No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
RIS-Assisted Secure Communications: Low-Complexity Beamforming Design
Abstract
Joint active and passive beamforming optimization is investigated to enhance the physical layer security of a reconfigurable intelligent surface (RIS)-assisted multiple-antenna communication system. The problems are formulated under two criteria: secrecy rate maximization and power consumption minimization. For each design problem, a novel collaborative design algorithm is proposed by capitalizing on the mathematical structure of the optimal active beamforming vector, which requires no iterative updating between the transmit beamformer and the RIS-reflecting beamformer. Numerical results demonstrate that the proposed algorithms enjoy much lower computational complexity than the state-of-the-art alternating optimization-based methods while achieving almost identical secrecy performance.
... Wireless systems are vulnerable to various security threats due to their broadcast nature. The secrecy performance at the physical layer can be improved by exploiting a multiantenna array's spatial degrees of freedom; see [1]- [3] and the references therein. Nevertheless, its fully digital implementation with a dedicated radio frequency (RF) chain at each antenna is costly in size, power, and hardware. ...
The joint antenna selection and secure beamforming optimization problem is considered for a multi-antenna line-of-sight (LOS) wiretap channel. By utilizing the mathematical property of the optimal secure beamformer and physical property of the LOS channel, a branch-and-bound (BAB)-based method is proposed to achieve the optimal secrecy performance with a reduced time complexity than the brute-force search. To further improve the security-complexity trade-off, a greedy-based method is developed to achieve a close to optimal secrecy performance while involving much lower complexity than the BAB-based method. Numerical results confirm the effectiveness of the proposed methods compared to baseline schemes.
With the commercialization of the fifth generation mobile networks, researchers are now focusing on discovering the potential key techniques of the next generation mobile networks, which are expected to provide more accurate perception, lower latency, and higher network capacity. As the communication equipments increase exponentially, wireless transmission environment becomes more complex, leveraging wireless security challenges more and more severe, such as computationally powerful interception, intelligent malicious jamming, communication behavior monitoring. The physical layer security (PLS) techniques have been widely explored as a complement to traditional encryption schemes by exploiting the randomness characteristics of wireless channels to achieve the security from the physical layer. Additionally, reconfigurable intelligent surface (RIS) is considered as a key enabling technology for the six generation (6G) mobile networks, due to its ability to achieve the reconstruction of wireless channel, which is also regarded as a good match with PLS techniques for improving communication security. This paper presents a comprehensive review of the latest research on the integration of RIS and PLS. First, we introduce the principles of PLS from the development of secure communications and the basics of RIS based on the generalized Snell’s law. Then, we categorize RIS according to different hardware architectures, of which the corresponding scenarios are also presented. Subsequently, we review recent works on RIS-assisted PLS in different communication networks, and classify the security scenarios in which RIS is integrated with various advanced communication technologies. Finally, we discuss the potential future research directions and challenges of RIS-aided PLS communications.
This work proposes a novel secure beamforming design for discrete lens array (DLA)-based continuous aperture phased (CAP) multiple-input multiple-output wiretap channels. The base station exploits a switching network to connect a subset of its analog beams or DLA feed antennas to the available radio frequency chains. The switching network and transmit beamformers are jointly designed to maximize the weighted secrecy sum-rate for this setting. The principal design problem reduces to an NP-hard mixed-integer non-linear programming. We invoke the fractional programming technique and the penalty dual decomposition method to develop a tractable iterative algorithm that effectively approximates the optimal design. Our numerical investigations validate the effectiveness of the proposed algorithm and its superior performance compared with the benchmark.
A realistic performance assessment of any wireless technology requires the use of a channel model that reflects its main characteristics. The independent and identically distributed Rayleigh fading channel model has been (and still is) the basis of most theoretical research on multiple antenna technologies in scattering environments. This letter shows that such a model is not physically appearing when using a reconfigurable intelligent surface (RIS) with rectangular geometry and provides an alternative physically feasible Rayleigh fading model that can be used as a baseline when evaluating RIS-aided communications. The model is used to revisit the basic RIS properties, e.g., the rank of spatial correlation matrices and channel hardening.
In this paper, we propose intelligent reflecting surface (IRS) aided multi-antenna physical layer security. We present a power efficient scheme to design the secure transmit power allocation and the surface reflecting phase shift. It aims to minimize the transmit power subject to the secrecy rate constraint at the legitimate user. Due to the non-convex nature of the formulated problem, we propose an alternative optimization algorithm and the semidefinite programming (SDP) relaxation to deal with this issue. Also, the closed-form expression of the optimal secure beamformer is derived. Finally, simulation results are presented to validate the proposed algorithm, which highlights the performance gains of the IRS to improve the secure transmission.
The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.
The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we study a masked beamforming scheme that radiates power isotropically in all directions and show that it attains near-optimal performance in the high SNR regime. Insights into the scaling behavior of the capacity in the large antenna regime as well as extensions to ergodic fading channels are also provided.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifoldsoffers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
In intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) systems, the IRS can be utilized to suppress the information leakage towards malicious terminals. This can lead to significant secrecy gains. This work exploits these gains via a tractable
joint
design of downlink beamformers and IRS phase-shifts. In this respect, we consider a generic IRS-aided MIMO wiretap setting and invoke fractional programming and alternating optimization to iteratively find the beamformers and phase-shifts that maximize the achievable weighted secrecy sum-rate. Our design is comprised of two low-complexity algorithms. Performance of the proposed algorithms are numerically evaluated and compared to the benchmark. The results reveal that integrating IRSs into MIMO systems not only boosts the secrecy performance, but also improves the robustness against passive eavesdropping.
Beamspace multiple-input multiple-output (MIMO) systems leverage the lens antenna array to reduce their hardware cost, which is a promising technology in millimeter wave (mmWave) frequency bands. This letter proposes a novel signal-to-leakage-plus-noise ratio (SLNR)-based beamspace precoding and beam selection scheme to improve the downlink sum rate (SR) of the beamspace mmWave massive MIMO channels. First, for a given beam subset, a SLNR maximization-based beamspace precoder is designed to mitigate the inter-user interference caused by leakage power, thus enhancing the SR. Then, an approximated expression of the SR is formulated, based on which an iterative radio frequency (RF) precoding and beam selection method is designed to further improve the system SR. Numerical results demonstrate a superior SR performance of the proposed scheme over state-of-the-art methods.
Reconfigurable intelligent surfaces (RISs), also known as intelligent reflecting surfaces (IRSs), or large intelligent surfaces (LISs),
<sup>1</sup>
have received significant attention for their potential to enhance the capacity and coverage of wireless networks by smartly reconfiguring the wireless propagation environment. Therefore, RISs are considered a promising technology for the sixth-generation (6G) of communication networks. In this context, we provide a comprehensive overview of the state-of-the-art on RISs, with focus on their operating principles, performance evaluation, beamforming design and resource management, applications of machine learning to RIS-enhanced wireless networks, as well as the integration of RISs with other emerging technologies. We describe the basic principles of RISs both from physics and communications perspectives, based on which we present performance evaluation of multiantenna assisted RIS systems. In addition, we systematically survey existing designs for RIS-enhanced wireless networks encompassing performance analysis, information theory, and performance optimization perspectives. Furthermore, we survey existing research contributions that apply machine learning for tackling challenges in dynamic scenarios, such as random fluctuations of wireless channels and user mobility in RIS-enhanced wireless networks. Last but not least, we identify major issues and research opportunities associated with the integration of RISs and other emerging technologies for applications to next-generation networks.
<sup>1</sup>
Without loss of generality, we use the name of RIS in the remainder of this paper.
</fn
The effective combination of physical layer security communication and intelligent reflecting surface (IRS) technology has recently attracted extensive attention to improve the system security. Unlike existing works that mostly focus on single-carrier systems, we consider an IRS-assisted multi-carrier MIMO wireless physical layer security communication system, which consists of a legitimate transmitter, a legitimate receiver, an IRS node and an eavesdropper. With the aim of maximizing the sum secrecy rate, the multi-carrier transmit beamforming and IRS reflecting coefficient matrix are jointly optimized under the constraints on the transmit power budget and unit modulus of IRS reflecting coefficients. Since the formulated problem is non-convex, an alternate optimization (AO) algorithm is proposed to deal with it. Specifically, for the given IRS reflecting coefficient matrix, the minorization-maximization (MM) scheme is adopted to approximate the objective function of the subproblem and following that, the closed-form solution of the multi-carrier transmit beamforming is obtained through the Lagrange multiplier method. Then, for the given multi-carrier beamforming, the IRS reflecting coefficient matrix is also optimized through the MM scheme and a suboptimal closed-form solution that satisfies the KKT conditions is derived. Moreover, the discussion is extended to the discrete IRS phase shift case and a heuristic projection method (HPM) is then proposed. Finally, the simulation results validate the effectiveness of the proposed AO based algorithm.
In this letter, the use of intelligent reflecting surface (IRS) to enhance the physical layer security of downlink wireless communication is investigated. Assuming a single-antenna legitimate user and a multi-antenna eavesdropper, we propose an effective algorithm to jointly optimize the active and passive beamforming. In the proposed algorithm, the optimal transmit beamforming vector at the BS under fixed IRS phase shifts is derived, and a low-complexity algorithm based on fractional programming (FP) and manifold optimization (MO) is proposed to obtain near optimal IRS phase shifts. Simulation results demonstrate that the proposed algorithm can almost achieve the performance upper bound with a fast convergence rate.
IRS is a new and revolutionizing technology that is able to significantly improve the performance of wireless communication networks, by smartly reconfiguring the wireless propagation environment with the use of massive low-cost passive reflecting elements integrated on a planar surface. Specifically, different elements of an IRS can independently reflect the incident signal by controlling its amplitude and/or phase and thereby collaboratively achieve fine-grained 3D passive beamforming for directional signal enhancement or nulling. In this article, we first provide an overview of the IRS technology, including its main applications in wireless communication, competitive advantages over existing technologies, hardware architecture as well as the corresponding new signal model. We then address the key challenges in designing and implementing the new IRS-aided hybrid (with both active and passive components) wireless network, as compared to the traditional network comprising active components only. Finally, numerical results are provided to show the great performance enhancement with the use of IRS in typical wireless networks.
In this letter, we consider the problem of channel estimation for large intelligent metasurface (LIM) assisted massive multiple-input multiple-output (MIMO) systems. The main challenge of this problem is that the LIM integrated with a large number of low-cost metamaterial antennas can only passively reflect the incident signals by certain phase shifts, and does not have any signal processing capability. To deal with this, we introduce a general framework for the estimation of the transmitter-LIM and LIM-receiver cascaded channel, and propose a two-stage algorithm that includes a sparse matrix factorization stage and a matrix completion stage. Simulation results illustrate that the proposed method can achieve accurate channel estimation for LIM-assisted massive MIMO systems.
We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed forms, respectively. The convergence of the proposed algorithm is guaranteed theoretically. Simulations results validate the performance advantage of the proposed optimized design.
An intelligent reflecting surface (IRS) can adaptively adjust the phase shifts of its reflecting units to strengthen the desired signal and/or suppress the undesired signal. In this letter, we investigate an IRS-aided secure wireless communication system where a multi-antenna access point (AP) sends confidential messages to a single-antenna user in the presence of a single-antenna eavesdropper. In particular, we consider the challenging scenario where the eavesdropping channel is stronger than the legitimate communication channel and they are also highly correlated in space. We maximize the secrecy rate of the legitimate communication link by jointly designing the AP’s transmit beamforming and the IRS’s reflect beamforming. While the resultant optimization problem is difficult to solve, we propose an efficient algorithm to obtain high-quality suboptimal solution for it by applying the alternating optimization and semidefinite relaxation methods. Simulation results show that the proposed design significantly improves the secrecy communication rate for the considered setup over the case without using the IRS, and outperforms a heuristic scheme.
As a complement to high-layer encryption techniques, physical layer security has been widely recognised as a promising way to enhance wireless security by exploiting the characteristics of wireless channels, including fading, noise, and interference. In order to enhance the received signal power at legitimate receivers and impair the received signal quality at eavesdroppers simultaneously, multiple-antenna techniques have been proposed for physical layer security to improve secrecy performance via exploiting spatial degrees of freedom. This article provides a comprehensive survey on various multipleantenna techniques in physical layer security, with an emphasis on transmit beamforming designs for multiple-antenna nodes. Specifically, we provide a detailed investigation on multipleantenna techniques for guaranteeing secure communications in point-to-point systems, dual-hop relaying systems, multiuser systems, and heterogeneous networks. Finally, future research directions and challenges are identified.
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.
A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the derivatives of this function. Matrix differentiation results are derived and summarized in tables which can be exploited in a wide range of signal processing related situations
- P.-A Absil
- R Mahony
- R Sepulchre
P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on
Matrix Manifolds, Princeton, NJ, USA: Princeton Univ. Press, 2009.