Probability Of Non-zero Secrecy Capacity Research Articles

Secrecy Performance of Satellite Wiretap Channels With Multi-User Opportunistic Scheduling

This letter investigates the secrecy performance of a satellite wiretap channel with multi-user opportunistic scheduling. By considering some practical effects, such as satellite multi-beam pattern and path loss, and assuming that the satellite channel undergoes Shadowed-Rician fading with the channel parameters being integer, we derive closed-form expressions of the probability of non-zero secrecy capacity, the secrecy outage probability and the average secrecy capacity for the satellite wiretap channels. Numerical results confirm the correctness and effectiveness of the secrecy performance analysis.

Physical layer secrecy performance analysis of multi-user hybrid satellite-terrestrial relay networks

This paper investigates the secrecy performance of a downlink multi-user amplify-and-forward hybrid satellite-terrestrial relay network (HSTRN) with opportunistic scheduling of terrestrial users. By considering Shadowed-Rician fading for satellite link and Nakagami-m fading for terrestrial links, we derive accurate and asymptotic expressions for secrecy outage probability (SOP). Based on the asymptotic behaviour of SOP expression at high signal-to-noise ratio regime, we illustrate practical insights on the achievable diversity order of the system. Subsequently, we also deduce the expression for probability of non-zero secrecy capacity. Finally, numerical and simulation results are provided to vindicate our analysis and to show the impact of various key channel/system parameters such as shadowing severity and number of users on the physical layer secrecy performance of HSTRNs.

On the Secrecy Performance of Land Mobile Satellite Communication Systems

In this paper, we investigate the secrecy performance against eavesdropping of a land mobile satellite (LMS) system, where the satellite employs the spot beam technique, and both the terrestrial user and eavesdropper are equipped with multiple antennas and utilize maximal ratio combining to receive the confidential message. Specifically, in terms of the availability of the eavesdropper’s CSI at the satellite, we consider both passive (Scenario I) and active (Scenario II) eavesdropping. For Scenario I where the eavesdropper’s channel state information (CSI) is unknown to the satellite, closed-form expressions for the probability of non-zero secrecy capacity and secrecy outage probability are derived. Furthermore, expressions for the asymptotic secrecy outage probability are also presented to reveal the secrecy diversity order and array gain of the considered system. For Scenario II where the eavesdropper’s CSI is available at the satellite, novel expressions for the exact and asymptotic average secrecy capacity are obtained. Based on a simple asymptotic formula, we can characterize the high signal-to-noise ratio (SNR) slope and high SNR power offset of the LMS systems. Finally, simulations are provided to validate our theoretical analysis and show the effect of different parameters on the system performance.

Cascaded <inline-formula> <tex-math notation="LaTeX">$\alpha-\mu$ </tex-math> </inline-formula> Fading Channels: Reliability and Security Analysis

In this paper, the cascaded $\alpha -\mu$ fading distribution is first introduced and mathematically characterized, which arises as a generalization of the cascaded Rayleigh, Weibull, and Nakagami- ${m}$ fading distribution, by properly selecting fading parameters $\alpha$ and $\mu$ with specific values. In particular, the statistical characterization of the cascaded $\alpha -\mu$ fading channels, namely, the probability density function and cumulative distribution function, are first studied. This set of new statistical results is applied to the modeling and analysis of the reliability and security performance of wireless communication systems over the cascaded $\alpha -\mu$ fading channel. Regarding system reliability, the amount of fading, outage probability, average channel capacity, and the average symbol error probability with coherent and non-coherent demodulation schemes are derived with respect to the univariate Fox’s $H$ -function. In terms of security analysis, the secrecy outage probability $\mathcal {P}_{\text {out}}$ , the probability of non-zero secrecy capacity $\mathcal {P}_{\text {nz}}$ , and the average secrecy capacity are analyzed in the exact closed-form expressions which are derived in the presence of an active eavesdropper. In addition, an asymptotic analysis of all aforementioned metrics is carried out, in order to gain more insights of the effect of the key system parameters on the reliability and security. Tractable results are computed in terms of the Fox’s $H$ -function and later on are successfully validated through Monte-Carlo simulations.

On Physical Layer Security Over the Fisher-Snedecor ${\mathcal{F}}$ Wiretap Fading Channels

In this paper, we initially investigate the physical layer security over device-to-device communications, where the channel is modeled from the Fisher–Snedecor $\mathcal {F}$ distribution. To be specific, secrecy metrics, including the secrecy outage probability, the probability of non-zero secrecy capacity, and the average secrecy capacity, are well derived with exact closed-form expressions, which are given in terms of the Meijer’s $G$ -function. The accuracies of our mathematical expressions are further validated by Monte Carlo simulation results.

The Physical Layer Security Experiments of Cooperative Communication System with Different Relay Behaviors.

Physical layer security is an attractive security mechanism, which exploits the randomness characteristics of wireless transmission channel to achieve security. However, it is hampered by the limitation of the channel condition that the main channel must be better than the eavesdropper channel. To alleviate the limitation, cooperative communication is introduced. Few studies have investigated the physical layer security of the relay transmission model. In this paper, we performed some experiments to evaluate the physical layer security of a cooperative communication system, with a relay operating in decode-and-forward (DF) cooperative mode, selfish and malicious behavior in real non-ideal transmission environment. Security performance is evaluated in terms of the probability of non-zero secrecy capacity. Experiments showed some different results compared to theoretical simulation: (1) to achieve the maximum secrecy capacity, the optimal relay power according to the experiments result is larger than that of ideal theoretical results under both cooperative and selfish behavior relay; (2) the relay in malicious behavior who forwards noise to deteriorate the main channel may deteriorate the eavesdropper channel more seriously than the main channel; (3) the optimal relay positions under cooperative and selfish behavior relay cases are both located near the destination because of non-ideal transmission.

Secrecy Performance Analysis of Cognitive Decode-and-Forward Relay Networks in Nakagami- $m$ Fading Channels

This paper investigates the physical layer security problem of cognitive decode-and-forward relay networks over Nakagami-m fading channels. We consider the relaying communication between one secondary user (SU) source and one SU destination by using an opportunistic relay selection from multiple SU relays and sharing the licensed spectrum of multiple primary users (PUs) in the underlay network. While the transmission between the SUs imposes interference on each PU, the relayed transmission is intercepted by one SU eavesdropper. In the absence of the eavesdropper's channel state information, the relay selection is based on the largest channel gain of relay-to-destination link, which is assumed to be outdated due to feedback delay. We derive the exact probability of non-zero secrecy capacity and the exact secrecy outage probability (SOP) in the closed form. Furthermore, we derive the asymptotic SOP in two different cases, and explicitly show the effects of system parameters on the secrecy diversity order and the secrecy diversity gain, respectively. Both asymptotic analysis and simulation results show that the secrecy performance can be improved by increasing either the number of relays or the Nakagami parameter of the legitimate relay channels, whereas the secrecy diversity gain deteriorates as the number of the PUs increases.

Secrecy performance analysis of TAS/MRC system in the presence of channel estimation error

This paper presents secure transmission in transmit antenna selection with maximal ratio combining (TAS/MRC) over Rayleigh fading channel for multiple input multiple output (MIMO) taking channel estimation error into account. In this paper, we evaluate the probability of non-zero secrecy capacity (PNZSC) and secrecy outage probability (SOP) for TAS/MRC system considering the impact of channel estimation error (CEE). The numerical results show that the system is valid for any transreceiving and eavesdropping antennas in general.

Cognitive radio network with secrecy and interference constraints

In this paper, we investigate the physical-layer security of a secure communication in single-input multiple-output (SIMO) cognitive radio networks (CRNs) in the presence of two eavesdroppers. In particular, both primary user (PU) and secondary user (SU) share the same spectrum, but they face with different eavesdroppers who are equipped with multiple antennas. In order to protect the PU communication from the interference of the SU and the risks of eavesdropping, the SU must have a reasonable adaptive transmission power which is set on the basis of channel state information, interference and security constraints of the PU. Accordingly, an upper bound and lower bound for the SU transmission power are derived. Furthermore, a power allocation policy, which is calculated on the convex combination of the upper and lower bound of the SU transmission power, is proposed. On this basis, we investigate the impact of the PU transmission power and channel mean gains on the security and system performance of the SU. Closed-form expressions for the outage probability, probability of non-zero secrecy capacity, and secrecy outage probability are obtained. Interestingly, our results show that the strong channel mean gain of the PU transmitter to the PU’s eavesdropper in the primary network can enhance the SU performance.

Wireless Information-Theoretic Security: Theoretical analysis & experimental measurements with multiple eavesdroppers in an outdoor obstacle-dense MANET

Wireless Information-Theoretic Security (WITS) has been suggested as a robust security scheme, especially for infrastructure-less networks. Based on the physical layer, WITS considers quasi-static Rayleigh fading instead of the classic Gaussian wiretap scenario. In this paper, the key parameters of WITS are investigated by implementing an 802.11n ad-hoc network in an outdoor obstacle-dense topology. Measurements performed throughout the topology allow for a realistic evaluation of a scenario with multiple moving eavesdroppers. Low speed user movement has been considered, so that Doppler spread can be discarded. A set of discrete field test trials have been conducted, based on simulation of human mobility throughout an obstacle-constrained environment. Average Signal-to-Noise Ratio (SNR) values have been measured for all moving nodes, and the Probability of Non-Zero Secrecy Capacity has been calculated for different eavesdropping cooperative schemes (Selection Combining and Maximal-Ratio Combining). In addition, the Outage Probability has been estimated with regard to a non-zero target Secrecy Rate for both techniques. The results have been compared with the respective values of WITS key parameters derived from theoretical analysis.

Secrecy outage analysis for underlay cognitive radio networks over correlated channels

This paper investigates the secrecy outage performance of underlay cognitive radio networks, in which a source in a secondary system transmits its confidential information to a legitimate destination in the presence of an eavesdropper. Specifically, the main (the source-to-destination) and eavesdropping (the sourceto- eavesdropper) channels are assumed to be correlated. Moreover, it is also assumed that the main channel and the channel from the source to the primary user’s receiver are correlated. Tight closed-form analytical expression for secrecy outage probability and the closed-form analytical expression for the probability of non-zero secrecy capacity are derived and validated by simulation results when the interference temperature limit is comparably large.

Analysis of Probability of Non-zero Secrecy Capacity for Multi-hop Networks in Presence of Hardware Impairments over Nakagami-m Fading Channels

Analysis of Probability of Non-zero Secrecy Capacity for Multi-hop Networks in Presence of Hardware Impairments over Nakagami-m Fading Channels

An Analysis Modeling Architecture for Supporting Physical Layer Security of Wireless Networks under Hardware Impairments

In this paper, we study physical layer security (PLS) of wireless networks in presence of one eavesdropper. Assume that the channel state information (CSI) of the eavesdropper cannot be obtained at the transmitter, such as CSI can be then estimated through the CSI of a torch node. In addition, a practical issue of wireless nodes, i.e., hardware impairment (HI), is considered at the source node of the network. System performances in terms of secrecy outage probability, probability of non-zero secrecy capacity and ergodic secrecy capacity are then investigated over Rayleigh fading channels. In particular, the closed-form expressions of the secrecy outage probability and probability of non-zero secrecy capacity are provided. Analytical results are then validated by Monte-Carlo simulation. Numerical results reveal the effects of the HI and the advantages of the use of the torch node in PLS of wireless communications.

Probability of Secrecy Outage in Cognitive Radio Networks over Rician-Fading Channels

Abstract In Rician-fading scenario, cognitive radio networks (CRNs) with a source in a secondary system transmitting its confidential information to a legitimate destination in the presence of an eavesdropper, are considered in this paper. Under CRNs, the interference power reaching at primary user (PU) is limited by some pre-defined threshold. Secrecy outage not only occurs when the achievable secrecy capacity for source-destination link is smaller than a target rate, but also occurs in the case that the interference power at PU is greater than that threshold. Analytical expression for secrecy outage probability has been derived and verified with simulation results. In addition, we have also derived the analytical expression for probability of non-zero secrecy capacity.

Physical layer security of MIMO STBC over Rayleigh fading channels in the presence of channel estimation error

This paper presents secure transmission in orthogonal space time block codes (OSTBC) in the presence of channel estimation error over multiple input multiple output (MIMO) wiretap channels. In this paper, we evaluate probability of non-zero secrecy capacity (PNZSC) and secrecy outage probability (SOP) for OSTBC system over Rayleigh fading channels considering the impact of channel estimation error (CEE). The numerical result demonstrates that the system is generic and valid for any transceiving and eavesdropper antennas.

Secrecy capacity and outage probability of multiuser MIMO systems with zero forcing receivers

In this paper, we evaluate the secrecy performance of the zero forcing receiver operating in the multiuser multiple-input multiple-output (MIMO) system with user scheduling. We first derive the exact closed form expressions for the probability of non-zero secrecy capacity (PNZSC). We consider Rayleigh fading with non-identical fading parameters of the eavesdropper’s channel. We further derive the secrecy outage probability (SOP) which accurately reveals the secrecy diversity order and the secrecy array gain. Numerical results shows that our system is valid and accurate for any number of transmitter, receiver and eavesdropper antennas.

Physical-Layer Security Over Non-Small-Scale Fading Channels

This paper investigates the performances of secure communications over non-small-scale fading channels. Specifically, considering three different cases when the main and eavesdropper channels experience independent lognormal fading, correlated lognormal fading, or independent composite fading, we study the average secrecy capacity and secrecy outage [including the probability of nonzero secrecy capacity (PNSC) and secure outage probability (SOP)] for these channel conditions. The approximated closed-form expressions for the average secrecy capacity, PNSC, and SOP are derived for these three different types of non-small fading channels. The accuracy of our performance analysis is verified by simulation.

Physical Layer Security for Multiple-Antenna Systems: A Unified Approach

Secrecy capacity is a fundamental information-theoretic performance metric to predict the maximum data rate of reliable communication, while the intended message is not revealed to the eavesdropper. Motivated by this consideration in this paper, a unified communication-theoretic framework for the analysis of the probability of nonzero secrecy capacity, the secrecy outage probability, and the secrecy capacity of multiple-antenna systems over fading channels is proposed. Specifically, a powerful frequency-domain approach is first developed in which the integrals involved in the evaluation of the probability of nonzero secrecy capacity and secrecy outage probability are transformed into the frequency domain, by employing Parseval’s theorem. A generic approach for the evaluation of the asymptotic secrecy outage probability at high signal-to-noise ratio (SNR) region is also introduced, thus providing useful insight as to the parameters affecting the secrecy performance. Finally, a unified numerical approach for computing the average secrecy capacity of multiple-antenna systems under arbitrary fading environments is developed. The proposed framework is general enough to accommodate any well-known multiantenna transmission technique and fading model. Finally, the secrecy performance of several multiple-antenna system setups is assessed, in the presence of generalized fading conditions and arbitrary antenna correlation, while various numerical and computer simulation results are shown and compared to substantiate the proposed mathematical analysis.

Secrecy Performances of Multicast Underlay Cognitive Protocols with Partial Relay Selection and without Eavesdropper’s Information

This paper considers physical-layer security protocols in multicast cognitive radio (CR) networks. In particular, we propose dual-hop cooperative decode-and-forward (DF) and randomize-and-forward (RF) schemes using partial relay selection method to enhance secrecy performance for secondary networks. In the DF protocol, the secondary relay would use same codebook with the secondary source to forward the source’s signals to the secondary destination. Hence, the secondary eavesdropper can employ either maximal-ratio combining (MRC) or selection combining (SC) to combine signals received from the source and the selected relay. In RF protocol, different codebooks are used by the source and the relay to forward the source message secretly. For each scheme, we derive exact and asymptotic closed-form expressions of secrecy outage probability (SOP), non-zero secrecy capacity probability (NzSCP) in both independent and identically distributed (i.i.d.) and independent but non-identically distributed (i.n.i.d.) networks. Moreover, we also give a unified formula in an integral form for average secrecy capacity (ASC). Finally, our derivations are then validated by Monte-Carlo simulations.

A New Secure Transmission Scheme With Outdated Antenna Selection

We propose a new secure transmission scheme in the multi-input multi-output multi-eavesdropper wiretap channel. In this channel, the N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> -antenna transmitter adopts transmit antenna selection (TAS) to choose the antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver to transmit, while the NB-antenna receiver and the N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> -antenna eavesdropper adopt maximal-ratio combining (MRC) to combine the received signals. We focus on the practical scenario where the channel state information (CSI) during the TAS process is outdated. In this scenario, we propose a new transmission scheme to prevent the detrimental effect of the outdated CSI on the wiretap codes design at the transmitter. To thoroughly assess the secrecy performance achieved by the proposed scheme, we derive new closed-form expressions for the exact secrecy outage probability and the probability of non-zero secrecy capacity for arbitrary SNRs. We also derive new compact expressions for the asymptotic secrecy outage probability at high SNRs. Notably, in the analysis, we take spatial correlation at the receiver into consideration. Apart from the advantage of our scheme over the conventional TAS/MRC scheme, we demonstrate that the outdated TAS reduces the secrecy diversity order from N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> to N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . We also demonstrate that antenna correlation improves the secrecy performance at low SNR but deteriorates the secrecy performance at medium and high SNRs, by affecting the secrecy array gain only.