Visible to the public Biblio

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2022-07-01
Shengnan, Cao, Xiangdong, Jia, Yixuan, Guo, Yuhua, Zhao.  2021.  Physical Layer Security Communication of Cognitive UAV Mobile Relay Network. 2021 7th International Symposium on Mechatronics and Industrial Informatics (ISMII). :267—271.
We consider that in order to improve the utilization rate of spectrum resources and the security rate of unmanned aerial vehicle (UAV) Communication system, a secure transmission scheme of UAV relay assisted cognitive radio network (CRN) is proposed. In the presence of primary users and eavesdroppers, the UAV acts as the decoding and forwarding mobile relay to assist the secure transmission from the source node to the legitimate destination node. This paper optimizes the flight trajectory and transmission power of the UAV relay to maximize the security rate. Since the design problem is nonconvex, the original problem is approximated to a convex constraint by constructing a surrogate function with nonconvex constraints, and an iterative algorithm based on continuous convex approximation is used to solve the problem. The simulation results show that the algorithm can effectively improve the average security rate of the secondary system and successfully optimize the UAV trajectory.
2022-05-06
Liu, Yao, Li, Luyu, Fan, Rong, Ma, Suya, Liu, Xuan, Su, Yishan.  2021.  A Physical Layer Security Mechanism based on Cooperative Jamming in Underwater Acoustic Sensor Networks. 2021 IEEE/CIC International Conference on Communications in China (ICCC Workshops). :239—243.
Due to broadcast nature of acoustic signal, underwater acoustic sensor networks face security challenge. In the paper, we propose a physical layer security transmission scheme with cooperative jamming. The proposed scheme takes advantage of the long propagation delay of the underwater acoustic channel to interfere with eavesdropper without affecting the reception of intended users. The results of both simulation and field experiment show that the proposed mechanism can improve the secrecy capacity of the network and effectively jam eavesdropper.
2022-03-01
Yin, Hoover H. F., Xu, Xiaoli, Ng, Ka Hei, Guan, Yong Liang, Yeung, Raymond w..  2021.  Analysis of Innovative Rank of Batched Network Codes for Wireless Relay Networks. 2021 IEEE Information Theory Workshop (ITW). :1–6.
Wireless relay network is a solution for transmitting information from a source node to a sink node far away by installing a relay in between. The broadcasting nature of wireless communication allows the sink node to receive part of the data sent by the source node. In this way, the relay does not need to receive the whole piece of data from the source node and it does not need to forward everything it received. In this paper, we consider the application of batched network coding, a practical form of random linear network coding, for a better utilization of such a network. The amount of innovative information at the relay which is not yet received by the sink node, called the innovative rank, plays a crucial role in various applications including the design of the transmission scheme and the analysis of the throughput. We present a visualization of the innovative rank which allows us to understand and derive formulae related to the innovative rank with ease.
2021-06-30
Ding, Xinyao, Wang, Yan.  2020.  False Data Injection Attack Detection Before Decoding in DF Cooperative Relay Network. 2020 Asia Conference on Computers and Communications (ACCC). :57—61.
False data injection (FDI) attacks could happen in decode-and-forward (DF) wireless cooperative relay networks. Although physical integrity check (PIC) can combat that by applying physical layer detection, the detector depends on the decoding results and low signal-to-noise ratio (SNR) further deteriorates the detecting results. In this paper, a physical layer detect-before-decode (DbD) method is proposed, which has low computational complexity with no sacrifice of false alarm and miss detection rates. One significant advantage of this method is the detector does not depend on the decoding results. In order to implement the proposed DbD method, a unified error sufficient statistic (UESS) containing the full information of FDI attacks is constructed. The proposed UESS simplifies the detector because it is applicable to all link conditions, which means there is no need to deal each link condition with a specialized sufficient statistic. Moreover, the source to destination outage probability (S2Dop) of the DF cooperative relay network utilizing the proposed DbD method is studied. Finally, numerical simulations verify the good performance of this DbD method.
2021-03-01
Chakravarty, S., Hopkins, A..  2020.  LoRa Mesh Network with BeagleBone Black. 2020 Fourth World Conference on Smart Trends in Systems, Security and Sustainability (WorldS4). :306–311.
This paper investigates the use of BeagleBone Black Wireless single-board Linux computers with Long Range (LoRa) transceivers to send and receive information in a mesh network while one of the transmitting/receiving nodes is acting as a relay in the system. An experiment is conducted to examine how long each LoRa node needed to learn the transmission intervals of any other transmitting nodes on the network and to synchronize with the other nodes prior to transmission. The spread factor, bandwidth, and coding rate are all varied for a total of 18 different combinations. A link to the Python code used on the BeagleBone Black is provided at the end of this paper. The best parameter combinations for each individual node and for the system as a whole is investigated. Additional experiments and applications of this technology are explored in the conclusions.
Lim, S., Ko, Y..  2020.  Intellectual Priority-based Low Latency Data Delivery Scheme for Multi-interface and Multi-channel Devices in Multi-hop Wireless Mesh Networks. 2020 IEEE International Conference on Big Data and Smart Computing (BigComp). :417–419.
In multi-hop wireless mesh networks, the end-to-end delay for a packet is getting longer as the relaying hops to the destination are increasing. The real-time packet such as the urgent safety message should be delivered within the stipulated deadline. Most previous studies have been focused to find out the optimal route to the destination. We propose an intellectual priority-based packet transmission scheme for multi-interface devices in multi-hop wireless mesh networks.
2021-02-23
Xie, L. F., Ho, I. W., Situ, Z., Li, P..  2020.  The Impact of CFO on OFDM based Physical-layer Network Coding with QPSK Modulation. 2020 IEEE Wireless Communications and Networking Conference (WCNC). :1—6.
This paper studies Physical-layer Network Coding (PNC) in a two-way relay channel (TWRC) operated based on OFDM and QPSK modulation but with the presence of carrier frequency offset (CFO). CFO, induced by node motion and/or oscillator mismatch, causes inter-carrier interference (ICI) that impairs received signals in PNC. Our ultimate goal is to empower the relay in TWRC to decode network-coded information of the end users at a low bit error rate (BER) under CFO, as it is impossible to eliminate the CFO of both end users. For that, we first put forth two signal detection and channel decoding schemes at the relay in PNC. For signal detection, both schemes exploit the signal structure introduced by ICI, but they aim for different output, thus differing in the subsequent channel decoding. We then consider CFO compensation that adjusts the CFO values of the end nodes simultaneously and find that an optimal choice is to yield opposite CFO values in PNC. Particularly, we reveal that pilot insertion could play an important role against the CFO effect, indicating that we may trade more pilots for not just a better channel estimation but also a lower BER at the relay in PNC. With our proposed measures, we conduct simulation using repeat-accumulate (RA) codes and QPSK modulation to show that PNC can achieve a BER at the relay comparable to that of point-to-point transmissions for low to medium CFO levels.
2020-12-02
Zhao, Q., Du, P., Gerla, M., Brown, A. J., Kim, J. H..  2018.  Software Defined Multi-Path TCP Solution for Mobile Wireless Tactical Networks. MILCOM 2018 - 2018 IEEE Military Communications Conference (MILCOM). :1—9.
Naval Battlefield Network communications rely on wireless network technologies to transmit data between different naval entities, such as ships and shore nodes. Existing naval battle networks heavily depend on the satellite communication system using single-path TCP for reliable, non-interactive data. While satisfactory for traditional use cases, this communication model may be inadequate for outlier cases, such as those arising from satellite failure and wireless signal outage. To promote network stability and assurance in such scenarios, the addition of unmanned aerial vehicles to function as relay points can complement network connectivity and alleviate potential strains in adverse conditions. The inherent mobility of aerial vehicles coupled with existing source node movements, however, leads to frequent network handovers with non-negligible overhead and communication interruption, particularly in the present single-path model. In this paper, we propose a solution based on multi-path TCP and software-defined networking, which, when applied to mobile wireless heterogeneous networks, reduces the network handover delay and improves the total throughput for transmissions among various naval entities at sea and littoral. In case of single link failure, the presence of a connectable relay point maintains TCP connectivity and reduces the risk of service interruption. To validate feasibility and to evaluate performance of our solution, we constructed a Mininet- WiFi emulation testbed. Compared against single-path TCP communication methods, execution of the testbed when configured to use multi-path TCP and UAV relays yields demonstrably more stable network handovers with relatively low overhead, greater reliability of network connectivity, and higher overall end-to-end throughput. Because the SDN global controller dynamically adjusts allocations per user, the solution effectively eliminates link congestion and promotes more efficient bandwidth utilization.
2020-09-18
Pham-Thi-Dan, Ngoc, Do-Dac, Thiem, Ho-Van, Khuong, Vo-Que, Son, Pham-Ngoc, Son.  2019.  On Security Capability of Cooperative Communications in Energy Scavenging Cognitive Radio Networks. 2019 International Conference on Advanced Technologies for Communications (ATC). :89—93.
In this paper, secrecy outage probability (SOP) of cooperative communications in ESCRNs is numerically evaluated by the recommended precise closed-form formula which is corroborated by numerous computer simulations. Results expose that the relay's location, energy scavenging time, message recovering time, and power division for energy scavenging and message recovering dramatically impact the SOP of the cooperative communications in ESCRNs. Moreover, results infer that the SOP is constant either in energy scavenging non-cognitive networks (ES-nonCRNs) or in ESCRNs with infinite power transmitters.
Pham-Thi-Dan, Ngoc, Ho-Van, Khuong, Do-Dac, Thiem, Vo-Que, Son, Pham-Ngoc, Son.  2019.  Security Analysis for Cognitive Radio Network with Energy Scavenging Capable Relay over Nakagami-m Fading Channels. 2019 International Symposium on Electrical and Electronics Engineering (ISEE). :68—72.
In this paper, we propose an exact closed-form expression of secrecy outage probability (SOP) for underlay cognitive network with energy scavenging capable relay over Nakagami-m fading channels and under both (maximum transmit and interference) power constraints. Various results validated the proposed expression and shed insights into the security performance of this network in key specifications.
2020-06-08
Boubakri, Wided, Abdallah, Walid, Boudriga, Noureddine.  2019.  Game-Based Attack Defense Model to Provide Security for Relay Selection in 5G Mobile Networks. 2019 IEEE Intl Conf on Parallel Distributed Processing with Applications, Big Data Cloud Computing, Sustainable Computing Communications, Social Computing Networking (ISPA/BDCloud/SocialCom/SustainCom). :160–167.

5G mobile networks promise universal communication environment and aims at providing higher bandwidth, increased communication and networking capabilities, and extensive signal coverage by using multiple communication technologies including Device-to-Device (D-to-D). This paradigm, will allow scalable and ubiquitous connectivity for large-scale mobile networks where a huge number of heterogeneous devices with limited resources will cooperate to enhance communication efficiency in terms of link reliability, spectral efficiency, system capacity, and transmission range. However, owing to its decentralized nature, cooperative D-to-D communication could be vulnerable to attacks initiated on relay nodes. Consequently, a source node has the interest to select the more protected relay to ensure the security of its traffic. Nevertheless, an improvement in the protection level has a counterpart cost that must be sustained by the device. To address this trade-off as well as the interaction between the attacker and the source device, we propose a dynamic game theoretic based approach to model and analyze this problem as a cost model. The utility function of the proposed non-cooperative game is based on the concepts of return on protection and return on attack which illustrate the gain of selecting a relay for transmitting a data packet by a source node and the reward of the attacker to perform an attack to compromise the transmitted data. Moreover, we discuss and analyze Nash equilibrium convergence of this attack-defense model and we propose an heuristic algorithm that can determine the equilibrium state in a limited number of running stages. Finally, we perform simulation work to show the effectiveness of the game model in assessing the behavior of the source node and the attacker and its ability to reach equilibrium within a finite number of steps.

2020-05-26
Soualfi, Abderrahim Hajji, Agoujil, Said, Qaraai, Youssef.  2019.  Performance Analysis of OLSR Protocol under MPR Attack in Progressive Size Grid MANET. 2019 International Conference on Wireless Networks and Mobile Communications (WINCOM). :1–5.
Mobile Ad-hoc NETwork (MANET) is a collection of mobile devices which interchange information without the use of predefined infrastructures or central administration. It is employed in many domains such as military and commercial sectors, data and sensors networks, low level applications, etc. The important constraints in this network are the limitation of bandwidth, processing capabilities and battery life. The choice of an effective routing protocol is primordial. From many routing protocols developed for MANET, OLSR protocol is a widely-used proactive routing protocol which diffuses topological information periodically. Thus, every node has a global vision of the entire network. The protocol assumes, like the other protocols, that the nodes cooperate in a trusted environment. So, all control messages are transmitted (HELLO messages) to all 1-hop neighbor nodes or broadcasted (TC and MID messages) to the entire network in clear. However, a node, which listens to OLSR control messages, can exploit this property to lead an attack. In this paper, we investigate on MultiPoint Relay (MPR) attack considered like one of the efficient OLSR attacks by using a simulation in progressive size gridMANET.
2020-04-10
Hao, Hao, Ying Li, Xin.  2019.  Research on Physical Layer Security of Cooperative Networks Based on Swipt. 2019 International Conference on Smart Grid and Electrical Automation (ICSGEA). :583—586.
In Cooperative Networks based on simultaneous wireless information and power transfer (SWIPT), relay nodes collect the energy of radio signals received from source node and transmit the information of source nodes to destination nodes, which not only prolongs the service life of energy-constrained nodes, but also improves the ability of long-distance transmission of information. Due to the openness of energy harvesting, there may be eavesdropping users with malicious decoding. In order to study the security performance of the Cooperative Networks based on SWIPT, this paper mainly studies the physical layer security performance of this network, derives and simulates the expression of system security outage probability and throughput. The simulation results show that the system security performance is mainly influenced by time allocation parameter of SWIPT and decreases with the increase of target rate.
2020-04-06
Naves, Raphael, Jakllari, Gentian, Khalife, Hicham, Conant, Vania, Beylot, Andre-Luc.  2018.  When Analog Meets Digital: Source-Encoded Physical-Layer Network Coding. 2018 IEEE 19th International Symposium on "A World of Wireless, Mobile and Multimedia Networks" (WoWMoM). :1–9.
We revisit Physical-Layer Network Coding (PLNC) and the reasons preventing it from becoming a staple in wireless networks. We identify its strong coupling to the Two-Way Relay Channel (TWRC) as key among them due to its requiring crossing traffic flows and two-hop node coordination. We introduce SE-PLNC, a Source-Encoded PLNC scheme that is traffic pattern independent and involves coordination only among one-hop neighbors, making it significantly more practical to adopt PLNC in multi-hop wireless networks. To accomplish this, SE-PLNC introduces three innovations: it combines bit-level with physical-level network coding, it shifts most of the coding burden from the relay to the source of the PLNC scheme, and it leverages multi-path relaying opportunities available to a particular traffic flow. We evaluate SE-PLNC using theoretical analysis, proof-of-concept implementation on a Universal Software Radio Peripherals (USRP) testbed, and simulations. The theoretical analysis shows the scalability of SE-PLNC and its efficiency in large ad-hoc networks while the testbed experiments its real-life feasibility. Large-scale simulations show that TWRC PLNC barely boosts network throughput while SE-PLNC improves it by over 30%.
2020-03-02
Illi, Elmehdi, Bouanani, Faissal El, da Costa, Daniel Benevides, Sofotasios, Paschalis C., Ayoub, Fouad, Mezher, Kahtan, Muhaidat, Sami.  2019.  On the Physical Layer Security of a Regenerative Relay-Based mixed RF/UOWC. 2019 International Conference on Advanced Communication Technologies and Networking (CommNet). :1–7.
This paper investigates the secrecy outage performance of a dual-hop decode-and-forward (DF) mixed radio-frequency/underwater optical wireless communication (RF/UOWC) system. We consider a one-antenna source node ( S), communicating with one legitimate destination node (D) via a multi-antenna DF relay (R) node. In this context, the relay node receives the incoming signal from S via an RF link, which is subject to Rayleigh fading, then performes selection-combining (SC) followed by decoding and then re-encoding for transmission to the destination over a UOWC link, subject to mixture Exponential-Gamma fading. Under the assumption of eavesdroppers attempting to intercept the S-R (RF side), a closed-form expression for the secrecy outage probability is derived. Our analytical results are corroborated through computer simulations, which verifies their validity.
Illi, Elmehdi, Bouanani, Faissal El, Ayoub, Fouad.  2019.  Physical Layer Security of an Amplify-and-Forward Energy Harvesting-Based Mixed RF/UOW System. 2019 International Conference on Advanced Communication Technologies and Networking (CommNet). :1–8.
This paper investigates the secrecy outage performance of an energy harvesting-based dual-hop amplify-and-forward (AF) mixed radio-frequency/underwater optical wireless communication (RF/UOWC) system. A single-antenna source node (S) is considered, communicating with one legitimate destination node (D) with the aid of a multi-antenna AF relay (R) device. In this setup, the relay node receives the incoming signal from S via an RF link, which is subject to Nakagami-m fading, then performs maximal-ratio-combining (MRC) followed by a fixed-gain amplification, before transmitting it to the destination via a UOWC link, subject to mixture Exponential-Gamma fading. Assuming the presence of a malicious eavesdropper attempting to intercept the S- R hop, a tight approximate expression for the secrecy outage probability is retrieved. The derived results provide useful insights into the influence of key system parameters on the secrecy outage performance. Our analytical results are corroborated through computer simulations, which verifies their validity.
2020-02-26
Kumar, A. Ranjith, Sivagami, A..  2019.  Balanced Load Clustering with Trusted Multipath Relay Routing Protocol for Wireless Sensor Network. 2019 Innovations in Power and Advanced Computing Technologies (i-PACT). 1:1–6.

Clustering is one of an eminent mechanism which deals with large number of nodes and effective consumption of energy in wireless sensor networks (WSN). Balanced Load Clustering is used to balance the channel bandwidth by incorporating the concept of HMAC. Presently several research studies works to improve the quality of service and energy efficiency of WSN but the security issues are not taken care of. Relay based multipath trust is one of the methods to secure the network. To this end, a novel approach called Balanced Load Clustering with Trusted Multipath Relay Routing Protocol (BLC-TMR2) to improve the performance of the network. The proposed protocol consists of two algorithms. Initially in order to reduce the energy consumption of the network, balanced load clustering (BLC) concepts is introduced. Secondly to secure the network from the malicious activity trusted multipath relay routing protocol (TMR2) is used. Multipath routing is monitored by the relay node and it computed the trust values. Network simulation (NS2) software is used to obtain the results and the results prove that the proposed system performs better the earlier methods the in terms of efficiency, consumption, QoS and throughput.

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.
2019-12-30
Shirasaki, Yusuke, Takyu, Osamu, Fujii, Takeo, Ohtsuki, Tomoaki, Sasamori, Fumihito, Handa, Shiro.  2018.  Consideration of security for PLNC with untrusted relay in game theoretic perspective. 2018 IEEE Radio and Wireless Symposium (RWS). :109–112.
A physical layer network coding (PLNC) is a highly efficient scheme for exchanging information between two nodes. Since the relay receives the interfered signal between two signals sent by two nodes, it hardly decodes any information from received signal. Therefore, the secure wireless communication link to the untrusted relay is constructed. The two nodes optimize the transmit power control for maximizing the secure capacity but these depend on the channel state information informed by the relay station. Therefore, the untrusted relay disguises the informed CSI for exploiting the information from two nodes. This paper constructs the game of two optimizations between the legitimate two nodes and the untrusted relay for clarifying the security of PLNC with untrusted relay.
2019-11-25
Benamira, Elias, Merazka, Fatiha, Kurt, Gunes Karabulut.  2018.  Joint Channel Coding and Cooperative Network Coding on PSK Constellations in Wireless Networks. 2018 International Conference on Smart Communications in Network Technologies (SaCoNeT). :132–137.
In this paper, we consider the application of Reed-Solomon (RS) channel coding for joint error correction and cooperative network coding on non-binary phase shift keying (PSK) modulated signals. The relay first decodes the RS channel coded messages received each in a time slot from all sources before applying network coding (NC) by the use of bit-level exclusive OR (XOR) operation. The network coded resulting message is then channel encoded before its transmission to the next relay or to the destination according to the network configuration. This scenario shows superior performance in comparison with the case where the relay does not perform channel coding/decoding. For different orders of PSK modulation and different wireless configurations, simulation results demonstrate the improvements resulting from the use of RS channel codes in terms of symbol error rate (SER) versus signal-to-noise ratio (SNR).
Arpitha, R, Chaithra, B R, Padma, Usha.  2019.  Performance Analysis of Channel Coding Techniques for Cooperative Adhoc Network. 2019 3rd International conference on Electronics, Communication and Aerospace Technology (ICECA). :752–756.
-In wireless networks, Cooperative communication can be used to increase the strength of the communication by means of spatial diversity. Basic idea that exists behind Cooperative communication is, if the transmission from source to destination is not successful, a helping node called relay can be used to send the same information to the destination through independent paths. In order to improve the performance of such communication, channel coding techniques can be used which reduces the Bit Error Rate. Previous works on cooperative communication only concentrated on improving channel capacity through cooperation. Hence this paper presents different Channel coding methods such as Turbo coding, Convolutional coding, and low-density parity-check coding over Rayleigh fading channels in the presence of Additive white Gaussian noise. Performance of these Channel coding techniques are measured in terms of noise power spectral density (NO ) vs. Bit error rate.
2017-12-20
Azaman, M. A. bin, Nguyen, N. P., Ha, D. B., Truong, T. V..  2017.  Secrecy outage probability of full-duplex networks with cognitive radio environment and partial relay selection. 2017 International Conference on Recent Advances in Signal Processing, Telecommunications Computing (SigTelCom). :119–123.

This paper investigates the secrecy performance of full-duplex relay mode in underlay cognitive radio networks using decode-and-forward relay selection. The analytical results prove that full-duplex mode can guarantee security under critical conditions such as the bad residual self-interference and the presence of hi-tech eavesdropper. The secrecy outage probability is derived based on the statistical characteristics of channels in this considered system. The system is examined under five circumferences: 1) Different values of primary network's desired outage probability; 2) Different values of primary transmitter's transmit power; 3) Applying of multiple relays selection; 4) Systems undergo path-loss during the transmission process; 5) Systems undergo self-interference in relays. Simulation results are presented to verify the analysis.

2017-02-14
A. A. Zewail, A. Yener.  2015.  "The two-hop interference untrusted-relay channel with confidential messages". 2015 IEEE Information Theory Workshop - Fall (ITW). :322-326.

This paper considers the two-user interference relay channel where each source wishes to communicate to its destination a message that is confidential from the other destination. Furthermore, the relay, that is the enabler of communication, due to the absence of direct links, is untrusted. Thus, the messages from both sources need to be kept secret from the relay as well. We provide an achievable secure rate region for this network. The achievability scheme utilizes structured codes for message transmission, cooperative jamming and scaled compute-and-forward. In particular, the sources use nested lattice codes and stochastic encoding, while the destinations jam using lattice points. The relay decodes two integer combinations of the received lattice points and forwards, using Gaussian codewords, to both destinations. The achievability technique provides the insight that we can utilize the untrusted relay node as an encryption block in a two-hop interference relay channel with confidential messages.

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.