Artificial Noise Schemes Based on MIMO Technology in Secure Cellular Networks
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Keywords
MIMO Technology Physical Layer Security Average Secrecy Rate Instantaneous Secrecy Capacity Private CapacitySynonyms
Definition
Cellular communications and networks are particularly vulnerable to eavesdropping attacks due to the opened and broadcasting nature of wireless channels. Due to the rapid development of cellular networks and wireless business, the security issue has attracted a lot of attention. Physical layer security takes the advantages of channel randomness nature of transmission media to achieve communication confidentiality, which is the most important and interesting topic of privacy communication technologies. Artificial noise (AN) or jamming signals with MIMO technologies are supposed to implement physical layer security and enhance secrecy capacities in cellular networks, where AN signals along with confidential data confuse potential eavesdroppers via utilizing orthogonal spaces provided by transmit antennas. In these AN-based schemes, message streams were sent in a multiplexing mode via all eigen-subchannels (positive eigenvalue channels) at desired directions, and the AN signals can be transmitted to the null spaces (zero eigenvalue channels) of desired directions, so that they do not affect the desired user, while eavesdropper channels are degraded with a high probability. This chapter introduces a physical layer security review, covering the information theory and physical layer security schemes based on MIMO technologies, and provides an overview on the state-of-the-art works on the AN-based scheme along with conclusions and future research directions.
Historical Background
The origin of physical layer security research can be traced back to Wyner’s definition of an information-theoretic secrecy capacity (Wyner, 1975), which is a maximum message transmission rate in confidential communications. Compared to conventional cryptography that works to ensure all involved entities to load proper and authenticated cryptographic information, physical layer security technologies perform confidentiality functions without considering about how those security protocols are executed. In other words, it does not require to implement any extra security schemes or algorithms on other layers above the physical layer. In addition, the physical layer has the same confidentiality level with the one-time pad, which ensures its security performance. The concept of physical layer security has become more popular with the help of MIMO technologies, because these emerging technologies can improve the secrecy capacity massively via utilizing extra orthogonal spaces provided by multiple antennas.
Information Theory
In the last two decades, researchers have developed a significant amount of mathematical theories, such as secrecy capacity characterization, wiretap coding designs, wireless fading managements, etc. And the advancements in cellular technologies have improved physical layer security significantly, by exploring spatial diversities and multiplexing gains with the help of multi-antennas technologies.
Physical Layer Security Schemes Based on MIMO Technologies
From the traditional communication viewpoints, improving the link quality of the main channel is one of the most feasible approaches to improve the secrecy capacities with existing installations of cellular networks, because most of the cellular wireless communication technologies can improve the channel spectrum utilization, and if the eavesdropping channel spectrum utilization is unchanged, these traditional wireless communication technologies will undoubtedly improve the secrecy capacities. However, this viewpoint has a great security risk, i.e., the secrecy capacities are small if the eavesdropper has a better channel quality than the desired users. Therefore, current research insists on another viewpoint that jointly uses more degree of freedom of main channels and artificial randomness to protect messages while reduces the quality of eavesdropping channels. Prospectively, the randomness of multipath fading of a MIMO channel is stronger than a single channel. Multiplexing technologies of MIMO are promising ways to enhance the degree of freedom of main channels. And AN signals can interfere with eavesdroppers while they are sent into the null spaces of desired directions.
As in Fig. 1a, unitary beamforming techniques use unitary matrices, semi-unitary matrices, or unitary vectors as transmit precoding, which is similar with traditional beamforming technologies of cellular networks. Unitary beamforming techniques send a message stream via multi-antennas to make it as close to the main channel direction as possible. ZF beamforming is shown in Fig. 1b, which is a secure beamforming technology based on ZF precoding, where the message stream is transmitted to a desired receiver via a shifted beamforming direction, which is orthogonal to the eavesdropper’s channel. The illustrative diagram of CVX-based precoding can be seen in Fig. 1c. The problem of optimizing secrecy capacities is usually non-convex in MIMO systems, but Newton methods or Lagrangian dual transformations can be used to trap it in a local maximum problem and address the transmit covariance matrix optimization based on convex optimization tools. AN signals can be transmitted to the null spaces of desired directions, so that they do not affect the desired user, while an eavesdropper’s channel is degraded with a high probability, as in Fig. 1d. This AN-based precoding exploits a fraction of the transmit power to send artificially generated noise signals, so the power for transmitting messages will be reduced.
AN-based schemes have been seen as promising methods because this type of techniques has two advantages. Firstly, there are no requirements on the condition of better main channels. Secondly, when the number of transmit antennas is larger the number of the eavesdroppers, the main channel state information (CSI) and precoding matrices of security schemes can be broadcasted to both legitimate receivers and eavesdroppers. We do not need to worry about the leakage of key precoding messages. More details of the second advantage can be seen in Liu et al. (2017b).
Artificial Noise Schemes
The section will introduce a general AN-based model, which is first provided in Liu et al. (2017b). Assuming t is the number of transmit antennas, messages are encoded in s (which is a variable) strongest eigen-subchannels based on ordered eigenvalues of Wishart matrices (HH^{†} or H^{†}H, here, H is the main channel CSI matrix), while AN signals are generated in remaining t − s eigen-subchannels. This scheme treats the number of eigen-subchannels for message streams, i.e., s, as an optimization objective that can be leveraged to optimize secrecy capacities.
General AN-Based Model
In this AN-based scheme, there are s (s ≤ t) message-sending eigen-subchannels, which are selected by Alice based on the CSI feedback from Bob. More specifically, Alice performs SVD of \({\mathbf {H}}^\dagger \mathbf {H}\in \mathbb {C}^{t\times t}\) in a preprocessor, whose output is a unitary matrix \(\mathbf {U}\in \mathbb {C}^{t\times t}\), its Hermitian transpose form \({\mathbf {U}}^{\dagger }\in \mathbb {C}^{t\times t}\), and a diagonal matrix \(\boldsymbol {\varLambda }\in \mathbb {R}^{t\times t}\), which consists of positive and zero eigenvalues of H^{†}H. Then, Alice generates a message precoding matrix \(\mathbf {B} \in \mathbb {C}^{t \times s}\), whose columns are the eigenvectors corresponding to the first to the sth largest eigenvalues of H^{†}H, and an AN precoding matrix \(\mathbf {Z} \in \mathbb {C}^{ t\times d}\) (s + d = t), whose columns are the eigenvectors of the remaining eigenvalues of H^{†}H.
Theorem 1
The AN signal can be eliminated at Bob if and only if [HB]^{†}HZ = 0 (Liu et al.,2017b).
Theorem 2
The AN signal cannot be eliminated at Eve if and only if t > e, [HB]^{†}H_{e}Z ≠ 0, and [H_{e}B]^{†}H_{e}Z ≠ 0 (Liu et al.,2017b).
Secrecy Metric
Secrecy metrics with their conditions
Measures | Symbols | Conditions |
---|---|---|
Instantaneous secrecy capacity | C_{s} | H_{e} is available and optimal input distribution. |
Average secrecy capacity | \(\tilde {C}_s\) | H_{e} is unavailable and optimal input distribution |
Instantaneous secrecy rate | R_{s} | H_{e} is available and Gaussian distribution input |
Average secrecy rate | \(\tilde {R}_s\) | H_{e} is unavailable and Gaussian distribution input |
Instantaneous Secrecy Capacity
Average Secrecy Capacity
Instantaneous Secrecy Rate
Average Secrecy Rate
Correlated Matrices
Simulations
Simulation results are provided to investigate joint impacts of the number of antennas and the number of selected message-sending eigen-subchannels on the average secrecy rates.
Conclusion and Further Work
Physical layer security will play a critical role in the future security architecture of cellular communications. This research should keep competing with cryptography and quantum communications, which are believed to be the three major security architectures for cellular communication systems. AN-based schemes are seen as promising methods and now have produced a raft of fascinating and important results. However, these AN-based schemes are optimal only under the condition of that the number of transmit antennas is larger than eavesdropper antennas. When the number of transmitted antennas is constrained or even smaller than that of eavesdropper antennas, AN-based schemes cannot get positive secrecy capacities or rates. This motivates us to design a better AN-based scheme. In addition, the secrecy capacity (rate) quantization is a great challenge in AN-based schemes. Without perfect CSI of eavesdroppers, it is hard for encoders to calculate instantaneous secrecy capacities or rates. And the influence of fading does not allow us to use a simple AWGN or Rayleigh channel model to calculate a secrecy rate. It seems that we need to investigate main and wiretap fading channels that belong to other models of cellular communications. At last, power allocation in cellular networks should be investigated further, because power allocation problems are usually non-convex ones with a lot of cellular users.
Appendix
Lemma 1 (Proved in Gupta and Nagar 1999)
where \(s\in \mathbb {R}\) and t ≥ s.
Key Applications
Artificial noise (AN) schemes based on MIMO technologies can be applied to various cellular scenarios. For example, Massive MIMO systems have an enormous number of antennas, which offer more degrees of freedom for wireless channels, and a more secure performance in terms of secrecy capacities and the number of AN beamforming. The small call base stations deployed as cooperative jammers in cellular networks can be used to provide well-designed AN signals. In addition, the long-term evolution advanced (LTE-A) system supports device to device (D2D) communications, which is defined as the direct communications between two mobile users via shared radio resources with cellular users. D2D interference caused by the shared radio resources can be seen as AN signals to interfere with the illegitimate eavesdropper.
Cross-References
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