Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2010.12938 · IEEE Transactions on Vehicular Technology

Comments on “Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels”

Mahdi Khojastehnia, Sergey L. Loyka

Published Oct 28, 2020• 1 citation
arXivHTMLPDF

Abstract

Several gaps and errors in “Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels” by Fang et al. are identified and corrected. While accommodating these corrections, a rigours proof is given that the successive convex approximation algorithm of Fang et al. for secrecy rate maximization (SRM) does generate an increasing and bounded sequence of true secrecy rates and hence converges. It is further shown that its convergence point is a KKT point of the original SRM problem and, if the original problem is convex, this convergence point is globally-optimal, which is not necessarily the case in general. An interlacing property of the sequences of the true and approximate secrecy rates is established.

DOI
10.1109/tvt.2020.3034529

Related papers

Comments on ‘Precoding for secrecy rate maximisation in cognitive MIMO wiretap channels’

Mahdi Khojastehnia, Sergey L. Loyka

Several gaps and errors in Fang et al. (2015) are identified. Their corrections as well as new results are reported. After these corrections, the successive convex approximation algorithm in Fang et al. (2015) is shown to generate an increasing, converging sequence of secrecy rates, which, for a degraded channel, converges to its secrecy capacity. The failure of the popular convex solver CVX to maximise secrecy rate is illustrated. Alternative algorithms are pointed out.

Electronics Letters•Jun 5, 2020•5 citations

Comments on “AN-Aided Secrecy Precoding for SWIPT in Cognitive MIMO Broadcast Channels”

Mahdi Khojastehnia, Sergey L. Loyka

Several gaps and errors in (B. Fanget al.,“AN-aided secrecy precoding for SWIPT in cognitive MIMO broadcast channels,”IEEE Commun. Lett.,vol. 19, no. 9, pp. 1632–1635, Sep. 2015) are identified. Their corrections as well as new results are reported. After these corrections in the analysis, the successive convex approximation algorithm for secrecy rate maximization with artificial noise is shown to generate an increasing, converging sequence of secrecy rates. For a degraded channel, (i) this sequence converges to the maximum secrecy rate of the channel, and (ii) it is optimal to use no artificial noise. For a reversely-degraded channel, the maximum achievable secrecy rate is zero.

IEEE Communications Letters•Jan 10, 2020•0 citations

Energy-efficient secrecy precoding for general MIMOME wiretap channels

Bing Fang, Zuping Qian, Zhong Wei +1 more

In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 1, 2015•2 citations

Precoding for secrecy rate maximisation in cognitive MIMO wiretap channels

Bing Fang, Zuping Qian, Zhong Wei +1 more

The problem of physical layer security in a cognitive MIMO wiretap channel is studied. The problem is formulated as a secrecy rate maximisation (SRM) problem, and solved by a successive convex approximation (SCA) method. With the SCA method, the non‐convex part of the SRM problem is approximated by its first‐order Taylor expansion. Then, relying on solving a series of convexified optimisation problems, an iterative precoding algorithm is developed.

Electronics Letters•Oct 1, 2015•2 citations

AN-Aided Secrecy Precoding for SWIPT in Cognitive MIMO Broadcast Channels

Bing Fang, Zuping Qian, Zhong Wei +1 more

In this letter, we study the secrecy precoding problem for simultaneous wireless information and power transfer (SWIPT) in a cognitive multiple-input multiple-output (MIMO) broadcast channel. We adopt an artificial noise (AN)-aided precoding scheme and formulate the problem as a secrecy rate maximization (SRM) problem, which is subject to both an interference power constraint imposed to protect the primary user (PU) and an energy harvesting constraint required by the secondary energy receiver (SER). Since the formulated SRM problem constitutes a difference convex (DC)-type programming problem, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the SRM problem can be locally linearized to its first-order Taylor expansion. Then, relying on solving a series of convexified optimization problems, an iterative precoding algorithm is developed. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can achieve a near-optimal performance with guaranteed convergence.

IEEE Communications Letters•Sep 1, 2015•54 citations

Joint Precoding and Artificial Noise Design for MU-MIMO Wiretap Channels

Eunsung Choi, Mintaek Oh, Jinseok Choi +3 more

Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.

arXiv:2207.09823•IEEE Transactions on Communications•Dec 7, 2022•31 citations
Several gaps and errors in “Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels” by Fang et al. are identified and corrected. While accommodating these corrections, a rigours proof is given that the successive convex approximation algorithm of Fang et al. for secrecy rate maximization (SRM) does generate an increasing and bounded sequence of true secrecy rates and hence converges. It is further shown that its convergence point is a KKT point of the original SRM problem and, if the original problem is convex, this convergence point is globally-optimal, which is not necessarily the case in general. An interlacing property of the sequences of the true and approximate secrecy rates is established.
Several gaps and errors in (B. Fanget al.,“AN-aided secrecy precoding for SWIPT in cognitive MIMO broadcast channels,”IEEE Commun. Lett.,vol. 19, no. 9, pp. 1632–1635, Sep. 2015) are identified. Their corrections as well as new results are reported. After these corrections in the analysis, the successive convex approximation algorithm for secrecy rate maximization with artificial noise is shown to generate an increasing, converging sequence of secrecy rates. For a degraded channel, (i) this sequence converges to the maximum secrecy rate of the channel, and (ii) it is optimal to use no artificial noise. For a reversely-degraded channel, the maximum achievable secrecy rate is zero.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.
In this letter, we study the secrecy precoding problem for simultaneous wireless information and power transfer (SWIPT) in a cognitive multiple-input multiple-output (MIMO) broadcast channel. We adopt an artificial noise (AN)-aided precoding scheme and formulate the problem as a secrecy rate maximization (SRM) problem, which is subject to both an interference power constraint imposed to protect the primary user (PU) and an energy harvesting constraint required by the secondary energy receiver (SER). Since the formulated SRM problem constitutes a difference convex (DC)-type programming problem, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the SRM problem can be locally linearized to its first-order Taylor expansion. Then, relying on solving a series of convexified optimization problems, an iterative precoding algorithm is developed. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can achieve a near-optimal performance with guaranteed convergence.
Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.