Secrecy Rate Performance Research Articles

Downlink Secrecy Rate of One-Bit Massive MIMO System With Active Eavesdropping

In this study, we consider the physical layer security in the downlink of a Massive MIMO system employing one-bit quantization at the base station (BS). We assume an active eavesdropper that attempts to spoiling the channel estimation acquisition at the BS for a legitimate user, whereas overhearing on downlink transmission. We consider the two most widespread methods for degrading the eavesdropper's channel, the nullspace artificial noise (NS-AN) and random artificial noise (R-AN). Then, we present a lower bound on the secrecy rate and asymptotic performance, considering zero-forcing beamforming (ZF-BF) and maximum-ratio transmission beamforming (MRT-BF). Our results reveal that even when the eavesdropper is close enough to the intercepted user, a positive secrecy rate --which tends to saturation with increasing the number of BS antennas $N$---is possible, as long as the transmit power of eavesdropper is less than that of the legitimate user during channel training. We show that ZF-BF with NS-AN provides the best performance. It is found that MRT-BF and ZF-BF are equivalent in the asymptotic limit of $N$ and hence the artificial noise technique is the performance indicator. Moreover, we study the impact of \emph{power-scaling law} on the secrecy rate. When the transmit power of BS is reduced proportional to $1/N$, the performance is independent of artificial noise asymptotically and hence the beamforming technique is the performance indicator. In addition, when the BS's power is reduced proportional to $1/\sqrt{N}$, all combinations of beamforming and artificial noise schemes are equally likely asymptotically, independent of quantization noise. We present various numerical results to corroborate our analysis.

Directional Modulation-Enhanced Multiple Antenna Arrays for Secure and Precise Wireless Transmission.

Directional modulation (DM) technique has the ability to enhance the physical layer security (PLS) of wireless communications. Conventional DM schemes are usually based on a single antenna array with the basic assumption that eavesdroppers (Eves) and legitimate users (LUs) are in different directions. However, it is possible that Eves are in the same direction as LUs in practical applications. As a result, signals received by Eves will be approximately the same or even in better quality than those received by LUs. To address the neighbor security issue, we introduce a multiple antenna arrays model at the transmitter side with the help of the artificial noise (AN)-aided DM technique to achieve secure and precise DM transmission in this paper. Meanwhile, to recover the mixed useful signals, two novel DM schemes based on single- and multi-carrier multiple antenna arrays model are proposed, respectively. In addition, the symbol error rate (SER), secrecy rate, and robustness performance of the proposed DM schemes were analyzed and simulated. Simulations validate the effectiveness of the proposed DM schemes and demonstrate that multiple antenna arrays model based DM methods outperform single antenna array model aided DM methods in security.

Directional Modulation: A Physical-Layer Security Solution to B5G and Future Wireless Networks

Directional modulation (DM), as an efficient secure transmission method, offers security through its directive property and is suitability for LoP channels such as millimeter wave, UAV, satellite communication, and smart transportation. If the direction angle of the desired user is known, the desired channel gain vector is obtainable. Thus, in advance, the DM transmitter knows the values of the directional angles of the desired user and eavesdropper, or their DOAs because the BVCM andANPM are mainly determined by the directional angles of the desired user and eavesdropper. For a DM transceiver, working as a receiver, the first step is to measure the DOAs of the desired user and eavesdropper. Then, in the second step, using the measured DOAs, the BVCM and ANPM are designed. In this article, we describe DOA measurement methods, power allocation, and beamforming in DM networks. A machine learning-based DOA measurement method is proposed to make a substantial secrecy rate (SR) performance gain compared to single-snapshot measurement without machine learning for a given null-space projection beamforming scheme. However, for a conventional DM network, there still exists a serious security issue: the eavesdropper moves inside the main beam of the desired user and may intercept the CMs intended for the desired users because the BVCM and ANPM are only angle-dependent. To address this problem, we present a new concept of SPWT, where the transmit waveform has two-dimensional dependency by using DM, random subcarrier selection with randomization procedure, and phase alignment at the DM transmitter.

Antenna Selection Method of Maximizing Secrecy Rate for Green Secure Spatial Modulation

In secure spatial modulation systems, an active antenna-group (AAG) selection of maximizing the average secrecy rate (SR) is proposed to avoid the disadvantage that conventional AAG selection scheme of minimizing bit error ratio at desired receiver may lead to a substantial SR loss. However, due to the limited active antenna pattern and finite-alphabet inputs, it is very hard for us to optimize the SR without closed-form expression. To address the two issues, first, by exploiting the relationship between minimum mean-square error and mutual information, the expression of SR in the low signal-to-noise ratio (SNR) region is derived. Using the expression, the problem of maximizing SR (Max-SR), called Max-SR I, is converted to integer programming problem. In the high SNR region, we derive an asymptotical lower bound for SR, and find the fact that the Max-SR can be reduced to maximizing the difference of Bob’s minimum Euclidean distance and Eve’s one, called Max-SR II. Through this conclusion, we can find the relationship between SR and bit-error rate. Furthermore, Max-SR III is proposed to overcome the disadvantage of the SR performance loss for the above two asymptotical algorithms in the moderate SNR region, where an approximate expression is exploited as the efficient metric to design AAG. Numerical results show that the SR performance of the proposed Max-SR III is close to that of optimal exhaustive search method, and the Max-SR I and Max-SR II can achieve acceptable SR performance with extremely low complexity.

High-Performance Power Allocation Strategies for Secure Spatial Modulation

Optimal power allocation (PA) strategies can make a significant rate improvement in secure spatial modulation (SM). Due to the lack of secrecy rate (SR) closed-form expression in secure SM networks, it is hard to optimize the PA factor. In this paper, two PA strategies are proposed: gradient descent (GD), and maximum product of signal-to-interference-plus-noise ratio (SINR) and artificial-noise-to-signal-plus-noise ratio (ANSNR) (Max-P-SINR-ANSNR). The former is an iterative method and the latter is a closed-form solution. Compared to the former, the latter is of low-complexity. Simulation results show that the proposed two PA methods can approximately achieve the same SR performance as the exhaustive search method and perform far better than three fixed PA ones. With extremely low complexity, the SR performance of the proposed Max-P-SINR-ANSNR performs slightly better and worse than that of the proposed GD in the low to medium, and high signal-to-noise ratio regions, respectively.

UAV-Enabled Secure Communications: Joint Trajectory and Transmit Power Optimization

This paper studies the physical layer security of an unmanned aerial vehicle (UAV) network, where a UAV base station (UAV-B) transmits confidential information to multiple information receivers (IRs) with the aid of a UAV jammer (UAV-J) in the presence of multiple eavesdroppers. We formulate an optimization problem to jointly design the trajectories and transmit power of UAV-B and UAV-J in order to maximize the minimum average secrecy rate over all IRs. The optimization problem is non-convex and the optimization variables are coupled, which leads to the optimization problem being mathematically intractable. As such, we decompose the optimization problem into two subproblems and then solve it by employing an alternating iterative algorithm and the successive convex approximation technique. Our results show that the average secrecy rate performance of the proposed scheme provides about 20% and 150% performance gains over the joint trajectory and transmit power optimization without UAV-J scheme and the transmit power optimization with fixed trajectory scheme at flight period $T=150$ s, respectively.

Opportunistic Scheduling for Average Secrecy Rate Enhancement in Fading Downlink Channel With Potential Eavesdroppers

In this paper, we consider user scheduling and power allocation techniques for downlinks where transmitted message must be kept confidential from all other unintended users and the number of users is larger than that of access point (AP) antennas. In order to maximize network secrecy rate with a limited number of antennas, the AP schedules a user who can achieve the largest secrecy rate and exploits multiple antennas for transmitting artificial noise to the unintended users. We derive the closed-form expressions of the optimal power allocation for the artificial noise and the average network secrecy rate through asymptotic analysis. The analysis results provide the insightful information on the behaviors of the user scheduling and the effect of system parameters on the network secrecy rate performance. It is shown that opportunistic scheduling with artificial noise transmission technique is more effective than the conventional precoding techniques for multiple confidential message transmissions in terms of network secrecy rate. Furthermore, we have also discussed a transmission strategy for the worst case scenarios where all unintended users are treated as colluding eavesdroppers. The simulations confirm the validity of the analysis results and provide additional information on the network performance in general cases.

Alternating iterative secure structure between beamforming and power allocation for UAV-aided directional modulation networks

In unmanned aerial vehicle (UAV) networks, directional modulation (DM) is adopted to improve the secrecy rate (SR) performance. In this paper, an alternating iterative structure (AIS) between beamforming and power allocation (PA) is proposed to further improve the SR performance. Specifically Alice, a ground base station, behaves as a control center, and Bob is a UAV of flying along a linear flight trajectory who optimizes its SR performance by dynamically adjusting its beamforming vectors and PA strategy. Per fixed time interval during the Bob’s flight process, the transmit beamforming vectors for useful messages and artificial noise (AN) projection are given by the rule of maximizing signal-to-leakage-and-noise ratio (Max-SLNR) and maximizing AN-and-leakage-to-noise ratio (ANLNR), and the optimal PA strategy is based on maximizing SR (Max-SR). Simulation results show that the proposed AIS converges rapidly, and can achieve substantial SR gains over Max-SLNR plus Max-ANLNR with fixed PA such as PA factor β=0.5, and 0.9. In particular, in the case of small-scale antenna array, the SR performance gain achieved by the proposed AIS is more attractive. Additionally, as the number of antennas tends to be large-scale, the average SR performance of the proposed AIS approaches an SR ceil.

UAV-Aided Secure Transmission in MISOME Wiretap Channels With Imperfect CSI

In this paper, we study secure cooperative transmission for the multiple-input-single-output multiple-eavesdropper (MISOME) systems, where a source (Alice) aims to send confidential messages to a legitimate user (Bob) with the aid of an unmanned aerial vehicle (UAV) enabled friendly jammer (Charlie) in the presence of multiple eavesdroppers (Eves). To further guarantee the secrecy performance, artificial noise (AN) beamforming together with cooperative Jamming (CJ) has been utilized in this considered system with only location and statistical channel state information of the Eves. Specifically, taking imperfect channel state information (CSI) between Charlie and Bob into account, we derive the exact closed-form expression of the secrecy outage probability (SOP) and develop an efficient scheme to solve the secrecy rate maximization (SRM) problem which has been verified as a convex one under certain SOP. Moreover, we propose an optimal UAV placement strategy to further enhance secrecy performance. The numerical results are provided to validate that the system security would seriously degenerate with channel uncertainty. Besides, the proposed scheme is verified to outperform the terrestrial CJ scheme in improving the secrecy rate and secure energy efficiency (EE) performance under perfect CSI or tolerable channel estimation errors. Finally, the effectiveness of the proposed UAV placement strategy in enhancing transmission security and the applicability of the proposed scheme has also been demonstrated.

MP-WFRFT and Chaotic Scrambling Aided Directional Modulation Technique for Physical Layer Security Enhancement

Directional modulation (DM) technique based on artificial noise (AN) enables the physical layer security (PLS) for wireless communications in free space. However, on one hand, the introduction of AN results in less power efficient for a DM system; on the other hand, the AN-aided DM technique is strongly dependent on the channel state information (CSI) of transceivers, which greatly limits its practical application. What is more, when the eavesdropper (EVE) is slowly approaching the legitimate user (LU) or the EVE and the LU are in the same direction, the transmission security cannot be guaranteed. To circumvent these problems, DM technique with multiple parameters weighted-type fractional Fourier transform (MP-WFRFT) and chaotic scrambling (CS) aided is proposed in this paper to realize the power-efficient and security-enhanced wireless transmissions. Then, the symbol error rate (SER), secrecy rate, robustness, and anti-interception performance of the proposed method are analyzed and simulated. The simulation results are presented to verify that the proposed method is more power-efficient than the traditional AN-aided DM schemes, and the PLS is guaranteed due to the proposed approach, albeit knowing the intended direction for an EVE.

On the Performance of Low-Altitude UAV-Enabled Secure AF Relaying With Cooperative Jamming and SWIPT

This paper proposes a novel cooperative secure unmanned aerial vehicle (UAV) aided transmission protocol, where a source (Alice) sends confidential information to a destination (Bob) via an energy-constrained UAV-mounted amplify-and-forward (AF) relay in the presence of a ground eavesdropper (Eve). We adopt destination-assisted cooperative jamming (CJ) as well as simultaneous wireless information and power transfer (SWIPT) at the UAV-mounted relay to enhance physical-layer security (PLS) and transmission reliability. Assuming a low altitude UAV, we derive connection probability (CP), secrecy outage probability (SOP), instantaneous secrecy rate, and average secrecy rate (ASR) of the proposed protocol over Air-Ground (AG) channels, which are modeled as Rician fading with elevation-angel dependent parameters. By simulations, we verify our theoretical results and demonstrate significant performance improvement of our protocol, when compared to conventional transmission protocol with ground relaying and UAV-based transmission protocol without destination-assisted jamming. Finally, we evaluate the impacts of different system parameters and different UAV's locations on the proposed protocol in terms of ASR.

Secure Hybrid Digital and Analog Precoder for mmWave Systems With Low-Resolution DACs and Finite-Quantized Phase Shifters

Millimeter wave (mmWave) communication has been regarded as one of the most promising technologies for the future generation wireless networks because of its advantages of providing a ultra-wide new spectrum and ultra-high data transmission rate. To reduce the power consumption and circuit cost for mmWave systems, hybrid digital and analog (HDA) architecture is preferred in such a scenario. In this paper, an artificial-noise (AN) aided secure HDA beamforming scheme is proposed for mmWave MISO system with low resolution digital-to-analog converters (DACs) and finite-quantized phase shifters on RF. The additive quantization noise model for AN aided HDA system is established to make an analysis of the secrecy performance of such systems. With the partial channel knowledge of eavesdropper available, an approximate expression of secrecy rate (SR) is derived. Then using this approximation formula, we propose a two-layer alternately iterative structure (TLAIS) for optimizing digital precoder (DP) of confidential message (CM), digital AN projection matrix (DANPM) and analog precoder (AP). The inner-layer iteration loop is to design the DP of CMs and DANPM alternatively given a fixed matrix of AP. The outer-layer iteration loop is in between digital baseband part and analog part, where the former refers to DP and DANPM, and the latter is AP. Then for a given digital part, we propose a gradient ascent algorithm to find the vector of AP vector. Given a matrix of AP, we make use of general power iteration (GPI) method to compute DP and DANPM. This process is repeated until the terminal condition is reached. Simulation results show that the proposed TLAIS can achieve a better SR performance compared to existing methods, especially in the high signal-to-noise ratio region.

Performance Analysis of Directional Modulation With Finite-Quantized RF Phase Shifters in Analog Beamforming Structure

The radio frequency (RF) phase shifter with finite quantization bits in analog beamforming (AB) structure forms quantization error (QE) and causes a performance loss of received signal to interference plus noise ratio (SINR) at the receiver (called Bob). By using the law of large numbers in probability theory, the closed-form expression of SINR performance loss is derived to be inversely proportional to the square of sinc (or sin(x)/x) function. Here, a phase alignment method is applied in directional modulation transmitter with AB structure. Also, the secrecy rate (SR) expression is derived with QE. From numerical simulation results, we find that the SINR performance loss gradually decreases as the number L of quantization bits increases. This loss is less than 0.3dB when L is larger than or equal to 3. As L exceeds 5, the SINR performance loss at Bob can be approximately trivial. Similarly, SR performance loss gradually reduces as L increases. In particular, the SR performance loss is about 0.1 bits/s/Hz for L=3 at signal-to-noise ratio of 15dB.

Joint Relay Selection and Power Allocation through a Genetic Algorithm for Secure Cooperative Cognitive Radio Networks

In cooperative cognitive radio networks (CCRNs), there has been growing demand of transmitting secondary user (SU) source information secretly to the corresponding SU destination with the aid of cooperative SU relays. Efficient power allocation (PA) among SU relays and multi-relay selection (MRS) are a critical problem for operating such networks whereas the interference to the primary user receiver is being kept below a tolerable level and the transmission power requirements of the secondary users are being satisfied. Subsequently, in the paper, we develop the problem to solve the optimal solution for PA and MRS in a collaborative amplify-and-forward-based CCRNs, in terms of maximizing the secrecy rate (SR) of the networks. It is found that the problem is a mixed integer programming problem and difficult to be solved. To cope with this difficulty, we propose a meta-heuristic genetic algorithm-based MRS and PA scheme to maximize the SR of the networks while satisfying transmission power and the interference requirements of the networks. Our simulation results reveal that the proposed scheme achieves near-optimal SR performance, compared to the exhaustive search scheme, and provides a significant SR improvement when compared with some conventional relay selection schemes with equal power allocation.

Nonlinear-Precoded Multiuser Secure Transmission With Cooperative Jamming and Adaptive Limited Feedback

This paper studies secure transceiver design for multiuser multiantenna systems with an external passive eavesdropper and a cooperative jamming helper. Due to the finite-rate constraint of feedback channels, only quantized channel state information (CSI) of the legitimate users is available at the transmitter and the helper. A nonlinear-precoded secure transmission strategy is proposed using Tomlinson–Harashima precoding at the transmitter and null-space beamforming at the helper based on the quantized CSI. The accurate closed-form expression of an approximation for the ergodic rate of each legitimate user is obtained using quantization cell approximation for random vector quantization of the channels. Assuming the quantized CSI of the legitimate channels and the helper's channel at the eavesdropper, closed-form expression of an upper bound of the ergodic rate of each user's message at the eavesdropper is also derived. Then, a closed-form expression of an approximation for the worst-case ergodic secrecy sum rate follows. We also theoretically show that, besides the advantage in ergodic rate over the linear precoding scheme, when the quantized CSI is not available at the eavesdropper, Tomlinson–Harashima precoding is also more effective in degrading the received signal quality at the eavesdropper, and, thus, is more capable to enhance the secrecy of the systems compared with the linear precoding scheme. Given the total bandwidth constraint of CSI-feedback channels, an adaptive feedback bit allocation algorithm is proposed for each legitimate user to optimize the ergodic secrecy rate performance. Numerical results illustrate that the proposed nonlinear-precoded secure transmission strategy outperforms the corresponding linear precoding scheme, and significant advantage can be achieved by adaptively allocating the total available feedback bits.

Achievable Secrecy Rate of Artificial Fast-Fading Techniques and Secret-Key Assisted Design for MIMO Wiretap Channels With Multiantenna Passive Eavesdropper

Artificial noise (AN) is an efficient way to enhance physical layer security of multiantenna wiretap channels with a passive eavesdropper (ED) whose channel state information is unavailable. However, the AN is known to be vulnerable to the eavesdropping attack with a large antenna array. To tackle the problem, the artificial fast fading (AFF) scheme has been developed to deliberately randomize the ED's effective channel so as to disrupt its channel estimation. Some recent progress has been made for the secrecy-rate performance of the AFF scheme in the multi-input single-output wiretap channels. However, it turns out that the performance is over-estimated. In this correspondence, we provide a comprehensive analysis on the secrecy-rate of the AFF scheme in general multi-input multi-output wiretap channels. Unfortunately, our analysis reveals a negative result that the conventional AFF is no better than the AN methods, without some pre-shared information among the legitimate parties. This is in fact in stark contrast to the previous observations. Motivated by our analysis, we propose a novel cross layer design by combining the AFF in the physical layer with the secret-keys in the upper layer crypto systems. Then, we mathematically prove that our method asymptotically nullifies the information leakage to the ED in the physical layer for any number of ED antennas even without the aid of the wiretap codes, while further enhancing the upper layer security, and thus provides an enhanced security over the layers. Finally, numerical results demonstrate the accuracy of our analysis and the efficiency of the proposed scheme.

Two High-Performance Schemes of Transmit Antenna Selection for Secure Spatial Modulation

In this paper, a secure spatial modulation system with artificial noise-aided is investigated. To achieve higher secrecy rate (SR) in such a system, two high-performance schemes of transmit antenna selection (TAS), leakage-based and maximum secrecy rate (Max-SR), are proposed and a generalized Euclidean distance-optimized antenna selection (EDAS) method is designed. From simulation results and analysis, the four TAS schemes have a decreasing order: Max-SR, leakage-based, generalized EDAS, and random (conventional), in terms of SR performance. However, the proposed Max-SR method requires the exhaustive search to achieve the optimal SR performance, thus its complexity is extremely high as the number of antennas tends to medium and large scale. The proposed leakage-based method approaches the Max-SR method with much lower complexity. Thus, it achieves a good balance between complexity and SR performance. In terms of bit error rate, their performances are in an increasing order: random, leakage-based, Max-SR, and generalized EDAS.

Dual-UAV-Enabled Secure Communications: Joint Trajectory Design and User Scheduling

In this paper, we investigate a novel unmanned aerial vehicle (UAV)-enabled secure communication system. Two UAVs are applied in this system where one UAV moves around to communicate with multiple users on the ground using orthogonal time-division multiple access while the other UAV in the area jams the eavesdroppers on the ground to protect communications of the desired users. Specifically, we maximize the minimum worst-case secrecy rate among the users within each period by jointly adjusting UAV trajectories and user scheduling under the maximum UAV speed constraints, the UAV return constraints, the UAV collision avoidance constraints, and the discrete binary constraints on user scheduling variables. Since the resulting optimization problem is very difficult to solve due to its highly nonlinear objective function and nonconvex constraints, we first equivalently transform it into a more tractable problem. In particular, the binary constraints are equivalently converted to a number of equality constraints. Then, we develop a novel joint optimization algorithm to handle the converted problem. In order to further improve the secrecy rate performance, we also extend the developed algorithm to the case with multiple jamming UAVs. The simulation results show that the proposed joint optimization algorithm achieves significantly better performance than the conventional algorithms.

Power Allocation Strategies for Secure Spatial Modulation

In secure spatial modulation (SM) networks, power allocation (PA) strategies are investigated in this paper under the total power constraint. Considering that there is no closed-form expression for secrecy rate (SR), an approximate closed-form expression of SR is presented, which is used as an efficient metric to optimize PA factor and can greatly reduce the computation complexity. Based on this expression, a convex optimization (CO) method of maximizing SR (Max-SR) is proposed accordingly. Furthermore, a method of maximizing the product of signal-to-leakage and noise ratio (SLNR) and artificial noise-to-leakage-and noise ratio (ANLNR) (Max-P-SAN) is proposed to provide an analytic solution to PA with extremely low-complexity. Simulation results demonstrate that the SR performance of the proposed CO method is close to that of the optimal PA strategy of Max-SR with exhaustive search and better than that of Max-P-SAN in the high signal-to-noise ratio (SNR) region. However, in the low and medium SNR regions, the SR performance of the proposed Max-P-SAN slightly exceeds that of the proposed CO.

Secrecy Rate Maximization for Untrusted Relay Networks With Nonorthogonal Cooperative Transmission Protocols

In this paper, a relay based network is considered where the source transmits confidential message to the destination via a nonregenerative relay. Due to the fact that the relay is unidentified, and thus may wiretap the relayed message from source to destination. In this regard, two new half-duplex nonorthogonal amplify-and-forward (NAF) secure communication protocols are proposed, with different assumptions on the transmission ability of the destination, i.e., NAF-I for destination without transmission ability and NAF-II for destination with transmission ability. We separately derive the sufficient and necessary conditions to yield positive secrecy rate for these protocols under fixed source/destination transmission power, and discuss their joint power allocation that maximizes the system secrecy rate. Despite the nonconvexity of the considered power allocation problems, alternative optimization approach is proved useful in dealing with these problems, and the corresponding algorithms are proposed. We further prove the convergence of the proposed algorithms and analyze their complexity. The discussion is also extended to the orthogonal amplify-and-forward (OAF) based protocols, i.e., OAF-I or OAF-II, for comparison purpose. Our numerical results demonstrate the gain of the secrecy rate performance of the proposed NAF protocols over existing transmission protocols, and also verify the effectiveness of the designed alternative optimization algorithms.