On the Zero-Outage Secrecy-Capacity of Dependent Fading Wiretap Channels

It is known that for a slow fading Gaussian wiretap channel without channel state information at the transmitter and with statistically independent fading channels, the outage probability of any given target secrecy rate is non-zero, in general. This implies that the so-called zero-outage secrecy capacity (ZOSC) is zero and we cannot transmit at any positive data rate reliably and confidentially. When the fading legitimate and eavesdropper channels are statistically dependent, this conclusion changes significantly. Our work shows that there exist dependency structures for which positive zero-outage secrecy rates (ZOSR) are achievable. In this paper, we are interested in the characterization of these dependency structures and we study the system parameters in terms of the number of observations at legitimate receiver and eavesdropper as well as average channel gains for which positive ZOSR are achieved. First, we consider the setting that there are two paths from the transmitter to the legitimate receiver and one path to the eavesdropper. We show that by introducing a proper dependence structure among the fading gains of the three paths, we can achieve a zero secrecy outage probability (SOP) for some positive secrecy rate. In this way, we can achieve a non-zero ZOSR. We conjecture that the proposed dependency structure achieves maximum ZOSR. To better understand the underlying dependence structure, we further consider the case where the channel gains are from finite alphabets and systematically and globally solve the ZOSC. In addition, we apply the rearrangement algorithm to solve the ZOSR for continuous channel gains. The results indicate that the legitimate link must have an advantage in terms of the number of antennas and average channel gains to obtain positive ZOSR. The results motivate further studies into the optimal dependency structures.

Secrecy Capacity of Time Reversal Beamforming for Multi-User MIMO System under Spatial Correlation

In this paper, for strengthening the security of wireless transmission system, the time reversal (TR) beamforming method is proposed for the downlink of multi-user MIMO system with multiple users who potentially act as eavesdroppers. We develop a multi-input, single-output, multi-eavesdropper (MISOME) wiretap channel model in which Rayleigh fading and spatial correlation are taken into account. Using the proposed model, we further analyze the confidentiality provided by TR beamforming and we use achievable secrecy rates as our performance metrics. In particular, we derive novel closed-formed expressions for the average secrecy-SINR and the mean secrecy sum-rate in order to characterize the influences of propagation conditions on network secrecy metrics. These expressions provide deeper insights into the impact of network interference on communication confidentiality. We find that TR beamforming can deliver the maximum secrecy capacity potential in uncorrelated Rayleigh channels and achieve perfect confidential communication without any extra secrecy cost. On the other hand, even weak inter-user correlation may cause a significant loss of achievable secrecy sum-rate and therefore result in high secrecy cost. But benefiting more from larger signal bandwidth and rich-scattering environment, the TR beamforming technique is still an attractive and cost-effective solution for low-power indoor applications.

An overview of generic tools for information-theoretic secrecy performance analysis over wiretap fading channels

Physical layer security (PLS) has been proposed to afford an extra layer of security on top of the conventional cryptographic techniques. Unlike the conventional complexity-based cryptographic techniques at the upper layers, physical layer security exploits the characteristics of wireless channels, e.g., fading, noise, interference, etc., to enhance wireless security. It is proved that secure transmission can benefit from fading channels. Accordingly, numerous researchers have explored what fading can offer for physical layer security, especially the investigation of physical layer security over wiretap fading channels. Therefore, this paper aims at reviewing the existing and ongoing research works on this topic. More specifically, we present a classification of research works in terms of the four categories of fading models: (i) small-scale, (ii) large-scale, (iii) composite, and (iv) cascaded. To elaborate these fading models with a generic and flexible tool, three promising candidates, including the mixture gamma (MG), mixture of Gaussian (MoG), and Fox’s H-function distributions, are comprehensively examined and compared. Their advantages and limitations are further demonstrated via security performance metrics, which are designed as vivid indicators to measure how perfect secrecy is ensured. Two clusters of secrecy metrics, namely (i) secrecy outage probability (SOP), and the lower bound of SOP; and (ii) the probability of nonzero secrecy capacity (PNZ), the intercept probability, average secrecy capacity (ASC), and ergodic secrecy capacity, are displayed and, respectively, deployed in passive and active eavesdropping scenarios. Apart from those, revisiting the secrecy enhancement techniques based on Wyner’s wiretap model, the on-off transmission scheme, jamming approach, antenna selection, and security region are discussed.

E - Capacity - Equivocation Region of Wiretap Channel

One of the problems of information - theoretic security concerns secure communication over a wiretap channel. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). We introduce and investigate the E - capacity - equivocation region and the E - secrecy capacity function for the wiretap channel, which are, correspondingly, the generalizations of the capacity - equivocation region and secrecy - capacity studied by Csiszár and Körner (1978). The E - capacity equivocation region is the closure of the set of all achievable rate - reliability and equivocation pairs, where the rate - reliability function represents the optimal dependence of rate on the error probability exponent (reliability). By analogy with the notion of E - capacity, we consider the E - secrecy capacity function that for the given E is the maximum rate at which the message can be transmitted being kept perfectly secret from the wiretapper.

Secrecy-Capacity-Optimization-Artificial-Noise in Large-Scale MIMO: Ergodic Lower Bound on Secrecy Capacity and Optimal Power Allocation

The security of wireless information transmission in large-scale multi-input and multioutput (MIMO) is the focus of research in wireless communication. Recently, a new artificial noise—SCO-AN which shows no orthogonality to the channel, is proposed to overcome the shortcomings of traditional artificial noise. In the previous research, the optimization function of SCO-AN is not convex, and its extremum cannot be obtained. Usually, nonconvex optimization algorithms or iterative relaxation algorithms are used to get the maximum value of the optimization objective function. Nonconvex optimization algorithms or iterative relaxation algorithms are greatly affected by the initial value, and the extremum cannot be obtained by a nonconvex optimization algorithm or iterative relaxation algorithm. In this paper, we creatively apply the strong law of large numbers to obtain the optimal value of the optimization function of SCO-AN under the condition of large-scale MIMO: the strong law of large numbers is applied to obtain the ergodic lower bound (ELB) expression of SC for SCO-AN. The power allocation (PA) problem of the SCO-AN system is discussed. We use a statistical method to get the formula for calculating the optimal power distribution coefficient of the SCO-AN system. The transmitter can use the optimal power ratio of PA to distribute the transmitted power without using the PA algorithm. The effect of imperfect channel state information is discussed. Through simulation, we found that more power should be generated for SCO-AN if the channel estimation is imperfect and the proposed method can achieve better security performance in the large-scale MIMO system.

Cascaded κ-μ Fading Channels with Colluding and Non-Colluding Eavesdroppers: Physical-Layer Security Analysis

In this paper, the physical-layer security for a three-node wiretap system model is studied. Under the threat of multiple eavesdroppers, it is presumed that a transmitter is communicating with a legitimate receiver. The channels are assumed to be following cascaded κ-μ fading distributions. In addition, two scenarios for eavesdroppers’ interception and information-processing capabilities are investigated: colluding and non-colluding eavesdroppers. The positions of these eavesdroppers are assumed to be random in the non-colluding eavesdropping scenario, based on a homogeneous Poisson point process (HPPP). The security is examined in terms of the secrecy outage probability, the probability of non-zero secrecy capacity, and the intercept probability. The exact and asymptotic expressions for the secrecy outage probability and the probability of non-zero secrecy capacity are derived. The results demonstrate the effect of the cascade level on security. Additionally, the results indicate that as the number of eavesdroppers rises, the privacy of signals exchanged between legitimate ends deteriorates. Furthermore, in this paper, regarding the capabilities of tapping and processing the information, we provide a comparison between colluding and non-colluding eavesdropping.