z}\right)$
(26) $\displaystyle=-\frac{1}{\ln
2}\frac{\mathbf{H}_{1}}{\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{Z}\right)+\mathrm{Tr}\left(\mathbf{H}_{1}\mathbf{W}_{1}\right)+\sigma_{1}^{2}},$
$\displaystyle\nabla_{\mathbf{W}_{2}}N_{4}\left(\mathbf{W}_{2},\mathbf{Z}\right)=\nabla_{\mathbf{Z}}N_{4}\left(\mathbf{W}_{2},\mathbf{Z}\right)$
$\displaystyle=-\frac{1}{\ln
2}\frac{\mathbf{H}_{e}}{\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{W}_{2}\right)+\mathrm{Tr}\left(\mathbf{H}_{e}\mathbf{Z}\right)+\sigma_{e}^{2}}.$
(27)

Then, we can replace the nonconvex constraint C2 with the tractable expression
C2a in (14).

Based on the above the transformations, optimizing $\mathbf{w}_{2}$ and
$\mathbf{z}$ in $\mathbf{P1}$ is reduced to

$\displaystyle\mathbf{P3:}\qquad$
$\displaystyle\underset{\mathbf{W}_{2},\mathbf{Z}}{\min}\;\;\mathbf{\mathrm{Tr}}\left(\mathbf{W}_{2}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{Z}\right)$
$\displaystyle s.t.\qquad$ $\displaystyle\mathrm{C1b}:N_{2}+N_{3}$
$\displaystyle-\mathrm{Tr}\left(\nabla_{\mathbf{W}_{2}}N_{1}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\mathbf{W}_{2}\right)$
$\displaystyle-\mathrm{Tr}\left(\nabla_{\mathbf{Z}}N_{1}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\mathbf{Z}\right)$
$\displaystyle-\mathrm{Tr}\left(\nabla_{\mathbf{W}_{2}}N_{4}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\mathbf{W}_{2}\right)$
$\displaystyle-\mathrm{Tr}\left(\nabla_{\mathbf{Z}}N_{4}\left(\mathbf{W}_{2}^{\left(t\right)},\mathbf{Z}^{\left(t\right)}\right)\mathbf{Z}\right)\geq\delta_{1},$
$\displaystyle\mathrm{C2a}:\mathbf{\mathrm{Tr}}\left(\mathbf{W}_{2}\mathbf{H}_{2}\right)-\left(2^{\delta_{2}}-1\right)$
(28)
$\displaystyle\left(\mathbf{\mathrm{Tr}}\left(\mathbf{W}_{1}\mathbf{H}_{2}\right)+\mathbf{\mathrm{Tr}}\left(\mathbf{Z}\mathbf{H}_{2}\right)+\sigma_{2}^{2}\right)\geq
0,$ $\displaystyle\mathrm{C3}:\mathbf{Z}\succeq 0,$
$\displaystyle\mathrm{C6}:\mathbf{W}_{2}\succeq 0,$

where C6 is introduced to interpret the relaxation of the constraint
$\mathbf{W}_{2}=\mathbf{w}_{2}\mathbf{w}_{2}^{H}$ during the application of
the SDR method. For the convex problem $\mathbf{P3}$, the EVD with Gaussian
randomization can be applied to recover the optimal $\mathbf{w}_{2}$ and
$\mathbf{z}$ after the solutions $\mathbf{W}_{2}$ and $\mathbf{Z}$ are
obtained similar to restoring $\mathbf{w}_{1}$.

###  III-C Optimization of the IRS Phase Shifts
$\boldsymbol{\boldsymbol{\Phi}}$

In this system, by reconfiguring the wireless environments, IRS is introduced
to bring additional beamforming gains in the expected directions while
suppressing undesirable interference. Therefore, the passive beamforming gain
can theoretically help save active transmit power at the BS. Given the
beamformers $\mathbf{w}_{1},\mathbf{w}_{2}$ and the AN vector $\mathbf{z}$,
only constraints C1, C2 and C4 are involved in the optimization of
$\mathbf{P1}$. The main difficulty in solving the passive beamforming
subproblem lies in the highly intractable form of the nonconvex unit modulus
constraint C4.

By changing the variables
$\mathbf{h}_{k}^{H}\boldsymbol{\Phi}\mathbf{G}=\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{k}$
to
$\boldsymbol{\varTheta}_{k}=\mathrm{diag}\left(\mathbf{h}_{k}^{H}\right)\mathbf{G}$,
we can write C1 as follows:

$\displaystyle\mathrm{C1c}:R_{sec}$
$\displaystyle=\log_{2}\left(1+\frac{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{1}\mathbf{w}_{1}|^{2}}{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{1}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{1}^{2}}\right)$
(29)
$\displaystyle-\log_{2}\left(1+\frac{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{e}\mathbf{w}_{1}|^{2}}{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{e}\left(\mathbf{w}_{2}+\mathbf{z}\right)|^{2}+\sigma_{e}^{2}}\right)\geq\delta_{1}.$

However, analyzing the quadratic terms in (26) is still challenging. To
facilitate the SDR form, we define
$\mathbf{M}_{k,i}=\mathbf{w}_{i}^{H}\boldsymbol{\varTheta}_{k}^{H}\boldsymbol{\varTheta}_{k}\mathbf{w}_{i}$,
$\mathbf{M}_{k,z}=\mathbf{z}^{H}\boldsymbol{\varTheta}_{k}^{H}\boldsymbol{\varTheta}_{k}\mathbf{z}$,
$\boldsymbol{O}_{k}=\boldsymbol{\varTheta}_{k}^{H}\boldsymbol{\varTheta}_{k}$,
and $\boldsymbol{V}=\boldsymbol{v}\boldsymbol{v}^{H}$. Then, we can rewrite
$R_{sec}$ in (26) as

$\displaystyle R_{sec}$
$\displaystyle=\log_{2}\left(P_{t}\mathrm{Tr}\left(\boldsymbol{V}\boldsymbol{O}_{1}\right)+\sigma_{1}^{2}\right)$
$\displaystyle-\log_{2}\left(\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{1,2}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{1,z}\right)+\sigma_{1}^{2}\right)$
$\displaystyle-\log_{2}\left(P_{t}\mathrm{Tr}\left(\boldsymbol{V}\boldsymbol{O}_{e}\right)+\sigma_{e}^{2}\right)$
$\displaystyle+\log_{2}\left(\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,2}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,z}\right)+\sigma_{e}^{2}\right)\geq\delta_{1}$
$\displaystyle=-T_{1}+T_{2}+T_{3}-T_{4}\geq\delta_{1},$ (30)

where

$\displaystyle T_{1}$
$\displaystyle=-\log_{2}\left(P_{t}\mathrm{Tr}\left(\boldsymbol{V}\boldsymbol{O}_{1}\right)+\sigma_{1}^{2}\right),$
(31) $\displaystyle T_{2}$
$\displaystyle=-\log_{2}\left(\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{1,2}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{1,z}\right)+\sigma_{1}^{2}\right),$
(32) $\displaystyle T_{3}$
$\displaystyle=-\log_{2}\left(P_{t}\mathrm{Tr}\left(\boldsymbol{V}\boldsymbol{O}_{e}\right)+\sigma_{e}^{2}\right),$
(33)

and

$T_{4}=-\log_{2}\left(\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,2}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,z}\right)+\sigma_{e}^{2}\right).$
(34)

Because $T_{2}$ and $T_{3}$ are in convex form with $\boldsymbol{V}$ while the
terms $T_{1}$ and $T_{4}$ are in concave form with respect to
$\boldsymbol{V}$, $R_{sec}$ in (27) is a typical difference-of-convex form. To
approximate this nonconvex form, the first-order Taylor approximation in (28)
and (31) is applied, which can be written as

$\displaystyle T_{1}\left(\boldsymbol{V}\right)$ $\displaystyle\geq
T_{1}\left(\boldsymbol{V}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{1}\left(\boldsymbol{V}^{\left(t\right)}\right)\left(\boldsymbol{V}-\boldsymbol{V}^{\left(t\right)}\right)\right),$
(35) $\displaystyle T_{4}\left(\boldsymbol{V}\right)$ $\displaystyle\geq
T_{4}\left(\boldsymbol{V}^{\left(t\right)}\right)+\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{4}\left(\boldsymbol{V}^{\left(t\right)}\right)\left(\boldsymbol{V}-\boldsymbol{V}^{\left(t\right)}\right)\right),$
(36)

where

$\displaystyle\nabla_{\boldsymbol{V}}T_{1}\left(\boldsymbol{V}\right)$
$\displaystyle=-\frac{1}{\ln
2}\frac{\boldsymbol{O}_{1}}{P\mathrm{Tr}\left(\boldsymbol{V}\boldsymbol{O}_{1}\right)+\sigma_{1}^{2}},$
(37) $\displaystyle\nabla_{\boldsymbol{V}}T_{4}\left(\boldsymbol{V}\right)$
$\displaystyle=-\frac{1}{\ln
2}\frac{\mathbf{M}_{e,2}+\mathbf{M}_{e,z}}{\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,2}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{e,z}\right)+\sigma_{e}^{2}}.$
(38)

Accordingly, the secure rate $R_{sec}$ can be updated as follows:

$\displaystyle R_{sec}$ $\displaystyle=-T_{1}+T_{2}+T_{3}-T_{4}$
$\displaystyle=T_{2}+T_{3}-\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{1}\left(\boldsymbol{V}^{\left(t\right)}\right)\boldsymbol{V}\right)$
(39)
$\displaystyle-\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{4}\left(\boldsymbol{V}^{\left(t\right)}\right)\boldsymbol{V}\right)\geq\delta_{1}.$

In a similar manner as was done in (26), C2 can be recast to

$\displaystyle\mathrm{C2b}:R_{e}$
$\displaystyle=\log_{2}(1+\frac{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{2}\mathbf{w}_{2}|^{2}}{|\boldsymbol{v}^{H}\boldsymbol{\varTheta}_{2}\left(\mathbf{w}_{1}+\mathbf{z}\right)|^{2}+\sigma_{2}^{2}})\geq\delta_{2}$
$\displaystyle\Leftrightarrow\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{2,2}\right)-\left(2^{\delta_{2}}-1\right)$
(40)
$\displaystyle\left(\mathrm{Tr}\left[\boldsymbol{V}\left(\mathbf{M}_{2,1}+\mathbf{M}_{2,z}\right)\right]\right)\geq
0.$

After the above transformations, optimizing the reflection coefficients in
problem $\mathbf{P1}$ can be reduced to

$\displaystyle\mathbf{P4:}\qquad$
$\displaystyle\underset{\boldsymbol{V}}{\mathrm{Find}}\;\;\boldsymbol{V}$
$\displaystyle s.t.\qquad$
$\displaystyle\mathrm{C1c}:T_{2}+T_{3}-\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{1}\left(\boldsymbol{V}^{\left(t\right)}\right)\boldsymbol{V}\right)$
$\displaystyle-\mathrm{Tr}\left(\nabla_{\boldsymbol{V}}T_{4}\left(\boldsymbol{V}^{\left(t\right)}\right)\boldsymbol{V}\right)\geq\delta_{1},$
$\displaystyle\mathrm{C2b}:\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{2,2}\right)-\left(2^{\delta_{2}}-1\right)$
(41)
$\displaystyle\left(\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{2,1}\right)+\mathrm{Tr}\left(\boldsymbol{V}\mathbf{M}_{2,z}\right)\right)\geq
0,$ $\displaystyle\mathrm{C7}:\boldsymbol{V}\succeq 0,$
$\displaystyle\mathrm{C8}:\mathrm{Diag}\left(\boldsymbol{V}\right)=1_{N},$

where C7 is newly added to relax the equation constraint
$\boldsymbol{V}=\boldsymbol{v}\boldsymbol{v}^{H}$ during the SDR procedures,
and C8 is introduced to guarantee the unit modulus constraint.

Problem $\mathbf{P4}$ is now in convex form and hence is solvable. Given the
variables $\boldsymbol{V}^{*}$ obtained by the CVX tools, we then employ the
EVD with Gaussian randomization so the reflection phase shift matrix
$\boldsymbol{\Phi}$ can be restored similar to restoring $\mathbf{w}_{1}$.

To simplify the understanding of the proposed alternating optimization
framework, the overall optimization procedures of
$\mathbf{w}_{1},\mathbf{w}_{2},\mathbf{z}$ and $\boldsymbol{\Phi}$ are
summarized in Algorithm 1. To illustrate the convergence of the proposed
approach, we provide the corresponding proof in Proposition 1.

_Proposition 1:_ Algorithm 1 is guaranteed to converge when the proposed
alternating iterative framework is used.

###### Proof:

See Appendix A. ∎

Moreover, we provide a computational complexity analysis of the proposed
algorithm. As described in Algorithm 1, the complexity is dominated by steps
(a), (b) and (c). To be specific, running the SDP in (a) and (b) results in
the complexity of $\mathcal{O}\left(N_{A}^{4.5}\right)$ and
$\mathcal{O}\left(N_{B}^{4.5}\right)$ [42], respectively. Solving (c) for the
reflection coefficient requires the complexity of
$\mathcal{O}\left(\left(N+1\right)^{4.5}\right)$ [29]. The overall complexity
of Algorithm 1 is
$\mathcal{O}\left(L\left(N_{A}^{4.5}+N_{B}^{4.5}+\left(N+1\right)^{4.5}\right)\right)$,
where $L$ denotes the iteration number of the algorithm.

  1. 1.

Initialization: Set the iteration index to $t=1$, construct the general
beamformer
$\mathbf{w}_{2}^{*}=\sqrt{P_{t}^{*}}\frac{\mathbf{\left(\mathbf{h}_{2}^{\mathit{H}}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\right)}^{H}}{\|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\|}$,
and generate the initial AN vector $\mathbf{z}$ and initial IRS coefficient
matrix $\boldsymbol{\Phi}$.

  2. 2.

Repeat

    1. (a)

Obtain the confidential beamformer $\mathbf{w}_{1}^{\left(t\right)}$ by
solving $\mathbf{P2}$ with the given variables $\mathbf{w}_{2}^{*},\mathbf{z}$
and $\boldsymbol{\Phi}$.

    2. (b)

Obtain the general beamformer $\mathbf{w}_{2}^{\left(t\right)}$ and the AN
$\mathbf{z}^{\left(t\right)}$ by solving $\mathbf{P3}$ with the fixed
$\boldsymbol{\Phi}$ and $\mathbf{w}_{1}^{\left(t\right)}$.

    3. (c)

Find the reflection coefficient matrix $\boldsymbol{\Phi}^{\left(t\right)}$ by
solving $\mathbf{P4}$ with the fixed
$\mathbf{w}_{1}^{\left(t\right)},\mathbf{w}_{2}^{\left(t\right)}$ and
$\mathbf{z}^{\left(t\right)}$.

    4. (d)

Substitute the updated variables
$\mathbf{w}_{1}^{\left(t\right)},\mathbf{w}_{2}^{\left(t\right)}$ and
$\mathbf{z}^{\left(t\right)}$ into the original problem to obtain the power
$P_{t}^{\left(t\right)}$.

    5. (e)

Update $t=t+1.$

  3. 3.

Until $|\frac{P_{t}^{(t)}-P_{t}^{(t+1)}}{P_{t}^{(t+1)}}|<\delta$ or the
maximum number of iterations is reached. Then, terminate the algorithm.

Algorithm 1 Alternating Algorithm-based Transmit Power Minimization.

###  III-D The execution entity of the proposed scheme

Initially, the BS performs channel estimation through the pilots sent by users
and collects the channel state information of all involved users. Next, the
users write the required different security requests into the data packet and
transmit it to the BS. Then, the BS receives the service request of the users
and divides it into confidential subscribers or general communication users
according to the WAP. Finally, by running the proposed algorithm at the BS, we
can calculate the transmit beamforming vectors, the injected AN vector and the
reflection phase shifts. The beamforming design and artificial noise
superposition design are carried out for the transmitted signal at the BS. The
IRS controller adjusts the reflection amplitude and angle through the
instructions sent by the BS. Through the cooperation of the BS, the IRS and
UEs, the downlink secure transmission scheme is ensured.

##  IV Simulation Results

In this section, we evaluate the performance of the proposed algorithm in an
IRS-aided security classification wireless communication system.

###  IV-A Simulation Settings

Fig. 2: The simulated IRS-aided security-classification wireless communication
scenario.

The downlink transmission simulation setup is depicted in Fig. 2, where the
radius is three hundred meters. The coordinate of the IRS and the BS are
denoted by $\left(0,0\right)$ and $\left(0,200\right)$, respectively. The
confidential subscriber, the general communication user and Alice are located
at $\left(50,0\right),\left(50,50\right)$ and $\left(40,-30\right)$,
respectively. We assume that obstacles exist between the BS and the users;
therefore, the signals can be transmitted to the users only through the
BS–IRS–User link. The channel matrix $\mathbf{G}$ between the BS and the IRS
follows a Rician distribution because it is often deployed in open areas with
good channel quality. The channel matrix $\mathbf{G}$ is structured as
follows:

$\mathbf{G}=\sqrt{\beta}\left(\sqrt{\frac{\delta}{\delta+1}}\bar{\mathbf{G}}+\sqrt{\frac{\delta}{\delta+1}}\tilde{\mathbf{G}}\right),$
(42)

where $\beta$ is the large-scale fading coefficient, $\delta$ is the Rician
factor, and $\tilde{\mathbf{G}}$ is the non-line-of-sight (NLoS) channel
component whose elements are independent and identically distributed with
$\mathrm{\mathcal{CN}}\left(0,1\right)$ [43].

According to the uniform square planar array (USPA) model, $\bar{\mathbf{G}}$
represents the line-of-sight (LoS) channel component, as given by

$\bar{\mathbf{G}}=e^{-j2\pi\frac{d}{\lambda}}\mathbf{a}_{I}\left(\psi_{a},\psi_{e}\right)\mathbf{a}_{B}^{H}\left(\psi_{b}\right),$
(43)

where $d$ is the distance between the BS and the IRS. $\lambda$ is the
wavelength. $\psi_{a}$ and $\psi_{e}$ are the azimuth and elevation angles of
arrival at the IRS, respectively. $\psi_{b}$ is the angle of departure from
the BS to the IRS. $\mathbf{a}_{I}$ and $\mathbf{a}_{B}$ are the steering
vectors corresponding to the IRS and BS, respectively.

The channel matrix $\mathbf{h}_{k}$ between the IRS and the $k$-th user
follows the the Rayleigh distribution, and $\alpha$ is the path loss exponent.
$t$ is the maximum number of iterations, and $\epsilon$ is the error accuracy.
The main parameters used in our simulations are provided in Table II.

Table II: SIMULATION PARAMETERS  Carrier center frequency | 2.4 GHz
---|---
Distance between BS and IRS $d$ | 200 m
Path loss exponent $\alpha$ | 4
Path loss $\beta$ | $10^{-9}$
Rician factor $\delta$ | 10
Cell radius $R_{c}$ | 300 m
Noise power | -90 dBm
Maximum number of iterations $t$ | 1000
Error accuracy $\epsilon$ | $10^{-4}$

###  IV-B Performance Evaluation

To validate the performance of the proposed scheme, we selected four baseline
schemes for performance comparisons. The considered baseline designs are as
follows:

  * •

Baseline 1: We derive the confidential beamformer and the general beamformer
according to the maximum ratio transmission (MRT) based scheme, i.e.,
$\mathbf{w}_{1}^{*}=\sqrt{P_{t}^{*}}\frac{\mathbf{\left(\mathbf{h}_{1}^{\mathit{H}}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\right)}^{H}}{\|\mathbf{h}_{1}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\|}$
and
$\mathbf{w}_{2}^{*}=\sqrt{P_{t}^{*}}\frac{\mathbf{\left(\mathbf{h}_{2}^{\mathit{H}}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\right)}^{H}}{\|\mathbf{h}_{2}^{H}\mathbf{\boldsymbol{\Phi}}\mathbf{G}\|}$.
Then, we apply Algorithm 1 without further updating $\mathbf{w}_{1}$ and
$\mathbf{w}_{2}$ to obtain the other two: $\mathbf{z}$ and
$\boldsymbol{\Phi}$. This baseline is termed the “MRT-based scheme”.

  * •

Baseline 2: We randomly select the reflection phase shifts $\boldsymbol{\Phi}$
at the IRS, and the other three variables $\mathbf{w}_{1},\mathbf{w}_{2}$.
Then, $\mathbf{z}$ is attained by applying Algorithm 1 without updating the
$\boldsymbol{\Phi}$. This baseline is termed the “Rand phase-based scheme”.

  * •

Baseline 3: We obtain the beamformers $\mathbf{w}_{1},\mathbf{w}_{2}$ and the
reflection phase shifts $\boldsymbol{\Phi}$ using Algorithm 1 but remove the
procedure to inject the AN at the BS. This baseline is termed the “w/o AN-
based scheme”.

  * •

Baseline 4: We adopt the traditional relay based scheme without IRS, which
forwards the confidential information via amplification. This baseline is
termed the “Relay-based scheme”.

Fig. 3: Convergence behavior of the proposed algorithm.

As shown in Fig. 3, we investigated the convergence behavior of the proposed
algorithm. Under the scenarios of different antenna numbers and IRS numbers,
the proposed algorithm exhibits good convergence after a certain number of
iterations. As the number of transmit antennas and the reflecting elements
increase, the transmit power reduces accordingly. By maintaining the number of
transmit antennas and reducing the number of IRS reflecting elements, the
system transmit power decreases by only $10\%$. Conversely, when the number of
the IRS reflecting elements is fixed, reducing the number of the transmit
antennas can decrease the required transmit power by $30\%$. The result shows
that the number of transmit antennas contributes more to saving active power
consumption than does the IRS.

(a) Alice is located at (40,-30), and the confidential subscriber is moving
away from the IRS. (b) The confidential subscriber is located at (50,0), and
Alice is moving away from the IRS.

Fig. 4: Transmit power versus communication users’ distance (m).

In Fig. 4(a), we study the influence of the distance between the confidential
subscriber and the IRS on the system transmit power. In our setup, the
positions of the general communication user and Alice in the system are fixed
at $\left(50,50\right)$ and $\left(40,-30\right)$, respectively. The
confidential subscriber gradually moves from $\left(10,0\right)$ to
$\left(200,0\right)$ along the $x$-axis. It can be seen that as the distance
between the confidential subscriber and the IRS increases, the BS transmit
power must increase to ensure the security rate requirements of the
communication user. Meanwhile, adding more transmit antennas or reflection
units at the IRS can reduce the transmit power effectively.

Fig. 4(b) evaluates the impact of the distance between Alice and the IRS on
the system transmit power. The positions of the general communication user and
the confidential subscriber are fixed at $\left(50,50\right)$ and
$\left(50,0\right)$, respectively. Alice gradually moves from
$\left(0,-30\right)$ to $\left(200,-30\right)$ along the dotted line shown in
Fig. 4(b). As Alice started to stay away from the IRS, the required transmit
power decreases slowly. In contrast, as Alice moves to $\left(40,-30\right)$
and then outward, the required transmit power decreases faster. This is
because Alice is farther away from the IRS than the confidential subscriber.
When moving to $\left(185,-30\right)$, Alice is sufficiently far from the
coverage of the BS. The required transmit power remains almost unchanged as
Alice proceeds to move outward, and it can be considered that no eavesdroppers
are present in the system.

Fig. 5: System transmit power versus the rate requirement (bit/s/Hz).

Fig. 5 plots the system transmit power versus the communication rate
requirements. In Fig. 5(a), the minimum communication rate of the confidential
subscriber is set to 4 bits/s/Hz. As the minimum transmit rate of the general
communication user increases, the transmit power increases slowly. In Fig.
5(b), we set the minimum transmit rate of the general communication user to 4
bits/s/Hz. As the minimum transmit rate of the confidential subscriber
gradually increases, the BS transmit power increases rapidly. Under the same
rate requirement, the confidential subscriber requires more power (which is
more expensive) compared with the general communication user to transmit
information.

Fig. 6: System transmit power versus the numbers of transmit antennas and
reflecting units.

Fig. 6 compares the performances of the proposed algorithm and three baseline
algorithms under different numbers of transmit antennas and reflecting units.
The minimum communication rate requirements of the confidential subscriber and
the general communication user are fixed to $4$ bits/s/Hz. We can first
observe that the required system transmit power under different algorithms is
reduced significantly as the number of transmit antennas or reflecting units
increases. Moreover, under the same communication rate requirement, the
proposed algorithm leads to the lowest transmit power. The simulation results
show that the transmit power of the proposed algorithm is 20% below that of
the MRT-based scheme, which demonstrates that introducing the IRS and the AN
can offer significant benefits.

Fig. 7: System transmit power versus the number of transmit antennas compared
with the relay-based scheme.

Fig. 7 compares the proposed algorithm with the relay-based scheme. As the
number of transmit antennas increases, the BS transmit power required by the
proposed algorithm is 25% below that of the relay-based scheme. When the
minimum communication rate requirement $R_{c}$ increases, the transmit power
in the proposed algorithm has increased but it is still lower than the relay-
based scheme.

Fig. 8: System transmit power versus the confidential subscriber rate
requirement (bit/s/Hz).

In Fig. 8, we investigate the impact of the confidential subscriber’s minimum
rate requirement on the BS transmit power under different schemes. As the
minimum rate requirement increases, the BS transmit power corresponding to the
different schemes also increases. The proposed algorithm outperforms all the
baseline schemes in terms of power consumption. Under different numbers of
transmit antennas, all the schemes exhibit similar trends; however, as the
confidential subscriber rate requirement increases, the gap between the
proposed algorithm and the comparison schemes increases. In addition, we
compare the proposed algorithm with its lower bound. The transmit power
achieved by the proposed algorithm approaches the optimal power results,
indicating the effectiveness of the proposed algorithm.

Fig. 9: System transmit power under different setups versus the confidential
subscriber rate requirement (bit/s/Hz).

It is worth studying whether the system can realize a secure transmission when
Alice is closer to the IRS. The confidential subscriber is located at
$\left(50,0\right)$. We assume that Alice is fixed at $\left(30,0\right)$, the
IRS, Alice and the confidential subscriber are in the same link and Alice is
close to the IRS. This special scenario is termed the “Special Case”. We
regard it as the benchmark that Alice is located at $\left(40,-30\right)$. As
shown in Fig. 9, we investigate the impact of the confidential subscriber’s
minimum rate requirement on the BS transmit power in two different scenarios.
Compared with the benchmark, the BS will consume more transmit power to
achieve the same security rate of information transmission. However, it can
still achieve the security transmission in the “Special Case”. When Alice’s
position remains unchanged, increasing the number of reflection units at the
IRS can effectively reduce the transmit power, which demonstrates the great
potential of the IRS-aided scheme.

##  V Conclusion

In this paper, we proposed an IRS-aided security classification wireless
communication solution to achieve secure and green wireless transmission.
Based on users’ different security communication requirements, we designed a
security-selective transmission mechanism that reduces unnecessary energy
consumption. In the proposed scheme, the IRS serves as an auxiliary link to
assist communication users in secure information transmission. The AN is mixed
into the transmit signal, and then the BS designs the beamforming vectors to
perform the downlink transmissions. To minimize the BS transmit power, we
developed an alternating optimization framework and employed SDR to transform
the original nontrivial problem into LMI problems. Then, we designed a SCA
method to address the intractable QoS constraints with respect to the
beamformers. The simulation results demonstrated the superiority of the
proposed scheme over the baseline schemes in terms of transmit power
consumption. These results show the potential of the proposed scheme for
achieving secure and green information transmission.

##  Appendix A Proof of Proposition 1

If the optimal solution can be attained in each iteration, then we have

$\displaystyle\quad
P_{t}^{\left(t\right)}\left(\mathbf{w}_{1}^{\left(t\right)},\mathbf{w}_{2}^{\left(t\right)},\mathbf{z}^{\left(t\right)},\boldsymbol{\Phi}^{\left(t\right)}\right)$
$\displaystyle\geq
P_{t}^{\left(t+1\right)}\left(\mathbf{w}_{1}^{\left(t+1\right)},\mathbf{w}_{2}^{\left(t\right)},\mathbf{z}^{\left(t\right)},\boldsymbol{\Phi}^{\left(t\right)}\right)$
$\displaystyle\geq
P_{t}^{\left(t+1\right)}\left(\mathbf{w}_{1}^{\left(t+1\right)},\mathbf{w}_{2}^{\left(t+1\right)},\mathbf{z}^{\left(t+1\right)},\boldsymbol{\Phi}^{\left(t\right)}\right)$
$\displaystyle\geq
P_{t}^{\left(t+1\right)}\left(\mathbf{w}_{1}^{\left(t+1\right)},\mathbf{w}_{2}^{\left(t+1\right)},\mathbf{z}^{\left(t+1\right)},\boldsymbol{\Phi}^{\left(t+1\right)}\right)$
$\displaystyle=P_{t}^{\left(t\right)}\left(\mathbf{w}_{1}^{\left(t+1\right)},\mathbf{w}_{2}^{\left(t+1\right)},\mathbf{z}^{\left(t+1\right)},\boldsymbol{\Phi}^{\left(t+1\right)}\right),$
(44)

where $t$ is the iteration index in Algorithm 1. Since the objective
$P_{t}^{\left(t\right)}$ is monotonically decreasing and lower bounded due to
the fundamental QoS requirements, the proposed algorithm is guaranteed to
converge.

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|  Jintao Xing (S’18) received the B. S. degree from Wuhan University of
Technology, Wuhan, China, in 2016. He is currently pursuing the Ph.D. degree
in communication engineering with the School of Information and Communication
Engineering, Beijing University of Posts and Telecommunications (BUPT),
Beijing, China. His current research interests include physical layer
security, wireless communication, intelligent reflecting surface and cell-free
networks.
---|---
|  Tiejun Lv (M’08-SM’12) received the M.S. and Ph.D. degrees in electronic
engineering from the University of Electronic Science and Technology of China
(UESTC), Chengdu, China, in 1997 and 2000, respectively. From January 2001 to
January 2003, he was a Postdoctoral Fellow with Tsinghua University, Beijing,
China. In 2005, he was promoted to a Full Professor with the School of
Information and Communication Engineering, Beijing University of Posts and
Telecommunications (BUPT). From September 2008 to March 2009, he was a
Visiting Professor with the Department of Electrical Engineering, Stanford
University, Stanford, CA, USA. He is the author of three books, more than 100
published IEEE journal papers and 200 conference papers on the physical layer
of wireless mobile communications. His current research interests include
signal processing, communications theory and networking. He was the recipient
of the Program for New Century Excellent Talents in University Award from the
Ministry of Education, China, in 2006. He received the Nature Science Award in
the Ministry of Education of China for the hierarchical cooperative
communication theory and technologies in 2015.
---|---
|  Yashuai Cao (S’18) received the B.S. degree from Chongqing University of
Posts and Telecommunications (CQUPT), Chongqing, China, in 2017. He is
currently pursuing the Ph.D. degree in communication engineering with the
School of Information and Communication Engineering, Beijing University of
Posts and Telecommunications (BUPT), Beijing, China. His current research
interests include wireless resource allocation and signal processing
technologies for massive MIMO systems and intelligent reflecting surface
assisted wireless networks.
---|---
|  Jie Zeng (M’09–SM’16) received the B.S. and M.S. degrees from Tsinghua
University in 2006 and 2009, respectively, and received two Ph.D. degrees from
Beijing University of Posts and Telecommunications in 2019 and the University
of Technology Sydney in 2021, respectively. From July 2009 to May 2020, he was
with the Research Institute of Information Technology, Tsinghua University.
From May 2020 to April 2022, he was a postdoctoral researcher with the
Department of Electronic Engineering, Tsinghua University. Since May 2022, he
has been an associate professor with the School of Cyberspace Science and
Technology, Beijing Institute of Technology. His research interests include
5G/6G, URLLC, satellite Internet, and novel network architecture. He has
published over 100 journal and conference papers, and holds more than 40
Chinese and international patents. He participated in drafting one national
standard and one communication industry standard in China. He received
Beijing’s science and technology award of in 2015, the best cooperation award
of Samsung Electronics in 2016, and Dolby Australia’s best scientific paper
award in 2020.
---|---
|  Pingmu Huang Lecturer, School of Artificial Intelligence, Beijing
University of Posts and Telecommunications. He received the M.S. degrees from
Xi’an Jiaotong University, Xian, China, in 1996 and received Ph.D. degree of
Signal and Information Processing from Beijing University of Posts and
Telecommunications (BUPT), Beijing, China, in 2009. His current research
interests include machine learning and signal processing. He published more
than ten journal papers and conference papers on signal processing and machine
learning.
---|---