Full length articleSecure communication over RIS-aided underlay CR MIMO wiretap channel without Eve’s CSI☆
Introduction
Cognitive radio (CR) technology is an effective mean to alleviate the shortage of spectrum resources, where the secondary user (SU) shares the same spectrum with primary user (PU) [1], [2]. To be specific, there are three approaches for SU to access the spectrum in CR systems, i.e., interweave, overlay and underlay, and all the three approaches require that the interference exerted on PU is no more than a threshold [1], [3], [4], [5]. However, this interference can be eliminated under the paradigm of interweave or overlay if perfect channel state information (CSI) of PU is available at SU [6]. Unfortunately, while the CR technology is conducive to make full use of the licensed spectrum [1], sharing the same spectrum band with untrusted users may encounter serious security threads in CR networks [7].
Extensive efforts have been devoted to improve the physical layer security (PLS) for the CR network [2], [8], [9], [10], [11]. Specifically, the authors proposed a resource allocation scheme for spectrum leasing to maximize secrecy rates in danger of malicious attempt by an eavesdropper (Eve) based on perfect CSI [8]. More generally, the imperfect CSI was also taken into consideration for underlay CR and the secrecy performance with multiple PUs was analyzed in [9]. In [10], a single-input multiple-output (SIMO) underlay cognitive wiretap system over Nakagami-m channels was considered in the absence of Eve’s CSI. Different from [9], [10], the authors considered a two-way relay multiple-input multiple-output (MIMO) scenario in [2], where a pair of PUs and two pairs of SUs traded message. More conclusively, the outage secrecy performances with different antenna selection schemes were investigated in the presence and absence of Eve’s CSI in [11], respectively.
Reconfigurable intelligent surface (RIS), a revolutionary electromagnetic-material-surface technology, has been recognized as an effective mean to reshape wireless propagation environment [12], [13], [14], [15]. More generally, in [16], [17], RIS-aided multi-user MIMO system were considered based on the imperfect CSI and statistical CSI, respectively. Nowadays, many scholars have proposed that RIS can be employed to enhance performance in CR networks, which may avoid the excessive hardware loss and energy consumption by auxiliary helpers [18], [19], [20]. In [18], the authors jointly designed the beamforming vectors at the SUs and the phase-shifting matrix at the RIS to minimize transmit power in the RIS-enhanced CR network. Nevertheless, it may not be feasible to construct the power minimization problem if the quality-of-service (QoS) constraint and interference power constraint (IPC) are both taken into consideration for SU and PU [19], [21]. Thus, the authors investigated the SU’s achievable rate maximization problem with limited transmit power at BS and IPC imposed on PU in [19]. Besides, benefiting from its powerful ability to reconfigure wireless channels, RIS can also enhance PLS of wireless communications [22]. For example, a RIS-aided secure wireless system with a multi-antenna transmitter, a single-antenna receiver and a single-antenna Eve was investigated in [23]. This scenario was further extended in [24], where the legitimate user and Eve were all equipped with multiple antennas and an analytical approximated expression for ergodic secrecy rate was derived based on statistical CSI. Nevertheless, the aforementioned works overlooked the security issues in the RIS-assisted CR networks, which is more complicated since most potential Eves are malicious and IPC should be taken into consideration. In [20], the authors proposed novel numerical methods to maximize the secrecy rate in underlay CR multiple-input single-output (MISO) wiretap channels based on instantaneous CSI. However, the authors in both [20], [21] assumed that full CSI of legitimate primary and secondary user are available, while real-time coding and channel estimation are not so practical. Therefore, utilizing statistical CSI is more practical than instantaneous CSI since the former is more stable and easier to obtain.
Inspired by [20], we focus on enhancing the secrecy performance of a RIS-aided underlay CR MIMO wiretap channel where the SU concurrently occupies the licensed spectrum with the PU within the constraint of the primary QoS [1], [25], which is more practical for real channel conditions since we address the potential wiretap problem by exploiting statistical CSI. Assuming all devices are equipped with multiple antennas, the secure communication problem is very challenging since only statistical CSI is available at ST and Eve’s CSI is totally unknown. Compared with [24], our assumption is more reasonable since Eve’s channels are mostly unknown in reality and most potential Eves are malicious. Besides, the IPC at PU and QoS constraint at SU make the problem even more complicated. The main contributions of this paper are summarized as follows:
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We extend the RIS-aided underlay CR MISO wiretap channel into the MIMO scenario with only statistical CSI known at ST and obtain the large-system rate approximation for the achievable ergodic rate of SU. In the absence of Eve’s CSI, we minimize the transmit power at ST by exploiting SU’s statistical CSI. Specifically, we present a joint optimization problem of designing transmit covariance matrix and RIS phase-shifting matrix to minimize the transmit power with the IPC at PU and QoS constraint at SU.
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By transforming the power minimization problem to an ergodic rate maximization problem, we optimize the phase-shifting matrix for RIS with fixed transmit covariance matrix. By constructing the equivalent problem of the power minimization problem, we optimize the transmit covariance matrix at ST with fixed diagonal phase-shifting matrix.
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To enhance the secrecy rate of the RIS-aided underlay CR MIMO wiretap channel without Eve’s CSI, we design the covariance of artificial noise (AN) with residual power by aligning it into the null space of the SU channel and thus avert the harmful effect on SU. Finally, we estimate the actual achievable ergodic secrecy rate with the designed AN.
The remainder of the paper is organized as follows. In Section 2,we introduce the system model of the RIS-aided underlay CR MIMO wiretap channel and transmit power minimization problem of useful information. Section 3 constructs two sub-problems and proposes the alternating optimization (AO) algorithm to iteratively optimize the design of phase-shifting matrix and transmit covariance matrix. An AN-aided approach has been applied in this section to decrease the quality of communication at Eve. The numerical results are provided in Section 4 to evaluate the performance of the proposed algorithm. The conclusion is drawn in Section 5.
The notations for this article are as follows. Bold capitals () and lower-case () stand for matrix and vector, respectively. denotes the matrix whose elements are complex values. denotes the identity matrix. is Hermitian conjugate of and means the positive semi-definiteness. indicates mathematical expectation. tr and denote the trace and rank of , respectively. is the phase of each entry of and denotes a diagonal matrix whose diagonal entries are from .
Section snippets
System model
Consider a RIS-aided underlay CR MIMO wiretap channel consisting of one secondary transmitter (ST), one PU, one SU, and one Eve equipped with , , and antennas, respectively, and one reflecting-only passive RIS with passive elements (Fig. 1). Similar to the assumption in [19], [20], [21], primary transmitter is omitted in analysis.
PU, SU, and Eve can only receive reflected signal from RIS since the direct links are blocked by the obstacle. Besides, RIS gives assistance to secure
Design of phase-shifting matrix, transmit covariance matrix of useful signal and transmit covariance matrix of AN signal
In this section, we first propose an AO algorithm to jointly solve this nonconvex problem (7) and then design AN to further enhance the secrecy rate. The algorithm requires only SU’s statistical CSI. Firstly, we decouple (7) into two sub-problems, i.e., optimize with fixed and optimize with fixed . Then, to decrease the quality of communication at Eve, we utilize the residual transmit power to design AN.
Numerical results
In this section, to assess the actual achievable ergodic secrecy rate, we assume that Eve’s CSI is available at ST. Then, the received signal at the Eve can be expressed as Similar to , , and , we also adopt the Kronecker model to characterize the channel between ST and Eve, i.e., In the above channel model, and are the spatial correlation matrices at Eve and ST, respectively. is random matrix whose entries
Conclusions
In this paper, we investigate a RIS-aided underlay CR MIMO wiretap channel, where Eve’s CSI is assumed to be unavailable by considering the actual wiretap environment. Under the constraints of QoS and IPC, a power minimization problem is formulated and an AO algorithm is then proposed to jointly design the transmit covariance matrix and diagonal phase-shifting matrix. Besides, to further jam the communication at Eve, we take an AN-aided approach which utilizes the residual power to design AN.
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.
Xiaojun Huang, is currently pursuing the M.Sc. degree in communication engineering with the Nanjing University of Posts and Telecommunications. Her research interests include RIS aided communications and MIMO wireless communication.
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Cited by (0)
Xiaojun Huang, is currently pursuing the M.Sc. degree in communication engineering with the Nanjing University of Posts and Telecommunications. Her research interests include RIS aided communications and MIMO wireless communication.
Jiacheng Lu, is currently pursuing the M.Sc. degree in communication engineering with the Nanjing University of Posts and Telecommunications. His research interests include millimeter-wave communications 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 and Information Engineering from Nanjing University of Posts and 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 and Telecommunications. Her research interests include massive MIMO systems, space–time wireless communications, heterogeneous cellular networks, and Internet-of-Things.
Shu Cai, received the Ph.D. degree in communications engineering from Xidian University, Xi’an, China, in 2013. During his Ph.D. study, he visited Prof. Z.-Q. (Tom) Luo at the University of Minnesota Twin Cities, from 2011 to 2012. After his graduation, he joined Nanjing University of Posts and Telecommunications in 2013, where he is currently an Associate Professor. His main research interests include array signal processing and signal processing for communications.
Wenwan Xu, received the M.Sc. degree in communications engineering from Nanjing University of Posts and Telecommunications (NJUPT), Nanjing, China, in 2022. Her research interests include RIS aided communications and MIMO wireless communication.