Visible to the public Biblio

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2023-07-21
Dabush, Lital, Routtenberg, Tirza.  2022.  Detection of False Data Injection Attacks in Unobservable Power Systems by Laplacian Regularization. 2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop (SAM). :415—419.
The modern electrical grid is a complex cyber-physical system, and thus is vulnerable to measurement losses and attacks. In this paper, we consider the problem of detecting false data injection (FDI) attacks and bad data in unobservable power systems. Classical bad-data detection methods usually assume observable systems and cannot detect stealth FDI attacks. We use the smoothness property of the system states (voltages) w.r.t. the admittance matrix, which is also the Laplacian of the graph representation of the grid. First, we present the Laplacian-based regularized state estimator, which does not require full observability of the network. Then, we derive the Laplacian-regularized generalized likelihood ratio test (LR-GLRT). We show that the LR-GLRT has a component of a soft high-pass graph filter applied to the state estimator. Numerical results on the IEEE 118-bus system demonstrate that the LR-GLRT outperforms other detection approaches and is robust to missing data.
2023-04-28
Barac, Petar, Bajor, Matthew, Kinget, Peter R..  2022.  Compressive-Sampling Spectrum Scanning with a Beamforming Receiver for Rapid, Directional, Wideband Signal Detection. 2022 IEEE 95th Vehicular Technology Conference: (VTC2022-Spring). :1–5.
Communication systems across a variety of applications are increasingly using the angular domain to improve spectrum management. They require new sensing architectures to perform energy-efficient measurements of the electromagnetic environment that can be deployed in a variety of use cases. This paper presents the Directional Spectrum Sensor (DSS), a compressive sampling (CS) based analog-to-information converter (CS-AIC) that performs spectrum scanning in a focused beam. The DSS offers increased spectrum sensing sensitivity and interferer tolerance compared to omnidirectional sensors. The DSS implementation uses a multi-antenna beamforming architecture with local oscillators that are modulated with pseudo random waveforms to obtain CS measurements. The overall operation, limitations, and the influence of wideband angular effects on the spectrum scanning performance are discussed. Measurements on an experimental prototype are presented and highlight improvements over single antenna, omnidirectional sensing systems.
ISSN: 2577-2465
2022-10-16
Zhang, Ming, Shang, Yong, Zhao, Yaohuan.  2020.  Strategy of Relay Selection and Cooperative Jammer Beamforming in Physical Layer Security. 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall). :1–6.
In this paper, a novel strategy of relay selection and cooperative jammer beamforming is proposed. The proposed scheme selects one node from the intermediate nodes as relay and the rest nodes as friendly jammers. The relay operates in amplify-and-forward (AF) strategy. Jammer weights are derived to null the jamming signals at the destination and relay node and maximize the jamming signal at the eavesdropper. Furthermore, a closed-form optimal solution of power allocation between the selected relay and cooperative jammers is derived. Numerical simulation results show that the proposed scheme can outperform the conventional schemes at the same power consumption.
2022-08-12
Zhu, Zhen, Chi, Cheng, Zhang, Chunhua.  2021.  Spatial-Resampling Wideband Compressive Beamforming. OCEANS 2021: San Diego – Porto. :1—4.
Compressive beamforming has been successfully applied to the estimation of the direction of arrival (DOA) of array signals, and has higher angular resolution than traditional high-resolution beamforming methods. However, most of the existing compressive beamforming methods are based on narrow signal models. Wideband signal processing using these existing compressive beamforming methods is to divide the frequency band into several narrow-bands and add up the beamforming results of each narrow-band. However, for sonar application, signals usually consist of continuous spectrum and line spectrum, and the line spectrum is usually more than 10dB higher than the continuous spectrum. Due to the large difference of signal-to-noise ratio (SNR) of each narrow-band, different regularization parameters should be used, otherwise it is difficult to get an ideal result, which makes compressive beamforming highly complicated. In this paper, a compressive beamforming method based on spatial resampling for uniform linear arrays is proposed. The signals are converted into narrow-band signals by spatial resampling technique, and compressive beamforming is then performed to estimate the DOA of the sound source. Experimental results show the superiority of the proposed method, which avoids the problem of using different parameters in the existing compressive beamforming methods, and the resolution is comparable to the existing methods using different parameters for wideband models. The spatial-resampling compressive beamforming has a better robustness when the regularization parameter is fixed, and exhibits lower levels of background interference than the existing methods.
2022-07-01
Xu, Xiaorong, Bao, Jianrong, Wang, Yujun, Hu, Andi, Zhao, Bin.  2021.  Cognitive Radio Primary Network Secure Communication Strategy Based on Energy Harvesting and Destination Assistance. 2021 13th International Conference on Wireless Communications and Signal Processing (WCSP). :1—5.
Cognitive radio primary network secure communication strategy based on secondary user energy harvesting and primary user destination assistance is investigated to guarantee primary user secure communication in cognitive radio network. In the proposed strategy, the primary network selects the best secondary user to forward the traffic from a primary transmitter (PT) to a primary receiver (PR). The best secondary user implements beamforming technique to assist primary network for secure communication. The remaining secondary transmitters harvest energy and transmit information to secondary receiver over the licensed primary spectrum. In order to further enhance the security of primary network and increase the harvested energy for the remaining secondary users, a destination-assisted jamming signal transmission strategy is proposed. In this strategy, artificial noise jamming signal transmitted by PR not only confuses eavesdropper, but also be used to power the remaining secondary users. Simulation results demonstrate that, the proposed strategy allows secondary users to communicate in the licensed primary spectrum. It enhances primary network secure communication performance dramatically with the joint design of secondary user transmission power and beamforming vectors. Furthermore, physical layer security of primary and secondary network can also be guaranteed via the proposed cognitive radio primary network secure communication strategy.
2021-11-30
Yao, Li, Liu, Youjiang.  2020.  A Novel Optimization Scheme for the Beamforming Method Selection in Artificial-Noise-Aid MU-MISOME Broadcast Secure Communication System. 2020 International Symposium on Computer Engineering and Intelligent Communications (ISCEIC). :175–179.
This article investigates the beamforming method selection in artificial-noise-aid (AN-aid) multiuser multiple-input-single-output (MU-MISO) broadcast wiretap systems in slow fading channel environment. We adopt beamforming pre-coding matrix with artificial noise to achieve secure multiuser communication and optimize system performance, and compare the secure transmission performance of two beamforming methods. To overcome the complexity of this model, a novel optimization scheme expressed using semi-closed-form expressions and Monte Carlo method is employed to derive the relationship between transmission parameters and secure transmission performance. This scheme would help us to analyses performance of different beamforming methods.
Gao, Jianbang, Yuan, Zhaohui, Qiu, Bin.  2020.  Artificial Noise Projection Matrix Optimization Method for Secure Multi-Cast Wireless Communication. 2020 IEEE 8th International Conference on Information, Communication and Networks (ICICN). :33–37.
Transmit beamforming and artificial noise (AN) methods have been widely employed to achieve wireless physical layer (PHY) secure transmissions. While most works focus on transmit beamforming optimization, little attention is paid to the design of artificial noise projection matrix (ANPM). In this paper, compared with traditional ANPM obtained by zero-forcing method, which only makes AN power uniform distribution in free space outside legitimate users (LU) locations, we design ANPM to maximize the interference on eavesdroppers without interference on LUs for multicast directional modulation (MCDM) scenario based on frequency diverse array (FDA). Furthermore, we extend our approach to the case of with imperfect locations of Eves. Finally, simulation results show that Eves can be seriously affected by the AN with perfect/imperfect locations, respectively.
2021-05-18
Cho, Sunghwan, Chen, Gaojie, Coon, Justin P..  2020.  Enhancing Security in VLC Systems Through Beamforming. GLOBECOM 2020 - 2020 IEEE Global Communications Conference. :1–6.
This paper proposes a novel zero-forcing (ZF) beamforming strategy that can simultaneously cope with active and passive eavesdroppers (EDs) in visible light communication systems. A related optimization problem is formulated to maximize the signal-to-noise ratio (SNR) of the legitimate user (UE) while suppressing the SNR of active ED to zero and constraining the average SNR of passive EDs. The proposed beamforming directs the transmission along a particular eigenmode related to the null space of the active ED channel and the intensity of the passive ED point process. An inverse free preconditioned Krylov subspace projection method is used to find the eigenmode. The numerical results show that the proposed ZF beamforming scheme yields better performance relative to a traditional ZF beamforming scheme in the sense of increasing the SNR of the UE and reducing the secrecy outage probability.
Liu, Xiaodong, Chen, Zezong, Wang, Yuhao, Zhou, Fuhui, Ma, Shuai, Hu, Rose Qingyang.  2020.  Secure Beamforming Designs in MISO Visible Light Communication Networks with SLIPT. GLOBECOM 2020 - 2020 IEEE Global Communications Conference. :1–6.
Visible light communication (VLC) is a promising technique in the fifth and beyond wireless communication networks. In this paper, a secure multiple-input single-output VLC network is studied, where simultaneous lightwave information and power transfer (SLIPT) is exploited to support energy-limited devices taking into account a practical non-linear energy harvesting model. Specifically, the optimal beamforming design problems for minimizing transmit power and maximizing the minimum secrecy rate are studied under the imperfect channel state information (CSI). S-Procedure and a bisection search is applied to tackle challenging non-convex problems and to obtain efficient resource allocation algorithm. It is proved that optimal beamforming schemes can be obtained. It is found that there is a non-trivial trade-off between the average harvested power and the minimum secrecy rate. Moreover, we show that the quality of CSI has a significant impact on achievable performance.
2020-07-03
Viegas, P., Borges, D., Montezuma, P., Dinis, R., Silva, M. M..  2019.  Multi-beam Physical Security Scheme: Security Assessment and Impact of Array Impairments on Security and Quality of Service. 2019 PhotonIcs Electromagnetics Research Symposium - Spring (PIERS-Spring). :2368—2375.

Massive multiple-input multiple-output (mMIMO) with perfect channel state information (CSI) can lead array power gain increments proportional to the number of antennas. Despite this fact constrains on power amplification still exist due to envelope variations of high order constellation signals. These constrains can be overpassed by a transmitter with several amplification branches, with each one associated to a component signal that results from the decomposition of a multilevel constellation as a sum of several quasi constant envelope signals that are sent independently. When combined with antenna arrays at the end of each amplification branch the security improves due to the energy separation achieved by beamforming. However, to avoid distortion on the signal resulting from the combination of all components at channel level all the beams of signal components should be directed in same direction. In such conditions it is crucial to assess the impact of misalignments between beams associated to each user, which is the purpose of this work. The set of results presented here show the good tolerance against misalignments of these transmission structures.

2020-02-17
Chalise, Batu K..  2019.  ADMM-based Beamforming Optimization for Physical Layer Security in a Full-duplex Relay System. ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). :4734–4738.
Although beamforming optimization problems in full-duplex communication systems can be optimally solved with the semidefinite relaxation (SDR) approach, its computational complexity increases rapidly when the problem size increases. In order to circumvent this issue, in this paper, we propose an alternating direction of multiplier method (ADMM) which minimizes the augmented Lagrangian of the dual of the SDR and handles the inequality constraints with the use of slack variables. The proposed ADMM is then applied for optimizing the relay beamformer to maximize the secrecy rate. Simulation results show that the proposed ADMM performs as good as the SDR approach.
Liu, Xiaochen, Gao, Yuanyuan, Zang, Guozhen, Sha, Nan.  2019.  Artificial-Noise-Aided Robust Beamforming for MISOME Wiretap Channels with Security QoS. 2019 IEEE 19th International Conference on Communication Technology (ICCT). :795–799.
This paper studies secure communication from a multi-antenna transmitter to a single-antenna receiver in the presence of multiple multi-antenna eavesdroppers, considering constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers. The robust joint optimal beamforming (RJOBF) of secret signal and artificial noise (AN) is designed to minimize transmit power while estimation errors of channel state information (CSI) for wiretap channels are taken into consideration. The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs) along with semidefinite relaxation (SDR) technique. The simulation results illustrate that our proposed RJOBF is efficient for power saving in security communication.
2020-01-20
Vu, Thang X., Vu, Trinh Anh, Lei, Lei, Chatzinotas, Symeon, Ottersten, Björn.  2019.  Linear Precoding Design for Cache-aided Full-duplex Networks. 2019 IEEE Wireless Communications and Networking Conference (WCNC). :1–6.
Edge caching has received much attention as a promising technique to overcome the stringent latency and data hungry challenges in the future generation wireless networks. Meanwhile, full-duplex (FD) transmission can potentially double the spectral efficiency by allowing a node to receive and transmit simultaneously. In this paper, we study a cache-aided FD system via delivery time analysis and optimization. In the considered system, an edge node (EN) operates in FD mode and serves users via wireless channels. Two optimization problems are formulated to minimize the largest delivery time based on the two popular linear beamforming zero-forcing and minimum mean square error designs. Since the formulated problems are non-convex due to the self-interference at the EN, we propose two iterative optimization algorithms based on the inner approximation method. The convergence of the proposed iterative algorithms is analytically guaranteed. Finally, the impacts of caching and the advantages of the FD system over the half-duplex (HD) counterpart are demonstrated via numerical results.
2019-03-25
Son, W., Jung, B. C., Kim, C., Kim, J. M..  2018.  Pseudo-Random Beamforming with Beam Selection for Improving Physical-Layer Security. 2018 Tenth International Conference on Ubiquitous and Future Networks (ICUFN). :382–384.
In this paper, we propose a novel pseudo-random beamforming technique with beam selection for improving physical-layer security (PLS) in a downlink cellular network where consists of a base station (BS) with Ntantennas, NMSlegitimate mobile stations (MSs), and NEeavesdroppers. In the proposed technique, the BS generates multiple candidates of beamforming matrix each of which consists of orthogonal beamforming vectors in a pseudo-random manner. Each legitimate MS opportunistically feeds back the received signal-to-interference-and-noise ratio (SINR) value for all beamforming vectors to the BS. The BS transmits data to the legitimate MSs with the optimal beamforming matrix among multiple beam forming matrices that maximizes the secrecy sum-rate. Simulation results show that the proposed technique outperforms the conventional random beamforming technique in terms of the achievable secrecy sum-rate.
Li, Haipeng, Zheng, Cuie, Zhang, Jucheng.  2018.  Redundant Dictionary Construction via Genetic Algorithm. Proceedings of the 2Nd International Conference on Vision, Image and Signal Processing. :66:1–66:5.
Sparse representation of signals based on redundant dictionary is widely used in array signal processing. In this paper, a redundant dictionary construction method via genetic algorithm (GA) is proposed for array signal processing. The problem is formulated as a dictionary selection problem where the dictionary entries are produced by discretizing the angle space. We apply the orthogonality of the entries to evaluate the dictionary according to the Restricted Isometry Property (RIP). GA is used to discretize the angle space which can make the dictionary more orthogonal. Simulation results show that the proposed method can obtain a better division of angle, improving the orthogonality of dictionary effectively, and is suitable for arbitrary observation space compared with commonly used equal angle division and equal sine division.
2018-06-07
Zhaoye, X., Ruimin, L..  2017.  Physical layer security transmission in cognitive radio network composed of multi-downlinks SU network. 2017 IEEE 17th International Conference on Communication Technology (ICCT). :898–901.
In cognitive radio network, the primary user (PU) network and the secondary user (SU) network interfered with each other because of sharing the spectral resource. Also interference among multi-downlinks in SU network decreased the sum rate in SU network and the eavesdropper in PU network decreased the secrecy rate in PU network. Focusing on above problem, this paper raised two channel selection and beamforming methods based on singular value decomposition (SVD) and uplink-downlink duality respectively, and then analyzed the performance of them in physical layer security.
2018-01-10
Chen, W., Hong, L., Shetty, S., Lo, D., Cooper, R..  2016.  Cross-Layered Security Approach with Compromised Nodes Detection in Cooperative Sensor Networks. 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). :499–508.

Cooperative MIMO communication is a promising technology which enables realistic solution for improving communication performance with MIMO technique in wireless networks that are composed of size and cost constrained devices. However, the security problems inherent to cooperative communication also arise. Cryptography can ensure the confidentiality in the communication and routing between authorized participants, but it usually cannot prevent the attacks from compromised nodes which may corrupt communications by sending garbled signals. In this paper, we propose a cross-layered approach to enhance the security in query-based cooperative MIMO sensor networks. The approach combines efficient cryptographic technique implemented in upper layer with a novel information theory based compromised nodes detection algorithm in physical layer. In the detection algorithm, a cluster of K cooperative nodes are used to identify up to K - 1 active compromised nodes. When the compromised nodes are detected, the key revocation is performed to isolate the compromised nodes and reconfigure the cooperative MIMO sensor network. During this process, beamforming is used to avoid the information leaking. The proposed security scheme can be easily modified and applied to cognitive radio networks. Simulation results show that the proposed algorithm for compromised nodes detection is effective and efficient, and the accuracy of received information is significantly improved.

2017-12-20
Lu, W., Jiang, Y., Yin, C., Tao, X., Lai, P..  2017.  Security beamforming algorithms in multibeam satellite systems. 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). :1272–1277.
This paper investigates the physical layer security in a multibeam satellite communication system, where each legitimate user is surrounded by one eavesdropper. First of all, an optimization problem is formulated to maximize the sum of achievable secrecy rate, while satisfying the on-board satellite transmit power constraint. Then, two transmit beamforming(BF) schemes, namely, the zero-forcing (ZF) and the signal-to-leakage-and-noise ratio (SLNR) BF algorithms are proposed to obtain the BF weight vectors as well as power allocation coefficients. Finally, simulation results are provided to verify the validity of the two proposed methods and demonstrate that the SLNR BF algorithm outperforms the ZF BF algorithm.
Lin, J., Li, Q., Yang, J..  2017.  Frequency diverse array beamforming for physical-layer security with directionally-aligned legitimate user and eavesdropper. 2017 25th European Signal Processing Conference (EUSIPCO). :2166–2170.
The conventional physical-layer (PHY) security approaches, e.g., transmit beamforming and artificial noise (AN)-based design, may fail when the channels of legitimate user (LU) and eavesdropper (Eve) are close correlated. Due to the highly directional transmission feature of millimeter-wave (mmWave), this may occur in mmWave transmissions as the transmitter, Eve and LU are aligned in the same direction exactly. To handle the PHY security problem with directionally-aligned LU and Eve, we propose a novel frequency diverse array (FDA) beamforming approach to differentiating the LU and Eve. By intentionally introducing some frequency offsets across the antennas, the FDA beamforming generates an angle-range dependent beampattern. As a consequence, it can degrade the Eve's reception and thus achieve PHY security. In this paper, we maximize the secrecy rate by jointly optimizing the frequency offsets and the beamformer. This secrecy rate maximization (SRM) problem is hard to solve due to the tightly coupled variables. Nevertheless, we show that it can be reformulated into a form depending only on the frequency offsets. Building upon this reformulation, we identify some cases where the SRM problem can be optimally solved in closed form. Numerical results demonstrate the efficacy of FDA beamforming in achieving PHY security, even for aligned LU and Eve.
Cao, C., Zhang, H., Lu, T., Gulliver, T. A..  2017.  An improved cooperative jamming strategy for PHY security in a multi-hop communications system. 2017 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM). :1–4.
In this paper, an improved cooperative jamming (CJ) strategy is developed for physical layer (PHY) security in a multi-hop wireless communication system which employs beamforming in the last hop. Users are assigned to independent groups based on the merger-and-split rule in a coalition game. The secrecy capacity for a valid coalition is a non-convex optimization problem which cannot easily be solved. Therefore, restrictions are added to transform this into a convex problem, and this is solved to obtain a suboptimal closed-form solution for the secrecy capacity. Simulation results are presented which show that the proposed strategy outperforms other methods such as non-cooperation, relay cooperation, and previous CJ approaches in terms of the secrecy capacity. Further, it is shown that the proposed multi-hop solution is suitable for long distance communication systems.
2017-11-20
Li, Guyue, Hu, Aiqun.  2016.  Virtual MIMO-based cooperative beamforming and jamming scheme for the clustered wireless sensor network security. 2016 2nd IEEE International Conference on Computer and Communications (ICCC). :2246–2250.

This paper considers the physical layer security for the cluster-based cooperative wireless sensor networks (WSNs), where each node is equipped with a single antenna and sensor nodes cooperate at each cluster of the network to form a virtual multi-input multi-output (MIMO) communication architecture. We propose a joint cooperative beamforming and jamming scheme to enhance the security of the WSNs where a part of sensor nodes in Alice's cluster are deployed to transmit beamforming signals to Bob while a part of sensor nodes in Bob's cluster are utilized to jam Eve with artificial noise. The optimization of beamforming and jamming vectors to minimize total energy consumption satisfying the quality-of-service (QoS) constraints is a NP-hard problem. Fortunately, through reformulation, the problem is proved to be a quadratically constrained quadratic problem (QCQP) which can be solved by solving constraint integer programs (SCIP) algorithm. Finally, we give the simulation results of our proposed scheme.

2017-02-21
Chen Bai, S. Xu, B. Jing, Miao Yang, M. Wan.  2015.  "Compressive adaptive beamforming in 2D and 3D ultrafast active cavitation imaging". 2015 IEEE International Ultrasonics Symposium (IUS). :1-4.

The ultrafast active cavitation imaging (UACI) based on plane wave can be implemented with high frame rate, in which adaptive beamforming technique was introduced to enhance resolutions and signal-to-noise ratio (SNR) of images. However, regular adaptive beamforming continuously updates the spatial filter for each sample point, which requires a huge amount of calculation, especially in the case of a high sampling rate, and, moreover, 3D imaging. In order to achieve UACI rapidly with satisfactory resolution and SNR, this paper proposed an adaptive beamforming on the basis of compressive sensing (CS), which can retain the quality of adaptive beamforming but reduce the calculating amount substantially. The results of simulations and experiments showed that comparing with regular adaptive beamforming, this new method successfully achieved about eightfold in time consuming.

M. B. Amin, W. Zirwas, M. Haardt.  2015.  "Advanced channel prediction concepts for 5G radio systems". 2015 International Symposium on Wireless Communication Systems (ISWCS). :166-170.

Massive MIMO and tight cooperation between transmission nodes are expected to become an integral part of a future 5G radio system. As part of an overall interference mitigation scheme substantial gains in coverage, spectral as well as energy efficiency have been reported. One of the main limitations for massive MIMO and coordinated multi-point (CoMP) systems is the aging of the channel state information at the transmitter (CSIT), which can be overcome partly by state of the art channel prediction techniques. For a clean slate 5G radio system, we propose to integrate channel prediction from the scratch in a flexible manner to benefit from future improvements in this area. As any prediction is unreliable by nature, further improvements over the state of the art are needed for a convincing solution. In this paper, we explain how the basic ingredients of 5G like base stations with massive MIMO antenna arrays, and multiple UE antennas can help to stretch today's limits with an approximately 10 dB lower normalized mean square error (NMSE) of the predicted channel. In combination with the novel introduced concept of artificially mutually coupled antennas, adding super-directivity gains to virtual beamforming, robust and accurate prediction over 10 ms with an NMSE of -20 dB up to 15 km/h at 2.6 GHz RF frequency could be achieved. This result has been achieved for measured channels without massive MIMO, but a comparison with ray-traced channels for the same scenario is provided as well.

2015-05-01
Mirmohseni, M., Papadimitratos, P..  2014.  Scaling laws for secrecy capacity in cooperative wireless networks. INFOCOM, 2014 Proceedings IEEE. :1527-1535.

We investigate large wireless networks subject to security constraints. In contrast to point-to-point, interference-limited communications considered in prior works, we propose active cooperative relaying based schemes. We consider a network with nl legitimate nodes and ne eavesdroppers, and path loss exponent α ≥ 2. As long as ne2(log(ne))γ = o(nl) holds for some positive γ, we show one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given a fixed total power constraint for the entire network. We achieve this result with (i) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays, and (ii) the relays acting as a virtual multi-antenna to apply beamforming against the eavesdroppers. Our simpler parallel (two-stage) relaying scheme can achieve the same unbounded secure aggregate rate when neα/2 + 1 (log(ne))γ+δ(α/2+1) = o(nl) holds, for some positive γ, δ.