Probability Of Non-zero Secrecy Capacity Research Articles

Secrecy Performance Analysis of UAV Assisted Relay Transmission for Cognitive Network With Energy Harvesting

The unmanned aerial vehicle (UAV) assisted transmission can significantly improve the spectrum efficiency and coverage of the wireless communication network. The paper proposed a cooperative secrecy transmission mechanism, which can take advantage of transmitter signal of primary user (PU) as a dedicated radio frequency (RF) source with decode and forward (DF) UAV selection and energy harvesting (EH) under cognitive network. Specifically, the transmitting signal of PU in the cognitive network can be viewed and used as energy to drive secondary user (SU) nodes and multi-relay nodes to send signals. It was worth noting that the DF UAV relay may bring about the unexpected noise and decrease the received signal to noise ratio (SNR), therefore, the multiple UAV assisted relays selected with secrecy capacity maximization criteria under cognitive network was proposed and investigated in detail, where the destination node equipped with multiple antennas and adopted the optimal antenna selection receiver. Moreover, By using the function analysis method, the closed expressions of the system secrecy outage probability (SOP) and the probability of non-zero secrecy capacity were calculated and derived accurately. Furthermore, the asymptotic expressions of the UAV assisted relay system under the large SNR cases were analyzed in detail, where the expressions of secrecy diversity order and secrecy diversity gain of the UAV assisted relay cognitive system were obtained thoroughly. Simulation results verified the effectiveness of the proposed mechanism and the correctness of the calculation.

On the Physical Layer Security of Underlay Relay-Aided Device-to-Device Communications

In this paper, we study the underlay relay-aided Device-to-Device (D2D) communications to improve the physical layer (PHY) security of the cellular network. We propose a cooperative scheme, whereby the D2D pair, in return of being allowed to share the spectrum band of the cellular network, serves as a friendly jammer, through its multiple-input multiple-output relay, to degrade the wiretapped signal at an eavesdropper. This paper aims to show that spectrum sharing is advantageous for both D2D communications and cellular networks with respect to reliability and robustness for the former, and the physical layer security enhancement for the latter. To assess the proposed cooperative system model, closed-form expressions for the D2D outage probability, the secrecy outage probability, and the probability of non-zero secrecy capacity are derived. More importantly, the benefits due to the cooperation scheme are verified through numerical and simulation results.

Physical layer security in shotgun cellular systems over correlated/independent shadow fading channels

The shotgun cellular systems (SCSs) (modeling, generally, a dense cellular or wireless data network deployment and non-ideal regular hexagonal grid with site-acquisition difficulties, variable traffic load) are wireless communication systems with randomly placed base stations (BSs) over the entire plane according to a stochastic (e.g., Poisson) point process in n dimensions (n = 1, 2, and 3). Due to the good performance and the importance of the SCSs in today’s communications, the physical layer security of these systems is practically of importance, specifically, in more realistic channel propagation models. In this paper, by assuming that the channel coefficients are known at the receiver, we analyze the performance of the physical layer security for the classic Wyner’s three-node model in the SCSs over correlated/independent log-normal shadow fading channels. For this purpose, first, we calculate the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in an SCS. Then, the average secrecy capacity (ASC), the probability of non-zero secrecy capacity (PNSC), the secure outage probability (SOP), and the lower bound of SOP (LSOP) are obtained, and also, their approximated closed-form expressions are derived. Finally, analytical results are validated numerically.

Secure 3D Mobile UAV Relaying for Hybrid Satellite-Terrestrial Networks

In this paper, we propose a novel decode-and-forward (DF)-based secure 3D mobile unmanned aerial vehicle (UAV) relaying for hybrid satellite-terrestrial networks (HSTNs) in the presence of an aerial eavesdropper lying around a serving UAV relay in a circular plane. Herein, we adopt a stochastic mixed mobility (MM) model for mobilizing the UAV relays in a 3D cylindrical cell with a ground user equipment (UE). We consider the deployment of eavesdropper under the cases: (a) the eavesdropper is located at certain fixed distance around a serving UAV relay; (b) the eavesdropper is located uniformly random around the relay. By considering the opportunistic closest-, uniform-, and maximum-signal-to-noise ratio (maximum-SNR) UAV relay selection (URS) strategies, we analyze the secrecy performance of the considered HSTN in terms of probability of non-zero secrecy capacity (PNZSC) and secrecy outage probability (SOP). In particular, we derive exact PNZSC and SOP for the closest-URS (CURS) and uniform-URS (UURS). While, we derive analytical lower and upper bounds on PNZSC and SOP for maximum-SNR URS (MURS). We further carry out the corresponding asymptotic SOP analysis to assess the secrecy diversity order and coding gain of aforementioned URS strategies. Simulations are performed to corroborate the analysis.

Multiple Eavesdropper-Based Physical Layer Security in SIMO System With Antenna Correlation

In this paper, we investigate the impact of antenna correlation on secure transmission in a multi-eavesdropper single-input multiple-output (SIMO) system, where the receiver and eavesdroppers are equipped with correlated antennas. Based on the practical passive eavesdropping system, the new closed-form expressions of secrecy outage probability (SOP) and non-zero secrecy capacity probability are derived to explore the effect of antenna correlation on the system with multiple eavesdroppers. To further analyze the secrecy performance of the investigated system, we theoretically derive the expression of asymptotic SOP to clearly show the diversity order and array gain. Finally, Monte Carlo simulations verify the effectiveness of our theoretical results.

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

In this paper, secrecy performance is studied for the classic Wyner's wiretap channel which follows Generalised Gamma (GG) distribution. In order to evaluate the secrecy performance, we derived the exact Average Secrecy Rate (ASR) and closed form expression for the Probability of Non-Zero Secrecy Capacity (PNZSC) for different fading parameters corresponding to main and eavesdropper's channels. The results are then simulated and verified. It has been observed that the ASR of GG fading increases with the increase in the fading constant of the main channel.

Joint Obstacle Avoidance and 3D Deployment for Securing UAV-Enabled Cellular Communications

Unmanned aerial vehicle (UAV) can enable cellular mobile communications in unexpected or temporary scenarios, but there are information security problems raised in such applications. Physical layer security is now emerging as a promising alternative technology to realize secrecy in wireless communications. In the UAV-enabled communication systems, the fully controllable mobility of UAV provides new design degrees of freedom for enhancing physical layer security. This paper investigates an UAV-enabled cellular communication system where an ultralow-altitude UAV is equipped with a base station to serve a ground user in the presence of an eavesdropper. The probability of non-zero secrecy capacity is maximized subject to the airspace and obstacle constraints by adaptively optimizing the UAV's three-dimensional positions. The optimization problem is simplified by equivalent transformation and then solved by semidefinite relaxation (SDR). Two approaches termed as eigenvector approximation and random sampling are addressed to extract an approximation solution for the primal problem from the solution obtained by the SDR. Simulation results show that there is a slight difference between the probability of non-zero secrecy capacity achieved by the two solution approximation approaches.

Physical-Layer Security Enhancement via Relay-Aided D2D Communications Underlaying Cellular Networks

In this paper, we propose a relay-assisted device-to-device (D2D) communication as an underlay in a cellular network, where two sequential best relay nodes based on different selection criteria are chosen. Novel analytical expressions of the secrecy outage probability (SOP) and the probability of nonzero secrecy capacity (PNSC) are derived to evaluate the secrecy performance of the cellular network. In addition, we derive a simple and explicit approximation of the SOP in the high signal-to-noise ratio (SNR) to gain some insights on how various system parameters affect the aforementioned secrecy performance. Also, for the sake of comparison, the analytical SOP expression when only the cellular network exists, i.e., without the interference of the D2D communication, is obtained. Furthermore, to assess the usefulness of the cooperation between the D2D communication and the cellular network, we derive an analytical expression for the mutual outage probability (MOP) which represents the true outage probability across both the cellular and D2D networks. An asymptotic analysis of the MOP in the high SNR regime is obtained and the diversity order is derived. Finally, our proposed mathematical framework is compared with Monte-Carlo simulations to verify the accuracy of the derivations.

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

Secrecy Performance of Cooperative Cognitive Radio Networks Under Joint Secrecy Outage and Primary User Interference Constraints

In this paper, we investigate the secrecy performance of a Cooperative Cognitive Radio Network (CCRN) in the presence of an eavesdropper (EAV). The secondary users (SUs) are subject to three constraints which include peak transmit power level and interference limitation with respect to the primary user (PU) as well as secrecy outage constraints due to the EAV. Secrecy outage is achieved when the EAV cannot decode the targeted signal, but communications in the secondary network is still possible (non-zero capacity exists). Approximation expressions of the secrecy outage probability and the probability of non-zero secrecy capacity are derived to evaluate the secrecy performance. Monte Carlo simulations are provided to examine the accuracy of the derived approximation expressions. Based on this, power allocation policies for the SUs are derived, satisfying all the constraints while maximizing the secrecy performance as well as the quality of service performance of the secondary network. It can be concluded that with knowledge of the channel state information (CSI) of the EAV it is possible to calculate the optimal value for the secrecy outage threshold of the secondary user (SU) which in turn allows maximizing the secrecy performance. Most interestingly, our numerical results illustrate that the secrecy performance of the system is much improved when the parameters obtained using the CSI of the EAV are calculated optimally. Thence, the system can adjust the power allocation so that no eavesdropping occurs even without reducing quality of service (QoS) performance compared to a network without any EAV.

Physical layer security in cooperative amplify‐and‐forward relay networks over mixed Nakagami‐ m and double Nakagami‐ m fading channels: performance evaluation and optimisation

The authors investigate the secrecy performance of a cooperative relaying network, wherein a fixed source communicates with a fixed destination via an amplify-and-forward mobile relay in the presence of a passive mobile eavesdropper. They assume that the source-to-relay channel and relay-to-destination channel experience Nakagami-m fading, whereas relay-to-eavesdropper link follows double Nakagami-m fading. Under such a mixed fading environment, they derive the novel tight closed-form expressions for the secrecy outage probability (SOP), probability of non-zero secrecy capacity, and intercept probability of the considered system. They also deduce the asymptotic secrecy outage and intercept probability expressions in the high signal-to-noise ratio regime to highlight the impact of fading parameters and channel conditions on the secrecy diversity order. It is shown that the system can achieve secrecy diversity order of min( m SR , m RD ) in terms of SOP, and m RD in terms of intercept probability, where m SR and m RD represent the fading severity parameters between source and relay and between relay and destination, respectively. They also formulate and investigate analytically two optimisation problems, namely, optimal relay location with fixed power allocation and optimal power allocation with fixed relay location, to minimise the system SOP. They verify analytical findings via numerical and simulation results.

Improving Physical Layer Security of Cellular Networks Using Full-Duplex Jamming Relay-Aided D2D Communications

This paper investigates the physical layer security and data transmission in cellular networks with inband underlay Device-to-Device (D2D) communications, where there is no direct link between D2D users. We propose to apply full-duplex (FD) transmission and dual antenna selection at the D2D relay node. The relay node can simultaneously act as a friendly jammer to improve the secrecy performance of the cellular network while enhancing the D2D communication data transmission. This is an appealing and practical scheme where spectrum sharing is beneficial for the D2D and cellular networks in terms of reliability enhancement and security provisioning, respectively. The practical scenario, where the eavesdropper is passive, is considered. The eavesdropper uses either selection combining or maximal ratio combining to combine the wiretapped signals of the cellular network. The secrecy performance of the cellular network is analyzed, and closed-form expressions for the secrecy outage probability and the probability of non-zero secrecy capacity are derived. We show that increasing the number of FD jamming antennas enhances the secrecy performance of the cellular network. A closed-form expression of the D2D outage probability is also provided. Simulation and numerical results are provided to verify the efficiency of the proposed scheme and to validate the accuracy of the derived expressions.

On Physical-Layer Security of FDA Communications Over Rayleigh Fading Channels

In this paper, we investigate frequency diverse array (FDA) antenna for physical-layer security and analyze the system performance (i.e., average secrecy capacity and secrecy outage performance) over independent but not necessarily identical distributed Rayleigh fading channels. A single-antenna multiple-channel receiver structure is proposed to address the time-variance property of FDA antenna. The transmitter allocates part of its power to send artificial noise (AN) so as to ensure the security of communications, such that the channels other than the desired receiver’s are degraded. Specifically, we derive the closed-form expressions for average secrecy capacity, probability of nonzero secrecy capacity, and secrecy outage probability, respectively. The correctness of the proposed analysis is corroborated via simulations. Furthermore, the corresponding asymptotic expressions for average secrecy capacity and secrecy outage probability in high signal-to-interference-plus-noise ratio (SINR) regime are also provided, respectively, to have deep insights into the performance of the considered system. Numerical results show that the FDA communications significantly outperforms the phased-array (PA) scheme in range dimension for secure communication.

Secrecy Characteristics With Assistance of Mixture Gamma Distribution

Considering the fact that the mixture gamma (MG) distribution is a general model that can be used to elaborate most well-known distributions, including small-scale, large-scale, and composite fadings, this letter studies the security issue when the received signal-to-noise ratios (SNRs) follow MG distributions. Closed-form expressions for secrecy metrics including the secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZ), and the average secrecy capacity (ASC), are derived. Monte-Carlo simulations are presented to corroborate the accuracy of our derived results. Our derived secrecy metrics provide a general and unified analysis framework for the quick evaluation of the secrecy issue over wireless channels, even when the main channel and wiretap channel are subject to different wireless channels.

Physical-Layer Security for Frequency Diverse Array Communication System Over Nakagami-m Fading Channels

In this paper, we propose frequency diverse array (FDA) antenna for artificial-noise (AN) aided secure communication over independent but not necessarily identical distributed Nakagami-m fading channels, where a multichannel receiver structure is adopted to address the time-variance property of FDA beampattern. Closed-form expressions for probability of nonzero secrecy capacity, secrecy outage probability, and system secrecy throughput are derived to characterize the performance of the considered system. All derivations are verified by simulation results, which show that the proposed security scheme achieves higher probability of nonzero secrecy capacity, lower secrecy outage probability, and delivers superior secrecy throughput comparing with the conventional phased-array communication scheme. This implies that FDA provides superiority for physical-layer security communication in the range dimension, whereas in the angle dimension, we show that the performance comparison between the two schemes significantly relates to the angle difference of the desired and eavesdropper direction.

Optimal Placement of Low-Altitude Aerial Base Station for Securing Communications

Because of its cost-effective and on-demand deployment, low-altitude aerial base stations (BSs) are capable of providing emergency communication services in many scenarios. This letter investigates the security issue in emergency communications where the aerial BS is deployed optimally to serve ground users in the presence of an eavesdropper. We aim to maximize the probability of non-zero secrecy capacity to improve the possibility of physical-layer security transmission via the optimal placement of the aerial BS. The resulting nonconvex optimization problem will be simplified based on its geometric properties and equivalent transformation. The simplified problem will then be solved by using semidefinite relaxation. Numerical results show that the optimal placement of the aerial BS can significantly improve the probability of non-zero secrecy capacity.

On Physical Layer Security Over Fox's $H$-Function Wiretap Fading Channels

Most of the well-known fading distributions, if not all of them, could be encompassed by the Fox's H-function fading. Consequently, we investigate the physical layer security over Fox's H-function fading wiretap channels, in the presence of non-colluding and colluding eavesdroppers. In particular, for the non-colluding scenario, closed-form expressions are derived for the secrecy outage probability (SOP), the probability of non-zero secrecy capacity, and the average secrecy capacity. These expressions are given in terms of either univariate or bivariate Fox's H-function. In order to show the effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-m, α - μ, Fisher-Snedecor (F-S) F, and extended generalized-K. Our tractable results are not only straightforward and general, but also feasible and applicable, especially the SOP, which is usually limited to the lower bound in the literature due to the difficulty of deriving closed-from analytical expressions. For the colluding scenario, a super eavesdropper equipped with maximal ratio combining (MRC) or selection-combining (SC) schemes is characterized. The lower bound of SOP and exact PNZ are thereafter derived with closed-form expressions in terms of the multivariate Fox's H-function. In order to validate the accuracy of our analytical results, Monte Carlo simulations are subsequently conducted for the aforementioned fading channels. One can observe that for the former non-colluding scenario, we have perfect agreement between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results. On the contrary, the SOP and PNZ of colluding eavesdropper is greatly degraded with the increase of the number of eavesdroppers. Also, the so-called super eavesdropper with MRC is much powerful to wiretap the main channel than the one with SC.

Secrecy Performance of TAS/SC-Based Multi-Hop Harvest-to-Transmit Cognitive WSNs Under Joint Constraint of Interference and Hardware Imperfection.

In this paper, we evaluate the secrecy performance of multi-hop cognitive wireless sensor networks (WSNs). In the secondary network, a source transmits its data to a destination via the multi-hop relaying model using the transmit antenna selection (TAS)/selection combining (SC) technique at each hop, in the presence of an eavesdropper who wants to receive the data illegally. The secondary transmitters, including the source and intermediate relays, have to harvest energy from radio-frequency signals of a power beacon for transmitting the source data. Moreover, their transmit power must be adjusted to satisfy the quality of service (QoS) of the primary network. Under the joint impact of hardware imperfection and interference constraint, expressions for the transmit power for the secondary transmitters are derived. We also derive exact and asymptotic expressions of secrecy outage probability (SOP) and probability of non-zero secrecy capacity (PNSC) for the proposed protocol over Rayleigh fading channel. The derivations are then verified by Monte Carlo simulations.

Secrecy Analysis of Modify-and-Forward Relaying With Relay Selection

This paper investigates the physical-layer security of the modify-and-forward (MF) protocol in multi-relay and multieavesdropper networks. Three relay selection critera are developed according to the channel state information (CSI) acquisition. CriterionI requires the CSI of all main channels for relay selection. Criteria II and III rely only on the CSI of the source-relay and relay-destination channels, respectively. We derive the exact secrecy outage probability (SOP), probability of nonzero secrecy capacity, and the ergodic secrecy rate in the closed forms. The €-outage secrecy capacity is also evaluated. Asymptotic analysis of the SOP explicitly reveals that the secrecy diversity order of criterionI depends on the total number of relays, whereas those of criteriaII and III are 2 and 1, respectively. The probability of nonzero secrecy capacity asymptotically decreases with the SNR of the wiretap channel as the eavesdropper is close to the source and relays. CriterionI is always superior to criteriaII and III in terms of the ergodic secrecy rate and €-outage secrecy capacity. Simulations results also demonstrated that the €-outage secrecy capacity deteriorates as the SNR of the eavesdropper's channel increases.

Secrecy Performance of Land Mobile Satellite Systems With Imperfect Channel Estimation and Multiple Eavesdroppers

The inherent broadcast nature has exposed the land mobile satellite (LMS) communication systems to severe security threats in both the civil and military applications. This paper investigates the secrecy performance of a Shadowed-Rician fading multi-antenna LMS communication system with imperfect channel estimation, which consists of a satellite, a legitimate receiver and a cluster of unauthorized eavesdroppers who want to overhear the confidential message. Specifically, the analytical expressions for the probability of non-zero secrecy capacity are derived in terms of the Meijer-G functions, which provide an efficient means to evaluate the secrecy performance of the system. Then, both the exact and asymptotic secrecy outage probability expressions of the considered system are obtained. Furthermore, based on the simple asymptotic secrecy outage probability, we can reveal two key performance metrics, namely, the secrecy diversity order and secrecy array gain. Finally, simulation results are carried out to validate the theoretical results and show the superiority of employing multiple antennae in enhancing the secrecy performance for LMS communication systems. Our findings suggest that the secrecy diversity order only depends on the number of antennas at the legitimate receiver, and is independent of the imperfect channel estimation and the shadowing severities of both the main and eavesdropper channels.