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IEEE Wireless Communications Letters

Deep Neural Network Based Precoding for Wiretap Channels With Finite Alphabet Inputs

Mücahit Gümüş, Tolga M. Duman

Published Apr 28, 2021• 5 citations
Publisher

Abstract

We consider secure transmission over multi-input multi-output multi-antenna eavesdropper (MIMOME) wiretap channels with finite alphabet inputs. We use a linear precoder to maximize the secrecy rate, which benefits from the generalized singular value decomposition to obtain independent streams and exploits the function approximation abilities of deep neural networks (DNNs) for solving the required power allocation problem. It is demonstrated that the DNN learns the optimal power allocation without any performance degradation compared to the conventional technique with a significant reduction in complexity.

DOI
10.1109/lwc.2021.3076398

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We consider secure transmission over multi-input multi-output multi-antenna eavesdropper (MIMOME) wiretap channels with finite alphabet inputs. We use a linear precoder to maximize the secrecy rate, which benefits from the generalized singular value decomposition to obtain independent streams and exploits the function approximation abilities of deep neural networks (DNNs) for solving the required power allocation problem. It is demonstrated that the DNN learns the optimal power allocation without any performance degradation compared to the conventional technique with a significant reduction in complexity.
In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.
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.
This letter investigates secure transmission design for multiple-input single-output multi-antenna eavesdropper wiretap channels with finite alphabet inputs. With statistical channel state information of the eavesdropper's channel at the transmitter, we utilize an approximated ergodic secrecy rate to reduce the computational complexity. Then we study joint optimization of beamforming design and power control for maximizing the approximated ergodic secrecy rate. We transform the original multi-variable optimization problem into a single-variable optimization problem, which can be solved by 1-D optimization techniques. Numerical examples show that the proposed scheme is superior to the conventional schemes.
In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input-multiple-output-multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush-Kuhn-Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios.
In this paper, we investigate the precoding scheme for multiple-input multiple-output multiple antennas eavesdropper (MIMOME) channels under the constraint of finite-alphabet inputs to ensure secure transmission between the source and the destination in the presence of an eavesdropper. With finite-alphabet inputs, there are no closed-form solutions for mutual information (MI) and its gradient-minimum mean-square error (MMSE) matrix. Therefore traditional precoding schemes based on direct calculation of MI and MMSE matrix through numerical integration involve prohibitive computational burden. To address this problem, this paper first derives asymptotically optimal lower bounds of MI and ergodic MI with which the computational complexity can be significantly reduced compared with the direct computation of MI. With the derived lower bounds, a low-complexity precoding scheme is proposed to maximize the secrecy rate, wherein a gradient descent based algorithm is used to obtain the precoding result. In the low and high signal-to-noise ratio (SNR) regions, we demonstrate that the proposed precoding scheme gives the same result as directly maximizing the secrecy rate, which indicates that the proposed low-complexity precoding scheme is asymptotically optimal.
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. The input covariance matrix that achieves the secrecy capacity is determined. In particular, it is shown that the secrecy capacity of this channel can be achieved by linear precoding. Precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the secrecy capacity, are developed. The secrecy capacity is then compared with the achievable secrecy rate of generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed technique for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.