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IEEE Transactions on Vehicular Technology

Security Performance Analysis for MIMO Systems: From Artificial Noise's Power and Dimension Perspective

Panpan Xu, Zhenling Li, Chunguo Li, Weijie Tan

Published Feb 13, 2025• 1 citation
Publisher

Abstract

This paper analyzes the influence of power and dimension of artificial noise (AN) on security performance of multiple-input multiple-output (MIMO) system with multiple randomly located eavesdroppers. We derive the closed-form expressions of the secrecy outage probability (SOP) and the optimal secrecy capacity by utilizing the irrelevance among transmission channels, and the orthogonality between AN and the basis vectors of the legitimate channel matrix's null space. We use the Poisson point process to determine the number and location of eavesdroppers, then analyze the security performance of the communication system under the 3D channel condition of probability-based line-of-sight (LoS) or non-line-of-sight (NLoS) channel. The simulation results show the following conclusions. When the AN dimension reaches 1/4 highest dimension (i.e., one quarter of the number of transmitting antennae less than one) and the power splitter factor (PSF) falls in the open interval (0.6, 0.9), we can achieve a trade-off between secrecy capacity and design complexity.

DOI
10.1109/tvt.2025.3541682

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This paper analyzes the influence of power and dimension of artificial noise (AN) on security performance of multiple-input multiple-output (MIMO) system with multiple randomly located eavesdroppers. We derive the closed-form expressions of the secrecy outage probability (SOP) and the optimal secrecy capacity by utilizing the irrelevance among transmission channels, and the orthogonality between AN and the basis vectors of the legitimate channel matrix's null space. We use the Poisson point process to determine the number and location of eavesdroppers, then analyze the security performance of the communication system under the 3D channel condition of probability-based line-of-sight (LoS) or non-line-of-sight (NLoS) channel. The simulation results show the following conclusions. When the AN dimension reaches 1/4 highest dimension (i.e., one quarter of the number of transmitting antennae less than one) and the power splitter factor (PSF) falls in the open interval (0.6, 0.9), we can achieve a trade-off between secrecy capacity and design complexity.
In this paper, the dimension of artificial noise (AN) and corresponding transmit power in multiple-input multiple-output single-eavesdropper channels are investigated. It is widely known that AN is transmitted in the null space of the channel matrix of a legitimate link between a source and a destination. Here, the secrecy outage probabilities are derived for various dimensions of AN. Recognizing the fact that the secrecy outage performance depends on the dimension of the AN, an optimization problem is formulated to maximize the secrecy rate under a secrecy outage constraint. The optimal power splitting factor between the information and AN signals is then derived. Furthermore, the asymptotic behaviors of the optimal power splitting factor and the resulting maximum secrecy rate are examined. Through asymptotic analyses and numerical verification, it is formally shown that the full-dimension AN maximizes the secrecy rate under a secrecy outage constraint. Because the complexity of AN design increases as the dimension of the AN increases, we can achieve a tradeoff between secrecy performance and AN design complexity by determining the dimension of the AN. This study can provide a guideline of AN design specifically pertaining to the dimension of the AN.
The inherent openness of wireless networks exposes them to eavesdropping threats. In dense urban environments, signal propagation is frequently characterized by the keyhole effect, which causes channel rank deficiency and cascaded fading, challenging the assumptions of conventional multiple-input multiple-output (MIMO) physical layer security. This paper investigates the secrecy performance of MIMO multiple-antenna-eavesdropper (MIMOME) systems over keyhole channels with independent legitimate and eavesdropper links. We analyze the secrecy performance under three progressive scenarios: perfect CSI without artificial noise (AN), perfect CSI with AN-aided transmission, and practical imperfect CSI with AN. Specifically, we derive closed-form asymptotic expressions for the secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime using Meijer G-functions and Gauss hypergeometric functions, from which the secrecy diversity order and secrecy array gain are explicitly extracted. The analytical results reveal that AN injection successfully restores the secrecy diversity order from zero to one, while imperfect CSI causes AN leakage that leads to ASR saturation and an SOP floor. The derived asymptotic expressions are verified by Monte Carlo simulations. Our findings provide theoretical guidelines by quantifying the trade-off between AN suppression capabilities and self-interference in cascaded fading environments.
In massive multiple-input multiple-output (MIMO) systems, idle users may passively overhear the signal transmitted to the intended user, known as internal eavesdroppers. In order to improve the secrecy performance, artificial noise (AN) is used jointly with maximum ratio transmission (MRT) precoding. Since the idle users can be anywhere in the cell, we investigate the secrecy outage probability for the legitimate user by taking an expectation over the positions of all internal eavesdroppers. Furthermore, according to the secrecy performance of the legitimate user in the given location, we define a new concept Secrecy Area centered on the base station (BS) where all the legitimate users satisfy the secrecy quality-of-service (QoS) requirements i.e. secrecy outage probability. Then, in order to achieve the maximum Secrecy Area under the given secrecy QoS requirements, we derive the optimal power allocation factor for AN, which is irrelevant to the channel state information (CSI) of both the legitimate user and the eavesdropper. The analytical and simulation results show that, by AN-assisted MRT precoding, the secrecy performance is significantly improved and the Secrecy Area can be efficiently enlarged with a modest increase of the transmit power.
Artificial noise (AN) can be used to confuse eavesdroppers in a physical layer security system. One of the main issues concerned in AN schemes is how to improve secrecy capacities. Most existing AN schemes were proposed based on an assumption that the number of transmit antennas t is larger than that of receiver antennas r, such that they can utilize all r eigen-subchannels of a multiple-output multiple-input (MIMO) system to send messages, and use remaining t - r null spaces for transmitting AN signals. These AN signals null out legitimate receivers and degrade eavesdropper channels. However, transmitting messages in all eigen-subchannels is not always a good strategy. In particular, when the number of transmit antennas is constrained or even smaller than those of receivers, the secrecy capacities of legitimate receivers will be impaired significantly if using all eigen-subchannels for message transmission. To improve secrecy capacity, we propose an AN scheme where messages are encoded in s (which is a variable) strongest eigen-subchannels based on ordered eigenvalues of Wishart matrices, while AN signals are generated in remaining t - s spaces. We derive the average secrecy capacity of a single-user MIMO wiretap channel in the presence of an eavesdropper with multiple antennas. We show that the numerical results are in a good agreement with simulation results. The secrecy capacity of the proposed AN scheme can be improved by approximately 20% ~ 40% if compared with existing AN schemes.
This paper investigates artificial noise (AN) injection along the temporal and spatial dimensions of a legitimate system to secure its transmissions from potential eavesdropping. In particular, we consider a multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system in the presence of a multiple-antenna passive eavesdropper and characterize both the secrecy rate and average secrecy rate of the legitimate system. We assume that the legitimate transmitter knows the full channel state information (CSI) of the links connecting it with its legitimate receiver but does not know the instantaneous CSI of the passive eavesdropper. Closed-form expressions for the secrecy rate and average secrecy rate are derived for the asymptotic case of a large number of transmit antennas. We compare the degrading effects of spatial and temporal AN on the eavesdropper's rate. We also investigate the power allocation between the data and the AN and the power allocation between the spatial and the temporal AN. An upper bound on the secrecy rate loss due to the presence of the eavesdropper is also derived, and computer simulations are carried out to demonstrate the performance of our proposed AN scheme.
Physical layer security approaches enable secure message transmission without upper layer data encryption and thus draw intensive attention recently years. Following this topic, this paper proposes a novel approach to improve the security of multiple-input single-output (MISO) communications links in the presence of non-colluding passive Poisson distributed eavesdroppers. In the proposed approach, it is assumed that the channel state information (CSI) of the main channel is known and that of the eavesdropper channel is unknown. Through beamforming vectors, the transmitter transmits information signal to the legitimate receiver along with artificial noise (AN) to confuse the eavesdroppers. Secrecy outage probability (SOP) is adopted to describe the secrecy performance, and based on it, security region (SR) is used from the perspective of space to illustrate the security. In obtaining the SOP of the described transmission link, stochastic geometry theory is adopted. It is shown that the stochastic geometry theory provides a powerful tool in obtaining a solution of SOP. Furthermore, the secrecy performance between transmitting approaches with AN and without AN is compared. The SR is plotted and the factors impacting security are analyzed accordingly.