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On the Transmit Beamforming for MIMO Wiretap Channels: Large-System Analysis

Maksym A. Girnyk, Lars Kildehoj Rasmussen, Mikael Skoglund

Published Aug 17, 2016• 6 citations
OpenAlex

Abstract

With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual information. Leveraging results from random matrix theory, we are able to characterize the achievable ergodic secrecy rates. Based on this characterization, we address the problem of covariance optimization at the transmitter. Our numerical results demonstrate a good match between the large-system approximation and the actual simulated secrecy rates, as well as some interesting features of the precoder optimization.

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Secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While the optimality of Gaussian signaling and a general expression for the secrecy capacity have been well established, closed-form solutions for the optimal transmit covariance matrix are known for some special cases only, while the general case remains an open problem. This chapter reviews known closed-form solutions and presents a numerical algorithm for the general case with guaranteed convergence to the global optimum. The known solutions include full-rank and rank-1 cases (which, when combined, provide a complete solution for the case of two transmit antennas), the case of identical right singular vectors for the eavesdropper and legitimate channels, and the cases of weak, isotropic, and omnidirectional eavesdroppers, which also provide lower and upper bounds to the general case. Necessary optimality conditions and a tight upper bound for the rank of the optimal covariance matrix in the general case are discussed. Sufficient and necessary conditions for the optimality of three popular signaling strategies over MIMO channels, namely, isotropic and zero-forcing signaling as well as water-filling over the legitimate channel eigenmodes, are presented. The chapter closes with a detailed description of a numerical globally convergent algorithm to solve the general case, and gives some illustrative examples. Introduction Due to their high spectral efficiency, wireless MIMO (multiple input, multiple output) systems are widely adopted by academia and industry. The broadcast nature of wireless channels stimulated significant interest in their security aspects and the Gaussian MIMO wiretap channel (WTC) has emerged as a popular model to study information theoretic secrecy aspects of wireless systems [1]. A number of results have been obtained for this model, including the proof of optimality of Gaussian signaling [1–4], which is far from trivial and significantly more involved than that of the regular (no wiretap) MIMO channel. Once the functional form of the optimal input is established, the only unknown is its covariance matrix since the mean is always zero. This latter part has not been solved yet in the general case; only a number of special cases have been settled.

Cambridge University Press eBooks•Jun 16, 2017•2 citations
With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual information. Leveraging results from random matrix theory, we are able to characterize the achievable ergodic secrecy rates. Based on this characterization, we address the problem of covariance optimization at the transmitter. Our numerical results demonstrate a good match between the large-system approximation and the actual simulated secrecy rates, as well as some interesting features of the precoder optimization.
Security issues in wireless networks have become a subject of growing interest in recent years due to the broadcast nature of wireless channels. In this paper, we investigate secure communication over a multi-antenna wiretap channel in the presence of randomly distributed eavesdroppers. In the fast fading environment, the overall performance of this channel is traditionally characterized by the ergodic secrecy capacity, which, in general, cannot be derived explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation of an achievable ergodic secrecy rate for arbitrary inputs. In addition, we characterize the secrecy rates for practically relevant separate-decoding scheme at the receiver. We validate the proposed large-system approximation through numerical simulations and observe a good match with the actual secrecy rates. Finally, we also analyze some interesting behavior of the secrecy rates in the given scenario depending on the geometry of the nodes.
Wireless security has become an important issue for modern wireless networks. Due to the broadcast nature of wireless channels possibility of eavesdropping the transmission is provided for non-legitimate receivers. In the present paper, we consider a multi-antenna wiretap channel in a fast-fading environment with only statistical channel state information available at the receiver. The overall performance of such channel is characterized by the ergodic secrecy capacity, which, in general, cannot be characterized explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation for the achievable ergodic secrecy rate under arbitrary channel inputs. The obtained large-system approximation matches well with the actual simulated secrecy rates, revealing some interesting behavior of the secrecy rates in the given scenario.
© 2015 IEEE. In this paper, we study the multiple-input multiple-output wiretap channel for simultaneous wireless information and power transfer, in which there is a base station (BS), an information-decoding (ID) user, and an energy-harvesting (EH) user. The messages intended to the ID user is required to be kept confidential to the EH user. Our objective is to design the optimal transmit covariance matrix at the BS for maximizing the ergodic secrecy rate subject to the harvested energy requirement for the EH user exploiting only statistical channel state information at the BS. To this end, we begin by deriving an approximation for the ergodic secrecy rate using large-dimensional random matrix theory and the method of Taylor series expansion. This approximation enables us to derive the asymptotic-optimal transmit covariance matrix that achieves the tradeoff for ergodic secrecy rate and harvested energy. The simulation results are provided to verify the accuracy of the approximation and show that a bigger rate-energy region can be achieved when the Rician factor increases or the path loss exponent decreases. We also show that when the transmit correlation increases or the distance between the eavesdropper and the BS decreases, the harvested energy will be increased, while the achieved ergodic secrecy rate decreases.
We discuss the architecture of wireless multiple-input multiple-output (MIMO) channels with additive white Gaussian noise. The transmission optimization problem over covariance matrix for achieving MIMO channel capacity is reviewed under the assumption that the channel state information (CSI) is available from both the transmitter and the receiver. We also discuss several transmission strategies such as beamforming and water-filling algorithm. The information-theoretic approach to physical-layer security for wireless communications system is discussed. Physical-layer security which is different from cryptographic approach security is achieved by exploiting the physical-layer properties of wireless channel. The principal results and concepts in this field such as equivocation rate and secrecy capacity are reviewed. The wiretap channel model is considered. We mainly discussed the Gaussian MIMO wiretap channel and the methods for obtaining its secrecy capacity. The optimization problem for the secrecy capacity of Gaussian MIMO wiretap channel under total transmit power constraint is discussed. CVX, which is a modeling toolbox for solving convex optimization problems, is reviewed. The precision variable of CVX is also considered. The performances of CVX and Monte Carlo optimization are compared. Differential Evolution algorithm is used to compute the secrecy capacity of Gaussian MIMO wiretap channel. The case of weak eavesdropper is considered and the closed form solution based on the necessary KKT conditions is validated. The algorithm for general cases based on the linear approximation and reformulation of the original optimization problem is also investigated and validated. It has been verified that the lower bound and the upper bound of secrecy capacity can be obtained by such algorithm.
In this paper, we study the multiple-input multiple-output (MIMO) wiretap channel performing simultaneous wireless information and power transfer (SWIPT), where there are a multiple-antenna base station (BS), a multiple-antenna information decoding (ID) user, and a multiple-antenna energy harvesting (EH) user. The messages intended to the ID user need to be kept confidential to the EH user. The channels between BS and users are modeled as fading channels with different spatial correlations and line-of-sight (LoS) components. We assume that only statistical channel state information (CSI) is available at the BS. Our objective is to design the optimal transmit covariance matrix at the BS for maximizing the ergodic secrecy rate subject to the BS power constraint and the harvested energy requirement for the EH user. To this end, we present an approximation for the ergodic secrecy rate by using large dimensional random matrix theory and the method of Taylor series expansion. Based on this, an iterative algorithm is proposed to find the transmit covariance matrix. Simulation results are provided to verify the accuracy of the approximation and the performance of the design.
Secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While the optimality of Gaussian signaling and a general expression for the secrecy capacity have been well established, closed-form solutions for the optimal transmit covariance matrix are known for some special cases only, while the general case remains an open problem. This chapter reviews known closed-form solutions and presents a numerical algorithm for the general case with guaranteed convergence to the global optimum. The known solutions include full-rank and rank-1 cases (which, when combined, provide a complete solution for the case of two transmit antennas), the case of identical right singular vectors for the eavesdropper and legitimate channels, and the cases of weak, isotropic, and omnidirectional eavesdroppers, which also provide lower and upper bounds to the general case. Necessary optimality conditions and a tight upper bound for the rank of the optimal covariance matrix in the general case are discussed. Sufficient and necessary conditions for the optimality of three popular signaling strategies over MIMO channels, namely, isotropic and zero-forcing signaling as well as water-filling over the legitimate channel eigenmodes, are presented. The chapter closes with a detailed description of a numerical globally convergent algorithm to solve the general case, and gives some illustrative examples. Introduction Due to their high spectral efficiency, wireless MIMO (multiple input, multiple output) systems are widely adopted by academia and industry. The broadcast nature of wireless channels stimulated significant interest in their security aspects and the Gaussian MIMO wiretap channel (WTC) has emerged as a popular model to study information theoretic secrecy aspects of wireless systems [1]. A number of results have been obtained for this model, including the proof of optimality of Gaussian signaling [1–4], which is far from trivial and significantly more involved than that of the regular (no wiretap) MIMO channel. Once the functional form of the optimal input is established, the only unknown is its covariance matrix since the mean is always zero. This latter part has not been solved yet in the general case; only a number of special cases have been settled.