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IEEE Wireless Communications Letters

ASAP: Adversarial Learning Based Secure Autoprecoder Design for MIMO Wiretap Channels

Xinyao Wang, Zhong Zheng, Zesong Fei

Published Jun 29, 2022• 3 citations
Publisher

Abstract

To avoid the non-convex and complicated secrecy rate optimization in the multiple-input and multiple-output (MIMO) system, deep learning (DL) is introduced in the secure precoder design recently. However, existing works neglect the eavesdropper with learning capacity, which is constructed by neural networks (NNs) and capable of enhancing its receiver NN according to the optimal secure transmitter. In this letter, we propose an adversarial learning-based secure autoprecoder (ASAP) for the MIMO wiretap channels, where the modulation and the precoder are jointly optimized and adversarially trained with the eavesdropping receiver. Numerical results verify the convergence of the ASAP method, which enables an optimal trade-off between the information secrecy and reliability. Moreover, joint optimization is especially important against the evolved eavesdropper.

DOI
10.1109/lwc.2022.3187089

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To avoid the non-convex and complicated secrecy rate optimization in the multiple-input and multiple-output (MIMO) system, deep learning (DL) is introduced in the secure precoder design recently. However, existing works neglect the eavesdropper with learning capacity, which is constructed by neural networks (NNs) and capable of enhancing its receiver NN according to the optimal secure transmitter. In this letter, we propose an adversarial learning-based secure autoprecoder (ASAP) for the MIMO wiretap channels, where the modulation and the precoder are jointly optimized and adversarially trained with the eavesdropping receiver. Numerical results verify the convergence of the ASAP method, which enables an optimal trade-off between the information secrecy and reliability. Moreover, joint optimization is especially important against the evolved eavesdropper.
A novel precoding method based on supervised deep neural networks is introduced for the multiple-input multiple-output Gaussian wiretap channel. The proposed deep learning (DL)-based precoding learns the input covariance matrix through offline training over a large set of input channels and their corresponding covariance matrices for efficient, reliable, and secure transmission of information. Furthermore, by spending time in offline training, this method remarkably reduces the computation complexity in real-time applications. Compared to traditional precoding methods, the proposed DL-based precoding is significantly faster and reaches near-capacity secrecy rates. DL based precoding is also more robust than transitional precoding approaches to the number of antennas at the eavesdropper. This new approach to precoding is promising in applications in which delay and complexity are critical.
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.
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.
We consider the optimal precoding design under power constraint for the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, and an eavesdropper, each equipped with arbitrary number of antennas. The transmitter has access to full channel state information (CSI) of the legitimate link and eavesdropper link. Such an optimization problem is non-convex and an analytical optimal solution is difficult to obtain. In this paper, by resorting to the majorization theory, we develop a theoretical upper bound on the secrecy capacity which is proved useful in evaluating existing sub-optimal methods. Our analysis shows that, given that the number of antennas at the eavesdropper is no less than that of the transmitter, the generalized singular value decomposition (GSVD)-based method proposed in [1], albeit generally non-optimal, provides a near-optimal solution to the MIMO wiretap precoding design in the high signal-to-noise ratio (SNR) regime. Numerical results are provided to corroborate our theoretical results.
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.