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arXiv:2312.14791 · IEEE Wireless Communications Letters

EMF-Constrained Artificial Noise for Secrecy Rates With Stochastic Eavesdropper Channels

Stefan Roth, Aydin Sezgin

Published Jun 19, 2024• 5 citations
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Abstract

An information-theoretic confidential communication is achievable if the eavesdropper has a degraded channel compared to the legitimate receiver. In wireless channels, beamforming and artificial noise can enable such confidentiality. However, only distribution knowledge of the eavesdropper channels can be assumed. Moreover, the transmission of artificial noise can lead to an increased electromagnetic field (EMF) exposure, which depends on the considered location and can thus also be seen as a random variable. Hence, we optimize the$\varepsilon $-outage secrecy rate under a$\delta $-outage exposure constraint in a setup, where the base station (BS) is communicating to a user equipment (UE), while a single-antenna eavesdropper with Rayleigh distributed channels is present. Therefore, we calculate the secrecy outage probability (SOP) in closed-form. Based on this, we convexify the optimization problem and optimize the$\varepsilon $-outage secrecy rate iteratively. Numerical results show that for a moderate exposure constraint, artificial noise from the BS has a relatively large impact due to beamforming, while for a strict exposure constraint artificial noise from the UE is more important.

DOI
10.1109/lwc.2024.3416613

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An information-theoretic confidential communication is achievable if the eavesdropper has a degraded channel compared to the legitimate receiver. In wireless channels, beamforming and artificial noise can enable such confidentiality. However, only distribution knowledge of the eavesdropper channels can be assumed. Moreover, the transmission of artificial noise can lead to an increased electromagnetic field (EMF) exposure, which depends on the considered location and can thus also be seen as a random variable. Hence, we optimize theε\varepsilon ε-outage secrecy rate under aδ\delta δ-outage exposure constraint in a setup, where the base station (BS) is communicating to a user equipment (UE), while a single-antenna eavesdropper with Rayleigh distributed channels is present. Therefore, we calculate the secrecy outage probability (SOP) in closed-form. Based on this, we convexify the optimization problem and optimize theε\varepsilon ε-outage secrecy rate iteratively. Numerical results show that for a moderate exposure constraint, artificial noise from the BS has a relatively large impact due to beamforming, while for a strict exposure constraint artificial noise from the UE is more important.
This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.
The artificial noise (AN) aided beamforming design in the MISOME (multiple-input, single-output, multiple-eavesdropper) wiretap channel is studied from the perspective of secrecy outage. Unlike many existing works which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper's antennas from the perspective of secrecy outage. The power allocation problem is also studied and the closed-form optimal solution is obtained. It is found that the increase in the eavesdropper's antenna number is equivalent to requiring a smaller SOP.
This paper investigates cooperative security in wireless networks, where a source (Alice) intends to transmit a confidential message to a legitimate destination (Bob), with the help of a cooperative jammer (Charlie), coexisting with multiple passive eavesdroppers (Eves). In particular, by assuming knowledge of Bob's perfect channel state information (CSI) but only Eves’ statistical CSIs, secrecy beamforming with artificial noise (AN) is utilized for secure transmission, and cooperative jamming (CJ) is explored to further enhance secrecy. We first derive an accurate closed-form expression for the secrecy outage probability (SOP), and establish the condition under which positive secrecy rate is achievable. Then, we provide a secure transmit design for maximizing the SOP constrained secrecy rate. Moreover, based on a strict mathematical analysis, we characterize the impact of the main channel quality and the number of Eves on transmit design and secrecy performance. Specifically, optimal power allocation ratio between the information-bearing signal and the AN signal increases as the main channel quality improves, and decreases with the number of Eves. Numerical results confirm that our design achieves performance improvement in terms of both secrecy rate and secure energy efficiency, as compared to the approach without CJ.
This paper investigates the physical layer security in a multiple-input-single-output multicast channel, where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. We consider transmitting some artificial noise (AN) along with the information-bearing signal to improve secrecy. To find the optimal AN design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem. For solving this problem, we adopt a novel transformation of the intractable SOP constraint and establish an efficient algorithm which solves the transformed problem to global optimality. We also propose a low-complexity refinement method to reduce the conservatism incurred by the transformation and an efficient algorithm to find a suboptimal solution when the information-bearing signal is transmitted using single-stream beamforming. Our solution is found to be a valuable generalization of the traditional null-space AN scheme. According to our simulation results, when the number of receivers is less than that of transmit antennas, distributing AN uniformly in the null space of the legitimate channel vectors is near-optimal. When there is no valid null space, transmitting AN will interfere with some legitimate receivers, and the secrecy performance can also be improved with carefully designed AN.
In this paper, we study the secure multi-antenna transmission with artificial noise (AN) under slow fading channels coexisting with randomly located eavesdroppers. We provide a comprehensive secrecy performance analysis and system design/optimization under a stochastic geometry framework. Specifically, we first evaluate the secrecy outage performance, and derive a closed-form expression for the optimal power allocation ratio of the information signal power to the total transmit power that minimizes the secrecy outage probability (SOP). Subject to a SOP constraint, we then propose a dynamic parameter transmission scheme (DPTS) and a static parameter transmission scheme (SPTS) to maximize secrecy throughput, and provide explicit solutions on the optimal transmission parameters, including the wiretap code rates, the on-off transmission threshold and the power allocation ratio. Our results give new insight into secure transmission designs. For example, secrecy rate is a concave function of the power allocation ratio in DPTS, and AN plays a significant role under SOP constraints and in dense eavesdropper scenarios. In SPTS, transmission probability is a concave function of the power allocation ratio, and secrecy throughput is a quasi-concave function of the secrecy rate. Numerical results are demonstrated to validate our theoretical analysis.
The secrecy rate maximization with the artificial noise (AN) aided beamforming for the multipel-input-single-output (MISO) wiretap channel is addressed in this paper under the constraint of secrecy outage probability. The channel state information (CSI) of the main channel is assumed to be perfectly known while the CSI of the eavesdropper is modeled as a complex Gaussian random vector. The generalized AN scheme where the AN is not constrained to be orthogonal to the information-bearing signal is considered. The complete solution to the maximum achievable secrecy rate and the corresponding optimal power allocation between the information-bearing signal and the AN is obtained without making any approximation of the secrecy outage probability constraint. The result shows that the optimal AN is always orthogonal to the information-bearing signal.