Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming
TL;DR: This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers, and addresses the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario.
Abstract: In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.
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TL;DR: This survey introduces the fundamental theories of PHy-security, covering confidentiality and authentication, and provides an overview on the state-of-the-art works on PHY-security technologies that can provide secure communications in wireless systems, along with the discussions on challenges and their proposed solutions.
Abstract: Physical layer security (PHY-security) takes the advantages of channel randomness nature of transmission media to achieve communication confidentiality and authentication. Wiretap coding and signal processing technologies are expected to play vital roles in this new security mechanism. PHY-security has attracted a lot of attention due to its unique features and the fact that our daily life relies heavily on wireless communications for sensitive and private information transmissions. Compared to conventional cryptography that works to ensure all involved entities to load proper and authenticated cryptographic information, PHY-security technologies perform security functions without considering about how those security protocols are executed. In other words, it does not require to implement any extra security schemes or algorithms on other layers above the physical layer. This survey introduces the fundamental theories of PHY-security, covering confidentiality and authentication, and provides an overview on the state-of-the-art works on PHY-security technologies that can provide secure communications in wireless systems, along with the discussions on challenges and their proposed solutions. Furthermore, at the end of this paper, the open issues are identified as our future research directions.
530 citations
Cites background or methods from "Optimal and Robust Transmit Designs..."
...References [27] and [58] addressed the transmit covariance matrix optimization based on CVX tools for secrecy capacity maximization in MISO and MIMO, respectively....
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...The average SNR of the wiretap channel is r̄w....
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...The average SNR of the main channel is r̄m....
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...3) AN Precoding: Reference [25] proposed a simple scheme that uses only the knowledge of hb in choosing transmit directions, where a near-optimal performance is achieved in a high SNR region....
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...Obviously, when SNRm is less than SNRw, the secrecy capacity is zero....
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TL;DR: A cooperative wireless network in the presence of one or more eavesdroppers, and node cooperation for achieving physical (PHY) layer based security is considered, and an analytical solution is obtained for the DF scheme with a single eavesdropper and the multivariate problem is reduced to a problem of one variable.
Abstract: We consider a cooperative wireless network in the presence of one or more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme, cooperating nodes retransmit a weighted version of the source signal in a decode-and-forward (DF) fashion. In the second scheme, referred to as cooperative jamming (CJ), while the source is transmitting, cooperating nodes transmit weighted noise to confound the eavesdropper. We investigate two objectives: i) maximization of the achievable secrecy rate subject to a total power constraint and ii) minimization of the total power transmit power under a secrecy rate constraint. For the first design objective, we obtain the exact solution for the DF scheme for the case of a single or multiple eavasdroppers, while for the CJ scheme with a single eavesdropper we reduce the multivariate problem to a problem of one variable. For the second design objective, existing work introduces additional constraints in order to reduce the degree of difficulty, thus resulting in suboptimal solutions. Our work raises those constraints, and obtains either an analytical solution for the DF scheme with a single eavesdropper, or reduces the multivariate problem to a problem of one variable for the CJ scheme with a single eavesdropper. Numerical results are presented to illustrate the proposed results and compare them to existing work.
427 citations
Cites methods from "Optimal and Robust Transmit Designs..."
...Like [ 31 ], we use the Charnes-Cooper transformation to reduce (49)....
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TL;DR: A detailed investigation on multiple-antenna techniques for guaranteeing secure communications in point-to-point systems, dual-hop relaying systems, multiuser systems, and heterogeneous networks is provided.
Abstract: As a complement to high-layer encryption techniques, physical layer security has been widely recognized 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 paper provides a comprehensive survey on various multiple-antenna techniques in physical layer security, with an emphasis on transmit beamforming designs for multiple-antenna nodes. Specifically, we provide a detailed investigation on multiple-antenna 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.
416 citations
Cites methods from "Optimal and Robust Transmit Designs..."
...Furthermore, a semi-definite programming (SDP) approach was used in [82] to solve a robust beamforming optimization problem in a scenario that both the legitimate and the eavesdropper CSI are imperfect....
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TL;DR: In this article, the authors investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective, where 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.
Abstract: 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 form, respectively. The convergence of the proposed algorithm is guaranteed theoretically. Simulation results validate the performance advantage of the proposed optimized design.
356 citations
TL;DR: This paper considers joint optimization of the transmit and AN covariances for secrecy rate maximization (SRM), with a design flexibility that the AN can take any spatial pattern, and derives an optimization approach to the SRM problem through both analysis and convex conic optimization machinery.
Abstract: Consider an MISO channel overheard by multiple eavesdroppers. Our goal is to design an artificial noise (AN)-aided transmit strategy, such that the achievable secrecy rate is maximized subject to the sum power constraint. AN-aided secure transmission has recently been found to be a promising approach for blocking eavesdropping attempts. In many existing studies, the confidential information transmit covariance and the AN covariance are not simultaneously optimized. In particular, for design convenience, it is common to prefix the AN covariance as a specific kind of spatially isotropic covariance. This paper considers joint optimization of the transmit and AN covariances for secrecy rate maximization (SRM), with a design flexibility that the AN can take any spatial pattern. Hence, the proposed design has potential in jamming the eavesdroppers more effectively, based upon the channel state information (CSI). We derive an optimization approach to the SRM problem through both analysis and convex conic optimization machinery. We show that the SRM problem can be recast as a single-variable optimization problem, and that resultant problem can be efficiently handled by solving a sequence of semidefinite programs. Our framework deals with a general setup of multiple multi-antenna eavesdroppers, and can cater for additional constraints arising from specific application scenarios, such as interference temperature constraints in interference networks. We also generalize the framework to an imperfect CSI case where a worst-case robust SRM formulation is considered. A suboptimal but safe solution to the outage-constrained robust SRM design is also investigated. Simulation results show that the proposed AN-aided SRM design yields significant secrecy rate gains over an optimal no-AN design and the isotropic AN design, especially when there are more eavesdroppers.
305 citations
References
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TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
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TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
23,986 citations
TL;DR: This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.
Abstract: SeDuMi is an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This paper describes how to work with this toolbox.
7,655 citations
"Optimal and Robust Transmit Designs..." refers background in this paper
...One exception where the SRM problem is found to be tractable is the MISO scenario — its optimal transmit design is shown to admit a closed-form solution, involving a generalized eigenvalue problem [4]....
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TL;DR: This paper finds the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission, and implies that there exists a Cs > 0, such that reliable transmission at rates up to Cs is possible in approximately perfect secrecy.
Abstract: We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (dmc) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second dmc). Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire-tapper. The designer attempts to build the encoder-decoder in such a way as to maximize the transmission rate R, and the equivocation d of the data as seen by the wire-tapper. In this paper, we find the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission. In particular, if d is equal to Hs, the entropy of the data source, then we consider that the transmission is accomplished in perfect secrecy. Our results imply that there exists a C s > 0, such that reliable transmission at rates up to C s is possible in approximately perfect secrecy.
7,129 citations
"Optimal and Robust Transmit Designs..." refers background in this paper
...While the concepts of physical-layer secrecy can be found back in the 70’s; e.g., the seminal works by Wyner [ 1 ], Leung-Yan-Cheong and Hellman [2], and Csisz´ar and Korner [3], this topic has attracted much...
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