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IEEE Wireless Communications Letters

Max-Min Fairness Precoding for Physical Layer Security With Partial Channel Knowledge

Sangmin Lee, Eunsung Choi, Jinseok Choi

Published Jun 13, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1109/lwc.2023.3285797

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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.
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.
In this paper, we consider a sum secrecy spectral efficiency (SE) maximization problem in a downlink rate-splitting multiple access (RSMA) system with multiple antennas. We also assume two types of users: secret users whose private streams require information security and normal users whose private streams do not require security. Due to its max and min operations in the wiretap SE and the SE of the common stream, respectively, which makes the non-convex problem even non-smooth, solving the problem is highly challenging. To deal with the difficulties, we reformulate the optimization problem into an approximated smooth problem using a LogSumExp approach. Then, we identify the first-order optimality condition and develop formulas into a generalized eigenvalue problem. We use a power iteration based algorithm to find the best local optimal solution. Simulations validate the proposed secure RSMA 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.
In this paper, we focus on the physical-layer security of a multiuser cellular downlink system. A multi-antenna base station (BS) communicates with several legitimate users, where a target user is overheard by an eavesdropper in the downlink transmission. We aim at designing linear precoders for the BS to maximize the secrecy rate of target user under the condition that a certain Quality-of- Service (QoS) is guaranteed for the other legitimate users. To solve the non-convex optimization problem, we propose an iterative algorithm to transform the original problem into a sequence of approximate convex problems, which can be solved using interior point method. Simulation results reveal that compared with two other methods dealing with the similar optimization problem in previous works, our proposed method can achieve a higher secrecy rate.
In this paper, we propose a robust and adaptable secure precoding framework designed to encapsulate a intricate scenario where legitimate users have different information security: secure private or normal public information. Leveraging rate-splitting multiple access (RSMA), we formulate the sum secrecy spectral efficiency (SE) maximization problem in downlink multi-user multiple-input multiple-output (MIMO) systems with multi-eavesdropper. To resolve the challenges including the heterogeneity of security, non-convexity, and non-smoothness of the problem, we initially approximate the problem using a LogSumExp technique. Subsequently, we derive the first-order optimality condition in the form of a generalized eigenvalue problem. We utilize a power iteration-based method to solve the condition, thereby achieving a superior local optimal solution. The proposed algorithm is further extended to a more realistic scenario involving limited channel state information at the transmitter (CSIT). To effectively utilize the limited channel information, we employ a conditional average rate approach. Handling the conditional average by deriving useful bounds, we establish a lower bound for the objective function under the conditional average. Then we apply the similar optimization method as for the perfect CSIT case. In simulations, we validate the proposed algorithm in terms of the sum secrecy SE.
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.