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IEEE Transactions on Information Forensics and Security

Secrecy Capacity Analysis of Artificial Noisy MIMO Channels—An Approach Based on Ordered Eigenvalues of Wishart Matrices

Yiliang Liu, Hsiao‐Hwa Chen, Liangmin Wang

Published Nov 9, 2016• 44 citations
Publisher

Abstract

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.

DOI
10.1109/tifs.2016.2627219

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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.
Recent research on physical security of wireless systems focus on artificial noise aided security. The main metric for analysis of such systems is the secrecy capacity of the system. Most of the AN schemes proposed in recent research are based on an hypothesis that the number of transmit antennas is larger than that of the receiver antennas. Under this assumption the system can utilize all eigen-subchannels, equal to number of receiver antennas, of a MIMO system to send messages, and use remaining null spaces for transmitting AN signals. These AN signals null out at the legitimate receivers and degrade illegitimate receiver's channels. However, this strategy can significantly impair the secrecy capacity of the system if number of transmit antennas is constrained or even smaller than number of receive antennas. Recently, a new strategy has been proposed, 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 spaces. In this paper, this strategy has been extended to Rician channels. The transmitter-receiver link is supposed to be effected by Rician fading while the illegitimate link is experiencing Rayleigh fading and consequently the secrecy capacity of such system is computed.
Recent research on the physical layer security of wireless systems focuses on artificial noise (AN) aided security. The main metric for analysis of such systems is the secrecy capacity of the system. Most of the AN schemes proposed in recent research are based on a hypothesis that the number of transmit antennas is larger than that of the receive antennas. Under this assumption, the system can utilize all eigensubchannels, equal to the number of the receive antennas, to send secret messages. The remaining null spaces are used for transmitting AN signals. These AN signals null out at the legitimate receivers and degrade illegitimate receiver's channels. However, this strategy can significantly impair the secrecy capacity of the system if the number of transmit antennas is constrained or even smaller than the number of receive antennas. Recently, a new strategy has been proposed, 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 spaces. This paper extends this strategy to Rician channels using the complex non-central Wishart distribution. A closed form expression for secrecy capacity of such system is computed using majorization theory. Performance of a MIMO communication system in Rician fading environment is simulated and effect of the Rician factor on secrecy capacity is studied. The same approach is then extended to decode and forward relay network. Secrecy capacity of the said network is computed, and the effect of AN is studied using the same methodology.
The existing investigations on artificial noise (AN) security systems assumed that only null spaces are used to send AN signals, and all eigen-subchannels should be used to transmit messages. Our previous work proposed an AN scheme that allocates some of eigen-subchannels to transmit AN signals for improving secrecy rates. Nevertheless, our previous work considered only uncorrelated MIMO Rayleigh fading channels. In fact, the correlations among antennas exist in realistic scattering channel environments. In this paper, we extend our previous AN scheme to spatially correlated Rayleigh fading channels at both legitimate receiver and eavesdropper sides and derive an exact theoretical expression for the ergodic secrecy rate of the AN scheme, along with an approximate analysis. Both numerical and simulation results show that the proposed AN scheme offers a higher ergodic secrecy rate than the existing schemes, revealing a fact that the correlation among eavesdropper's antennas can potentially improve the secrecy rate of an MIMO system.
In a multiple-input multiple-output (MIMO) wiretap channel system, it has been shown that artificial noise can be transmitted in the null space of the main channel to guarantee the secrecy at the intended receiver. Previous formulas for MIMO asymptotic capacity assume that all channel eigenmodes will be utilized. However, optimizing over possible antenna configurations requires partitioning the available eigenmodes. With only some eigenmodes used for signal transmission, finding an exact closed-form asymptotic solution is, in general, intractable. We present a large-scale MIMO approximation with eigenmode partitioning, accurate for realistic numbers of antennas, and with greatly reduced computational complexity.
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.
We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.