Elsevier

Physical Communication

Volume 44, February 2021, 101235
Physical Communication

Full length article
Intelligent reflecting surface-assisted secrecy wireless communication with imperfect CSI

https://doi.org/10.1016/j.phycom.2020.101235Get rights and content

Abstract

The intelligent reflecting surface (IRS) consist of multiple passive elements which make it can passively reflect signals by setting phase angles. The design of IRS has been widely discussed due to its low power consumption and low-cost in recent years. In this article, IRS is used to improve the performance in a secrecy communication system which compose of multiple eavesdroppers equipped with multiple receive antennas and a legitimate user equipped with single antenna. It is assumed that only the imperfect channel state information of the eavesdroppers is available at the base station. To save power consumption, we aim to design the beamforming vector and IRS phase shift matrix by minimizing the transmission power while meeting the requirement of secrecy communication in the worst case of channel. Since the optimization problems have some non-convex constraints, we propose an alternative optimization algorithm to design the beamforming vector and IRS phase shift matrix by employing the semi-relaxation, S-procedure, and difference-of-convex algorithm. Finally, we verify the convergence of the proposed algorithm and reveal the effects of the channel uncertainty, the number of antennas at eavesdropper, and the number of elements at IRS on the transmission power.

Introduction

Thanks to some new technologies applied in fifth-generation (5G) wireless communication system, such as massive multiple-input multiple-output (MIMO) and ultra-dense network (UDN), the capacity of wireless communication system has been greatly improved [1]. However, base stations (BSs) using massive MIMO technology are densely deployed in the UDN, which leads to high hardware cost and energy consumption since the efficient communication with massive MIMO requires a dedicated radio frequency (RF) chain and several active components. To meet the need for green communication, a new low-cost device called intelligent reflecting surface (IRS) that can be applied to a variety of wireless communication scenarios came into being. IRS is a reconfigurable metamaterial comprising a large number of low-cost passive elements which can change the phase and amplitude of the signals [2], [3]. Compared with traditional relays, IRS does not use a RF chain but only uses the passive array to reflect the received signals, so no additional power consumption is generated [4], [5]. In addition, IRS has some other advantages, such as small size and light weight, making them easy to install on the wall, and easy to disassemble which provides a high degree of flexibility for their actual deployment [1].

Due to the advantages mentioned above, IRS has been widely studied in the wireless communication academia. Specifically, [6], [7] considered the optimization of IRS phase in an IRS-assisted multi-user downlink MISO system. The semidefinite relaxation (SDR) algorithm was proposed in [6] to minimize the transmission power. In [7], the maximization problem of energy efficiency under the power and achievable rate constraints has been considered. Different from previous works, the authors in [8], [9] derived a large system approximation of ergodic capacity with the statistical channel state information (CSI). In [9], it is considered that there is only one user in the communication system and provided an optimal phase shift matrix design at IRS. Then, in [8], the effect of the number passive elements at IRS on the ergodic capacity was investigated in a multi-user MISO downlink system. The authors in [10] analyzed the outage performance of hybrid automatic repeat request (hybrid-ARQ) protocol with chase combining for an IRS-assisted system and reached some constructive conclusions. A unique blend that surveys the principles of operation of IRS, together with their optimization and performance analysis frameworks is provided in [11].

On the other hand, the issues related to physical layer security are widely studied in the field of wireless communication. In [12], the problem of secrecy rate maximization was studied for a multiple eavesdroppers downlink scenario. To further improve the system performance, the authors in [13] considered an IRS-assisted secrecy wireless communication in a simple scenario with single eavesdropper and single legitimate user. In [14], a system model consisting of a multi-antenna BS, an eavesdropper and a legitimate user is considered. The authors designed two effective algorithms to maximize the security rate, which advance the research of IRS in the field of secure communication. The authors in [15] studied a more general scenario where there are multiple eavesdroppers and multiple legitimate users. The secrecy rate was considered in [16] by jointly optimizing jamming and IRS. In [17], it is considered the artificial noise in an IRS-assisted communication system. To maximize the secrecy rate in an IRS-assisted millimeter wave and terahertz systems, an effective and feasible algorithm is proposed in [18]. Different from previous works, the average secrecy rate was optimized in [19] by employing the statistical CSI in a simple scenario of single eavesdropper and single legitimate user.

All of the above works only considered the scenario that the eavesdropper only equipped with single antenna. In [20], the authors considered a more general scenario that the eavesdroppers are equipped with multiple antennas, with the goal of maximizing the total rate of legitimate users with imperfect CSI, and meets the restriction condition that the eavesdropping rates are less than the threshold. To be general, we consider a secrecy wireless communication system composed of multiple eavesdroppers equipped with multiple receive antennas and one legitimate user. We assume that the eavesdroppers are legitimate idle users of the IRS-assisted communication systems who only communicate with the BS occasionally. In this case, it is difficult for the BS to obtain perfect CSI of eavesdroppers because that we can only estimate the eavesdroppers CSI based on past communications. Therefore, the BS only knows the imperfect CSI of the eavesdroppers. With the imperfect CSI, we can estimate the worst-case secrecy rate. To save power consumption, we aim to find the minimum power that can meet the users’ requirement for the worst-case secrecy rate is greater than the rate threshold. Our contributions are summarized as follows:

  • We consider a general scenario that the eavesdroppers are equipped with multiple receive antennas and the BS only knows the imperfect CSI of the eavesdroppers. Specifically, we present a joint optimization problem of beamforming vector and IRS phase shift matrix to minimize the transmit power under the constraint that the secrecy rate is greater than a threshold.

  • By transforming the power minimization problem to a semidefinite program (SDP) problem, we obtain a global optimal solution of beamforming vector. By using the difference-of-convex (DC) method and S-procedure, we obtain a suboptimal solution of the IRS phase shift matrix.

  • We propose an alternative optimization algorithm and reveal the effects of the channel uncertainty, the number of antennas at eavesdropper, and the number of passive elements at IRS on the performance in simulation results.

The notations for this article are as follows. Bold uppercase letters and bold lowercase letters are used to represent matrices and vectors, respectively. represents the Frobenius norm of a matrix or vector. ()H,()T indicate the operation of conjugate transpose and transpose respectively. Tr(),det() represent the trace and determinant values of the matrix respectively. rank() represents the rank of the matrix. A0 mean that A is a Hermitian positive semidefinite (definite) matrix. vec() indicates that the matrix is rewritten into a row vector by stacking the row vectors of the matrix. N×M represents the set of complex matrices of N rows and M columns. represents the Kronecker product operator. diag(x) denotes a diagonal matrix with each diagonal element being the corresponding element in x.

Section snippets

System model

As shown in Fig. 1, a downlink system that consists of a multi-antenna BS, an IRS, a single-antenna legitimate user, and K multi-antenna eavesdroppers is considered. The number of antennas for the BS, IRS, and the kth eavesdropper are M, Nr, and Ne,k, respectively. The BS uses IRS to establish communication with legitimate user and eavesdroppers eavesdrop on their communication content. We assume that the legitimate user uses single antenna and eavesdroppers use multiple antennas in order to

Alternating optimization

An alternating optimization method is used to solve the problem (9) which can be decomposed to two subproblems specifically.

Simulation results

We evaluate the proposed alternative algorithm and explore the insights between some optimized variables in this section. We set that there are two eavesdroppers in the system, where each eavesdropper has 2 antennas and the IRS has 5 passive elements if not mentioned. The channels G, hLU, and H̄k are generated according to the independent and identically distributed (i.i.d.) complex Gaussian distribution with zero mean and unit variance. We use η to evaluate the uncertainty of the channel to

Conclusion

In this paper, we investigated the downlink performance of a MISO system with single-antenna legitimate user and multi-antenna eavesdroppers. The BS could only acquire the imperfect channel state information of the eavesdroppers. We addressed the transmission power minimization problem subject to the constraint that the worst-case secrecy rate was greater than the threshold. Since the problem is non-convex, we proposed an alternative algorithm to design the beamforming vector and phase shift

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We would like to thank the referees for carefully reading our manuscript and for giving such constructive, insightful comments and suggestions, which substantially helped to improve the quality of our paper.

This work was supported in part by the National Natural Science Foundation of China under Grant U1805262, 62071247, 61671251, 61801244, and 61404130218, and in part by the Natural Science Foundation of Jiangsu Province, China under Grant BK20180754.

Dongqian Wang, is currently pursuing the M.Sc. degree in communication engineering with the Nanjing University of Posts and Telecommunications. His research interests include intelligent reflecting surface and MIMO wireless communication.

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  • Cited by (6)

    Dongqian Wang, is currently pursuing the M.Sc. degree in communication engineering with the Nanjing University of Posts and Telecommunications. His research interests include intelligent reflecting surface and MIMO wireless communication.

    Jun Zhang, received the M.S. degree in Statistics with Department of Mathematics from Southeast University, Nanjing, China, in 2009, and the Ph.D. degree in Communications Information System with the National Mobile Communications Research Laboratory, Southeast University, Nanjing, China, in 2013. From 2013 to 2015, he was a Postdoctoral Research Fellow with Singapore University of Technology and Design, Singapore. Since 2015, he is with the faculty of the Jiangsu Key Laboratory of Wireless Communications, College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, where he is currently an Associate Professor. His research interests include massive MIMO communications, physical layer security, edge caching and computing, and large dimensional random matrix theory. Dr. Zhang was a recipient of the Globcom Best Paper Award in 2016 and the IEEE APCC Best Paper Award in 2017. He serves as an Associate Editor for the IEEE Communications Letters.

    Qi Zhang, received the B.S. and Ph.D. degree in Electrical & Information Engineering from Nanjing University of Posts & Telecommunications (NJUPT), Nanjing, China, in 2010 and 2015, respectively. She was a postdoc research fellow at the Singapore University of Technology and Design from 2015 to 2017. She is currently with the faculty of the Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts & Telecommunications. Her research interests include massive MIMO systems, space–time wireless communications, heterogeneous cellular networks, and Internet-of-Things.

    Hairong Wang, received the B.S. and M.S. degrees from Nanjing University of Aeronautics and Astronautics, China, in 2000 and 2008, respectively. He received the Ph.D. degree from the School of Information Science and Engineering, Southeast University, Nanjing, China, in 2013. Since 2013, he has been with Key Laboratory of Wireless Communications, Jiangsu Province, Nanjing University of Posts and Telecommunications. His current research interests include MIMO communication systems, multiuser MIMO communications and cooperative communications.

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