Asymptotic Secrecy Outage Probability Research Articles

Secrecy Performance of Wireless Powered Communication Networks With Multiple Eavesdroppers and Outdated CSI

In this paper, we present a comprehensive secrecy performance analysis of wireless powered communication networks with multiple eavesdroppers, where an energy-limited information source with multiple antennas harvests the radio frequency energy from a dedicated power beacon (PB) before transmission. To exploit the benefits of multiple antennas at source, two popular multi-antenna transmission schemes, i.e., maximal ratio transmission and transmit antenna selection, are investigated for two intercepting ways at Eves, i.e., non-colluding and colluding scenarios, respectively. Specifically, adopting the time-switching protocol at PB, we derive exact closed-form expressions of the secrecy outage probability and the average secrecy rate for both two transmission schemes taking into account the outdated channel state information. Furthermore, in order to deeply extract insights on the system design, we further present tractable asymptotic secrecy outage probability and ergodic secrecy capacity at high signal-to-noise ratio regimes, which easily enable us to obtain the secrecy diversity order and coding gain of two transmission schemes, respectively. From our analysis, several important concluding remarks are obtained as follows: 1) full secrecy diversity order can be achieved by both two transmission schemes with no feedback delay, however, it reduces to one in the presence of feedback delay; 2) as the number of eavesdroppers increases, the secrecy performance gap between non-colluding and colluding scenarios becomes large; and 3) maximal ratio transmission (MRT) scheme always outperforms transmit antenna selection (TAS) scheme with no feedback delay. However, TAS scheme achieves a similar performance as MRT scheme or even better in moderate and even serious feedback delay conditions.

On Secure Underlay MIMO Cognitive Radio Networks With Energy Harvesting and Transmit Antenna Selection

In this paper, we consider an underlay multiple-input-multiple-output (MIMO) cognitive radio network (CRN) including a pair of primary nodes, a couple of secondary nodes, and an eavesdropper, where the secondary transmitter is powered by the renewable energy harvested from the primary transmitter in order to improve both energy efficiency and spectral efficiency. Based on whether the channel state information of wiretap links are available or not, the secrecy outage performance of the optimal antenna selection (OAS) scheme and suboptimal antenna selection (SAS) scheme for underlay MIMO CRN with energy harvesting are investigated and compared with traditional space-time transmission scheme. The closed-form expressions for exact and asymptotic secrecy outage probability are derived. Monte-Carlo simulations are conducted to testify the accuracy of the analytical results. The analysis illustrates that the OAS scheme outperforms SAS scheme. Furthermore, the asymptotic result shows that no matter which scheme is considered, the OAS and SAS schemes can achieve the same secrecy diversity order.

Impact of Feedback Errors on the Security of MIMO Wiretap Systems with Antenna Selection

This paper analyzes the impact of feedback errors on the security performances of multiple-input multiple-output (MIMO) wiretap channels. For the legitimate MIMO system, two schemes are considered: (1) transmit antenna selection/maximal ratio combining (TAS/MRC) and (2) transmit antenna selection/receive antenna selection (TAS/RAS). The eavesdropper uses either MRC or RAS techniques. We assume that both legitimate and eavesdropper receivers have the knowledge of their own channel state information. Furthermore, we consider that the index of the transmit antenna with the strongest signal-to-noise ratio is fed back from Bob to Alice. We derive closed-form expressions for the exact secrecy outage probability (SOP) and the probability of strictly positive secrecy capacity in Nakagami-m flat fading. In order to obtain the secrecy diversity order and the secrecy array gain, an asymptotic SOP expression is also derived.

Enhancing the Physical Layer Security of Non-Orthogonal Multiple Access in Large-Scale Networks

This paper investigates the physical layer security of non-orthogonal multiple access (NOMA) in large-scale networks with invoking stochastic geometry. Both single-antenna and multiple-antenna aided transmission scenarios are considered, where the base station (BS) communicates with randomly distributed NOMA users. In the single-antenna scenario, we adopt a protected zone around the BS to establish an eavesdropper-exclusion area with the aid of careful channel-ordering of the NOMA users. In the multiple-antenna scenario, artificial noise is generated at the BS for further improving the security of a beamforming-aided system. In order to characterize the secrecy performance, we derive new exact expressions of the security outage probability for both single-antenna and multiple-antenna aided scenarios. To obtain further insights, 1) for the single antenna scenario, we perform secrecy diversity order analysis of the selected user pair. The analytical results derived demonstrate that the secrecy diversity order is determined by the specific user having the worse channel condition among the selected user pair; and 2) for the multiple-antenna scenario, we derive the asymptotic secrecy outage probability, when the number of transmit antennas tends to infinity. Monte Carlo simulations are provided for verifying the analytical results derived and to show that: i)~The security performance of the NOMA networks can be improved by invoking the protected zone and by generating artificial noise at the BS; and ii)~The asymptotic secrecy outage probability is close to the exact secrecy outage probability.

Secrecy Outage Performance of Transmit Antenna Selection for MIMO Underlay Cognitive Radio Systems Over Nakagami- $m$ Channels

This paper considers a multiple-input–multiple-output (MIMO) cognitive wiretap system over Nakagami- $m$ channels with generalized selection combining (GSC), where confidential messages transmitted from a multiple-antenna transmitter to a multiple-antenna legitimate receiver are overheard by a multiple-antenna eavesdropper. Depending on whether the source node has the global channel state information (CSI) of both the main and wiretap channels, we investigate the secrecy outage performances of optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes for MIMO underlay cognitive radio systems over Nakagami- $m$ channels, and we compare them with the space-time transmission (STT) scheme. The closed-form expressions for the exact and asymptotic secrecy outage probability (SOP) for various schemes are derived. Simulations are conducted to validate the accuracy of our derived analytical results.

Improving physical layer security in untrusted relay networks: cooperative jamming and power allocation

The inherent broadcast characteristics of wireless medium make wireless data transmission difficult to be shielded from unintended recipients. As such, secure communication over wireless channels becomes a critical issue in the design of wireless networks. In this study, the authors study cooperative jamming and power optimisation in untrusted relay networks to improve physical layer security. By exploiting the direct link, a source-based jamming (SBJ) scheme is proposed to hinder the untrusted relay from intercepting the confidential message. Considering the total power budget, a power allocation strategy is also proposed to optimally determine the power of source and untrusted relay as well as the power of information and jamming signals. Furthermore, to evaluate the secrecy performance of the proposed SBJ scheme with the power allocation strategy, tight lower bound of ergodic secrecy capacity and asymptotic secrecy outage probability are derived in closed form. Simulation verifies the advantages of the proposed SBJ scheme and the power allocation strategy.

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.

Secure Hybrid VLC-RF Systems with Light Energy Harvesting

In this paper, a hybrid visible light communication-radio frequency (RF) system, including a legitimate receiver (R) and an eavesdropper (E) is considered. R can harvest energy from the light emitted by light emitting diodes (LEDs), which is used for the information transmission between R and the RF receiver which is close to the LED. It is assumed that E tries to eavesdrop the information delivered from R to the RF receiver and R is with finite energy storage. Considering the randomness of the locations of R and E, the statistical characteristics of the received signal-to-noise ratio at the RF receiver and E are characterized; then, we derive the analytical expressions for exact and asymptotic secrecy outage probability by using the stochastic geometry method. Finally, simulations are carried out to verify our proposed analytical models.

Performance Analysis of Secrecy Outage Probability for AF-Based Partial Relay Selection with Outdated Channel Estimates

We study the secrecy outage probability of the amplify-and-forward (AF) relaying protocol, which consists of one source, one destination, multiple relays, and multiple eavesdroppers. In this system, the aim is to transmit the confidential messages from a source to a destination via the selected relay in presence of eavesdroppers. Moreover, partial relay selection scheme is utilized for relay selection based on outdated channel state information where only neighboring channel information (source-relays) is available and passive eavesdroppers are considered where a transmitter does not have any knowledge of eavesdroppers’ channels. Specifically, we offer the exact secrecy outage probability of the proposed system in a one-integral form as well as providing the asymptotic secrecy outage probability in a closed-form. Numerical examples are given to verify our provided analytical results for different system conditions.

Secrecy Outage Analysis on Underlay Cognitive Radio System With Full-Duplex Secondary User

In this paper, an underlay cognitive radio system, which consists of a primary-user (PU) transmitter (TX), a PU receiver (RX), a secondary-user (SU) TX, and a SU_RX, is considered. Benefitting from the underlay mode, SU_TX can deliver its information to SU_RX by sharing the spectrum resource authorized to PU. It is assumed that SUs are equipped with a single transmitting antenna and a single receiving antenna, which are isolated, and work in full-duplex (FD) mode. By considering that the information signal transmitted from PU_TX to PU_RX may be eavesdropped by SU_TX if SU_TX is malicious, we investigate the secrecy outage performance of the PU system. The approximated closed-form expression for secrecy outage probability (SOP) and the lower boundary of the asymptotic SOP have been derived and verified by simulation results. Our results reveal the impact of the eavesdropping of the SU and the FD mode adopted at the SU transmitter on the secrecy performance of the PU system in underlay spectrum sharing mode.

Secure Multiuser Scheduling in Downlink Dual-Hop Regenerative Relay Networks Over Nakagami- $m$ Fading Channels

In this paper, we investigate the secrecy performance of multiuser dual-hop relay networks where a base station (BS) communicates with multiple legitimate users through the assistance of a trustful regenerative relay in the presence of multiple eavesdroppers. In particular, the maximal ratio transmission scheme is exploited at the BS and a threshold-based multiuser scheduling scheme is employed over the legitimate users, while concerning the imperfect decoding at the regenerative relay. To evaluate the secrecy performance of the considered system, two practical situations are addressed based on the availability of eavesdropper's channel state information (CSI), i.e., Scenario I, where the eavesdropper's CSI is not available at the relay, and Scenario II, where the eavesdropper's CSI is available at the relay. For both the scenarios, we further consider two eavesdropping modes, i.e., colluding eavesdropping and non-colluding eavesdropping. For Scenario I, new exact and asymptotic closed-form expressions for the secrecy outage probability (SOP) are derived. For Scenario II, we derive new exact and asymptotic closed-form expressions for the ergodic secrecy rate (ESR). The asymptotic SOPs demonstrate that the secrecy diversity order is independent of the number of legitimate users NB and eavesdroppers NE, the number of antennas equipped at eavesdroppers AE, as well as the fading factor of the wiretap channel mE. Furthermore, we also determine the secrecy multiplexing gain and the power cost to explicitly quantify the impact of the legitimate channel and wiretap channel on the ESR. Our findings demonstrate that increasing the switching threshold, the number of antennas at the BS, and the number of legitimate users has a positive impact on secrecy performance.

Artificial-Noise-Aided Transmission in Multi-Antenna Relay Wiretap Channels With Spatially Random Eavesdroppers

We design a new relay-aided secure transmission scheme, in which a source communicates with a destination through a trusted decode-and-forward relay in the presence of spatially random-distributed non-colluding eavesdroppers. We consider a general antenna configuration, in which the source, relay, destination, and eavesdroppers are equipped with multiple antennas. We assume that both the source and the relay transmit artificial noise signals in addition to information signals. We also assume that the source and the relay adopt different codebooks, and that the transmitted signals from the source and relay are not jointly processed at each eavesdropper. We first derive a closed-form expression for the transmission outage probability and a new expression for the secrecy outage probability. Notably, these expressions are valid for an arbitrary number of antennas at the source, relay, and destination. We then derive simple yet valuable expressions for the asymptotic transmission outage probability and the asymptotic secrecy outage probability, which reveal the secrecy performance when the number of antennas at the source grows sufficiently large. Using our expressions, we quantify a practical performance metric, namely, the secrecy throughput, under a secrecy outage probability constraint. We further determine the system and channel parameters that maximize the secrecy throughput, leading to analytical security solutions suitable for real-world deployment.

Secure Multiple Amplify-and-Forward Relaying With Cochannel Interference

We investigate the impact of cochannel interference on the security performance of multiple amplify-and-forward (AF) relaying networks, where $N$ intermediate AF relays assist the data transmission from the source to the destination. The relays are corrupted by multiple cochannel interferers, and the information transmitted from the relays to the destination can be overheard by the eavesdropper. In order to deal with the interference and wiretap, the best out of $N$ relays is selected for security enhancement. To this end, we derive a novel lower bound on the secrecy outage probability (SOP), which is then utilized to present two best relay selection criteria, based on the instantaneous and statistical channel information of the interfering links. For these criteria and the conventional max–min criterion, we quantify the impact of cochannel interference and relay selection by deriving the lower bound on the SOP. Furthermore, we derive the asymptotic SOP for each criterion, to explicitly reveal the impact of transmit power allocation among interferers on the secrecy performance, which offers valuable insights into practical design. We demonstrate that the all selection criteria achieve full secrecy diversity order $N$ , while the proposed two criteria in this paper outperform the conventional max–min scheme.

Physical layer security of underlay cognitive radio using maximal ratio combining

We investigate the secrecy outage performance of maximal ratio combining (MRC) in cognitive radio networks over Rayleigh fading channels. In a single-input multiple-output wiretap system, we consider a secondary user (SU-TX) that transmits confidential messages to another secondary user (SU-RX) equipped with M (M ≥ 1) antennas where the MRC technique is adopted to improve its received signal-to-noise ratio. Meanwhile, an eavesdropper equipped with N (N ≥ 1) antennas adopts the MRC scheme to overhear the information between SU-TX and SU-RX. SU-TX adopts the underlay strategy to guarantee the service quality of the primary user without spectrum sensing. We derive the closed-form expressions for an exact and asymptotic secrecy outage probability.

On Secrecy Performance of MISO SWIPT Systems With TAS and Imperfect CSI

In this paper, a multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system, including one base station (BS) equipped with multiple antennas, one desired single-antenna information receiver (IR), and $N$ ( $N > 1$ ) single-antenna energy-harvesting receivers (ERs) is considered. Assuming that the information signal to the desired IR may be eavesdropped by ERs if ERs are malicious, we investigate the secrecy performance of the target MISO SWIPT system when imperfect channel state information (CSI) is available and adopted for transmit antenna selection at the BS. Considering that each eavesdropping link experiences independent but not necessarily identically distributed Rayleigh fading, the closed-form expressions for the exact and the asymptotic secrecy outage probability, and the average secrecy capacity are derived and verified by simulations. Furthermore, the optimal power splitting factor is derived for each ER to realize the tradeoff between the energy harvesting and the information eavesdropping. Our results reveal the impact of the imperfect CSI on the secrecy performance of MISO SWIPT systems in the presence of multiple wiretap channels.

Exploiting Direct Links for Physical Layer Security in Multiuser Multirelay Networks

We present two physical layer secure transmission schemes for multiuser multirelay networks, where the communication from $M$ users to the base station is assisted by direct links and by $N$ decode-and-forward relays. In this network, we consider that a passive eavesdropper exists to overhear the transmitted information, which entails exploiting the advantages of both direct and relay links for physical layer security enhancement. To fulfill this requirement, we investigate two criteria for user and relay selection and examine the achievable secrecy performance. Criterion I performs a joint user and relay selection, while Criterion II performs separate user and relay selections, with a lower implementation complexity. We derive a tight lower bound on the secrecy outage probability for Criterion I and an accurate analytical expression for the secrecy outage probability for Criterion II. We further derive the asymptotic secrecy outage probabilities at high transmit signal-to-noise ratios and high main-to-eavesdropper ratios for both criteria. We demonstrate that the secrecy diversity order is ${\textbf{min}}\left(MN,M+N\right)$ for Criterion I, and $N$ for Criterion II. Finally, we present numerical and simulation results to validate the proposed analysis, and show the occurrence condition of the secrecy outage probability floor.

Artificial-Noise Aided Secure Transmission in Large Scale Spectrum Sharing Networks

We investigate beamforming and artificial noise generation at the secondary transmitters to establish secure transmission in large scale spectrum sharing networks, where multiple noncolluding eavesdroppers attempt to intercept the secondary transmission. We develop a comprehensive analytical framework to accurately assess the secrecy performance under the primary users’ quality of service constraint. Our aim is to characterize the impact of beamforming and artificial noise generation (BF&AN) on this complex large scale network. We first derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive an easy-to-evaluate asymptotic average secrecy rate and asymptotic secrecy outage probability when the number of antennas at the secondary transmitter goes to infinity. Our results show that the equal power allocation between the useful signal and artificial noise is not always the best strategy to achieve maximum average secrecy rate in large scale spectrum sharing networks. Another interesting observation is that the advantage of BF&AN over BF on the average secrecy rate is lost when the aggregate interference from the primary and secondary transmitters is strong, such that it overtakes the effect of the generated AN.

Secure Transmission in Cognitive MIMO Relaying Networks With Outdated Channel State Information

In this paper, we introduce transmit antenna selection/maximal-ratio combining (TAS/MRC) scheme in dual-hop randomize-and-forward (RaF) cognitive multiple-input multiple-output (MIMO) wiretap networks with outdated channel state information (CSI). In this network, the secondary transmitter adopts the TAS scheme to choose the antenna with the maximal received signal-to-noise ratio (SNR), while the secondary receiver and the eavesdropper adopt the MRC scheme to combine the received signals. To thoroughly assess the secrecy performance achieved by the TAS/MRC scheme and the impact of outdated CSI on the secrecy performance, we derive a new closed-form expression for the secrecy outage probability of dual-hop RaF cognitive MIMO wiretap networks. In order to achieve more insights on the application of TAS/MRC scheme, we further present tractable asymptotic secrecy outage probability at high SNR regimes under two distinct scenarios. From our analysis, several important concluding remarks are obtained as follows: 1) the RaF relaying strategy achieves better secrecy performance than that of the decode-and-forward relaying strategy for dual-hop cognitive MIMO wiretap networks; 2) outdated CSI decreases the secrecy diversity gain of the TAS/MRC scheme from ${N_{{R}}}\min \left ({ {{N_{{A}}},{N_{{B}}}} }\right )$ to $\min \left ({ {{N_{{R}}},{N_{{B}}}} }\right )$ ; and 3) although TAS/MRC scheme cannot attain full secrecy diversity gain for the considered system with outdated CSI, it still can achieve an extra secrecy coding gain compared with the random antenna selection/MRC scheme.

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.

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.