An Algorithm for Global Maximization of Secrecy Rates in Gaussian MIMO Wiretap Channels

Loyka, Sergey; Charalambous, Charalambos D.

doi:10.1109/tcomm.2015.2424235

Cited by 49 publications

(85 citation statements)

References 37 publications

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“…The secrecy capacity achieving input distribution over a Gaussian MIMO wiretap channel is proved to be Gaussian [4], [5]. While the optimal input covariance matrix is not available in closed form for the general case, effective numerical algorithms have been developed in [8] and [9] for its computation. As a result, much of the literature on physical layer security focuses on the Gaussian input assumption.…”

Section: (Corresponding Author: Tolga M Duman)mentioning

confidence: 99%

Joint Precoder and Artificial Noise Design for MIMO Wiretap Channels With Finite-Alphabet Inputs Based on the Cut-Off Rate

Aghdam

Duman

2017

IEEE Trans. Wireless Commun.

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Abstract-We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finitealphabet input assumption. We assume that the transmitter has access to the channel coefficients of the legitimate receiver and knows the statistics of the eavesdropper's channel. Accordingly, we propose a secrecy rate maximization algorithm using a gradient descent-based optimization of the precoder matrix and an exhaustive search over the power levels allocated to the AN. We also propose algorithms to reduce the complexities of direct ergodic secrecy rate maximization by: 1) maximizing a cut-off rate-based approximation for the ergodic secrecy rate, simplifying the mutual information expression, which lacks a closedform and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a pergroup precoding-based technique. Our numerical results reveal that jointly optimizing the precoder and the AN outperforms the existing solutions in the literature, which rely on the precoder optimization only. We also demonstrate that the proposed low complexity alternatives result in a small loss in performance while offering a significant reduction in computational complexity.Index Terms-Physical layer security, finite-alphabet inputs, precoding, artificial noise, cut-off rate, MIMO communications.

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Section: (Corresponding Author: Tolga M Duman)mentioning

confidence: 99%

Joint Precoder and Artificial Noise Design for MIMO Wiretap Channels With Finite-Alphabet Inputs Based on the Cut-Off Rate

Aghdam

Duman

2017

IEEE Trans. Wireless Commun.

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“…where We firstly fix Q as a constant and maximize R. Note that when Q is fixed, H B and H E are also fixed so that P1 is reduced to a secrecy capacity optimization problem of general Gaussian MIMO wiretap channel. To solve this problem, we apply the key Theorem 1 in [7] so that the original problem is equivalently transformed to a convexconcave max-min optimization problem. Then, we apply the existing algorithm in [7] which is based on barrier method in combination with Newton method and backtracking line search method to globally optimized R. Note that in [7], the algorithm was developed only based on real-valued channel matrix case.…”

Section: Channel Model and Problem Formulationmentioning

confidence: 99%

Secure MIMO Transmission via Intelligent Reflecting Surface

Dong

Wang

2020

IEEE Wireless Commun. Lett.

191

139

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In this letter, we consider an intelligent reflecting surface (IRS) assisted Guassian multiple-input multiple-output (MIMO) wiretap channel in which a multi-antenna transmitter communicates with a multi-antenna receiver in the presence of a multi-antenna eavesdropper. To maximize the secrecy rate of this channel, an alternating optimization (AO) algorithm is proposed to jointly optimize the transmit covariance R at transmitter and phase shift coefficient Q at IRS by fixing the other as a constant. When Q is fixed, existing numerical algorithm is used to search for global optimal R. When R is fixed, three sucessive approximation to the objective function to surrogate lower bound is applied and minorization-maximization (MM) algorithm is proposed to optimize the local optimal Q. Simulation results have be provided to validate the convergence and performance of the proposed AO algorithm.

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“…Note that the fast fading channel with only statistical CSIT can be verified as a degraded one, if, there exists A and B such that A B for each channel realization, where A and B are the covariance matrices of the equivalent noises at receivers 1 and 2. Then by Proposition 1 in [40] we know that solving the optimal input covariance matrix for a GWTC is a convex problem. For full CSIT cases we can use convex optimization tools to solve it numerically or some partial analytical results can be seen in [40,41], etc.…”

Section: Theorem 6 a Sufficient Condition To Have A Degraded Multiplmentioning

confidence: 99%

“…Then by Proposition 1 in [40] we know that solving the optimal input covariance matrix for a GWTC is a convex problem. For full CSIT cases we can use convex optimization tools to solve it numerically or some partial analytical results can be seen in [40,41], etc.…”

Section: Theorem 6 a Sufficient Condition To Have A Degraded Multiplmentioning

confidence: 99%

“…Under perfect CSIT assumption, in [45] the authors proved that the maximum secrecy capacity coincides with the saddle point of a min-max problem, which is by considering a Sato-type outer bound setting, i.e., Bob additionally knows what Eve knows, in addition to an additional parameter, i.e., a correlation matrix between the noises at Bob and Eve. Based on the min-max description, [40] then developed an algorithm to numerically solve this problem. An analytical solution is still unknown.…”

Section: Other Stochastic Ordersmentioning

confidence: 99%

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Multiuser Channels with Statistical CSI at the Transmitter: Fading Channel Alignments and Stochastic Orders, an Overview

Lin

Jorswieck

2017

Entropy

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Abstract:In this overview paper, we introduce an application of stochastic orders in wireless communications. In particular, we show how to use stochastic orders to investigate the ergodic capacity results for fast fading Gaussian memoryless multiuser channels when only the statistics of the channel state information are known at the transmitters (CSIT). In general, the characterization of the capacity region of multiuser channels with only statistical CSIT is open. To attain our goal, in this work we resort to classifying the random channels through their probability distributions by which we can obtain the capacity results. To be more precise, we derive sufficient conditions to attain some information theoretic channel orders such as degraded and very strong interference by exploiting the usual stochastic order and exploiting the same marginal property. After that, we apply the developed scheme to Gaussian interference channels and Gaussian broadcast channels. We also extend the framework to channels with multiple antennas. Possible scenarios for channel enhancement under statistical CSIT are also discussed. Several practical examples such as Rayleigh fading and Nakagami-m fading, etc., illustrate the application of the derived results.

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An Algorithm for Global Maximization of Secrecy Rates in Gaussian MIMO Wiretap Channels

Cited by 49 publications

References 37 publications

Joint Precoder and Artificial Noise Design for MIMO Wiretap Channels With Finite-Alphabet Inputs Based on the Cut-Off Rate

Joint Precoder and Artificial Noise Design for MIMO Wiretap Channels With Finite-Alphabet Inputs Based on the Cut-Off Rate

Secure MIMO Transmission via Intelligent Reflecting Surface

Multiuser Channels with Statistical CSI at the Transmitter: Fading Channel Alignments and Stochastic Orders, an Overview

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