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IEEE Transactions on Vehicular Technology

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

Sungyu Kim, Eunsung Choi, Mintaek Oh, Jinseok Choi

Published Jan 10, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tvt.2025.3525836

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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 propose secure max-min fairness (MMF) precoding for a downlink multi-antenna system with multiple users and eavesdroppers. Since the problem is non-convex and non-smooth and partial channel knowledge is assumed, it is highly challenging to solve. To resolve the difficulties, we first reformulate the problem with conditional average rates, allowing to exploit the partial channel knowledge. Then, we derive the original problem as an approximate smoothing problem using a LogSumExp approach. We identify the first-order optimality condition and cast it to a generalized eigenvalue problem. Solving the problem via a power iteration offers the best local optimal solution. Simulations validate the proposed secure-MMF precoding method.
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.
In this work, a robust artificial noise (AN) aided transmit method is proposed for a multicast multiple-input single-output (MISO) system in the presence of multiple single-antenna eavesdroppers. With the imperfect covariance-based channel state information (CSI), we aim to minimize the transmit power at the transmitter under the multicast secrecy rate constraint and the maximum transmit power constraint. The resulting optimization problem involves the joint optimization of the beamforming vector and AN covariance matrix. After using the semidefinite relaxation (SDR) technique, we derive the exact reformulation of the original optimization through the Lagrange duality. Then this non-convex problem is transformed into a one-variable optimization problem, which can be handled by solving a series of semidefinite programs (SDPs). Simulation results demonstrate the effectiveness of the proposed robust transmit method.
Secure transmission is becoming an essentially important aspect in visible light communication (VLC). In this paper, we investigate the designs of artificial noise (AN)-aided precoding to improve physical layer security in a multi-user single eavesdropper wiretap VLC channels. The AN-aided precoding is designed to solve the max-min fairness signal- to-interference-plus-noise ratio (SINR) problem among users in two different scenarios: unknown and known eavesdropper's channel state information (CSI) at the transmitter. In the former case, we adopt the traditional null- space AN scheme and then study the impact of the AN power on the fairness performance. In the case of known eavesdropper's CSI, the AN-aided precoding is designed in such a way that keeps the SINR of the eavesdropper below a predefined threshold. Numerical results show that in both cases, the design could significantly degrade the quality of the eavesdropper's channel, thus enhancing communication secrecy.
In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.