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:2207.09823 · IEEE Transactions on Communications

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

Eunsung Choi, Mintaek Oh, Jinseok Choi, Jeonghun Park, Namyoon Lee, Naofal Al‐Dhahir

Published Dec 7, 2022• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/tcomm.2022.3227284

Related papers

Joint and Simultaneous Optimization of Artificial Noise-aided Precoding for Secure Communications

Eunsung Choi, Mintaek Oh, Jin-Seok Choi +3 more

The joint design of secure precoding and artificial noise (AN) transmission scheme is promising to improve secrecy performance. However, in downlink multi-user multiple-input multiple-output (MU-MIMO) systems with multiple eavesdroppers, joint design of secure precoding and AN structure involves several challenges: an objective function is non-convex and non-smooth, and a precoding matrix and AN matrix have different design principles. Classically, to jointly design precoding and AN covariance matrix, an alternating optimization approach is used which has limitations in terms of the secrecy rate performance since it does not offer joint and simultaneous optimization of the precoding and AN covariance matrices. In this paper, we propose a novel optimization framework that optimizes the precoder and the AN covariance matrix jointly and simultaneously to maximize the secrecy rate. First, we approximate the objective function to a tractable non-convex form. Next, we derive the first-order optimality condition by leveraging the nonlinear eigenvalue problem (NEP) form. Finally, we utilize an efficient technique with low computational complexity for identifying the major eigenvector of the NEP which corresponds to the best stationary point. Simulations illustrate that the proposed methods enhance the secrecy rate performance compared to the existing secure precoding methods.

Globecom•Dec 4, 2023•0 citations

Artificial Noise-Aided Max-Min Fairness Secrecy Precoding With Partial Wiretap Channel Knowledge

Sungyu Kim, Eunsung Choi, Mintaek Oh +1 more

We propose an artificial noise (AN)-aided max-min fairness (MMF) secure precoding algorithm. The algorithm jointly optimizes precoders and AN covariance matrix without alternation for a multiuser multiple-input multiple-output system with multiple colluding eavesdroppers. The formulated AN-aided MMF problem involves several challenges such as non-convexity, non-smoothness, coupled optimization variables, and partial wiretap channel state information at a transmitter (CSIT). To address the challenges, we first consider the perfect wiretap CSIT and approximate the reformulated problem as a smooth problem. Then, we derive the first-order optimality condition and interpret it as a nonlinear eigenvalue problem. Finally, we adopt a power iteration method to solve the condition. To extend the algorithm to the partial wiretap CSIT scenario, we reformulate the problem with an average wiretap rate by deriving an approximate lower bound of the rate. This enables us to exploit the partial channel knowledge. Subsequently, we propose the algorithm for the partial wiretap CSIT. Simulations validate the proposed methods.

IEEE Transactions on Vehicular Technology•Jan 10, 2025•2 citations

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

Sina Rezaei Aghdam, Tolga M. Duman

We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finite-alphabet 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 closed-form and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a per-group 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.

IEEE Transactions on Wireless Communications•Mar 31, 2017•51 citations

Secrecy rate maximization for MIMO Gaussian wiretap channels with multiple eavesdroppers via alternating matrix POTDC

Jens Steinwandt, Sergiy A. Vorobyov, Martin Haardt

In this paper, we consider the problem of optimizing the transmit co-variance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convex difference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the co-variance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.

IEEE International Conference on Acoustics Speech and Signal Processing•May 1, 2014•18 citations

On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels

Arash Khabbazibasmenj, Maksym A. Girnyk, Sergiy A. Vorobyov +2 more

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

arXiv:1411.0103•Nov 1, 2014•8 citations

On the optimal precoding for MIMO Gaussian wire-tap channels

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

•Jan 1, 2013•0 citations
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.
The joint design of secure precoding and artificial noise (AN) transmission scheme is promising to improve secrecy performance. However, in downlink multi-user multiple-input multiple-output (MU-MIMO) systems with multiple eavesdroppers, joint design of secure precoding and AN structure involves several challenges: an objective function is non-convex and non-smooth, and a precoding matrix and AN matrix have different design principles. Classically, to jointly design precoding and AN covariance matrix, an alternating optimization approach is used which has limitations in terms of the secrecy rate performance since it does not offer joint and simultaneous optimization of the precoding and AN covariance matrices. In this paper, we propose a novel optimization framework that optimizes the precoder and the AN covariance matrix jointly and simultaneously to maximize the secrecy rate. First, we approximate the objective function to a tractable non-convex form. Next, we derive the first-order optimality condition by leveraging the nonlinear eigenvalue problem (NEP) form. Finally, we utilize an efficient technique with low computational complexity for identifying the major eigenvector of the NEP which corresponds to the best stationary point. Simulations illustrate that the proposed methods enhance the secrecy rate performance compared to the existing secure precoding methods.
We propose an artificial noise (AN)-aided max-min fairness (MMF) secure precoding algorithm. The algorithm jointly optimizes precoders and AN covariance matrix without alternation for a multiuser multiple-input multiple-output system with multiple colluding eavesdroppers. The formulated AN-aided MMF problem involves several challenges such as non-convexity, non-smoothness, coupled optimization variables, and partial wiretap channel state information at a transmitter (CSIT). To address the challenges, we first consider the perfect wiretap CSIT and approximate the reformulated problem as a smooth problem. Then, we derive the first-order optimality condition and interpret it as a nonlinear eigenvalue problem. Finally, we adopt a power iteration method to solve the condition. To extend the algorithm to the partial wiretap CSIT scenario, we reformulate the problem with an average wiretap rate by deriving an approximate lower bound of the rate. This enables us to exploit the partial channel knowledge. Subsequently, we propose the algorithm for the partial wiretap CSIT. Simulations validate the proposed methods.
We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finite-alphabet 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 closed-form and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a per-group 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.
In this paper, we consider the problem of optimizing the transmit co-variance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convex difference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the co-variance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.