We consider the problem of secure transmission in two-hop amplify-and-forward untrusted relay networks. We analyze the ergodic secrecy capacity (ESC) and present compact expressions for the ESC in the high signal-to-noise ratio regime. We also examine the impact of large scale antenna arrays at either the source or the destination. For large antenna arrays at the source, we confirm that the ESC is solely determined by the channel between the relay and the destination. For very large antenna arrays at the destination, we confirm that the ESC is solely determined by the channel between the source and the relay.
We consider the problem of secure transmission in two-hop amplify-and-forward untrusted relay networks. We analyze the ergodic secrecy capacity (ESC) and present compact expressions for the ESC in the high signal-to-noise ratio regime. We also examine the impact of large scale antenna arrays at either the source or the destination. For large antenna arrays at the source, we confirm that the ESC is solely determined by the channel between the relay and the destination. For very large antenna arrays at the destination, we confirm that the ESC is solely determined by the channel between the source and the relay.
This paper investigates the ergodic secrecy capacity (ESC) of multiple-antenna amplify-and-forward relay systems, where one eavesdropper can wiretap the relay. To reveal the capability of the multiple- antenna relay in improving the secrecy performance, we derive new tight closed-form lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. Based on the asymptotic analysis, we optimally allocate the power to the information signal and the artificial noise. Both the analysis and simulation results indicate that, in the moderate-to-high SNR regime, ANP achieves considerable performance gain over EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.
In this study, the authors study the problem of secure transmission in two‐hop amplify‐and‐forward systems with an untrusted relay. To prevent the untrusted relay from intercepting the source message and to achieve positive secrecy rate, the destination‐based cooperative jamming technique is used. In this method, the destination sends an intended jamming signal to the relay. This jamming signal helps protecting the source message from being captured reliably at the untrusted relay, while the destination cancels itself intended jamming signal. The optimal power allocation (OPA) strategy is considered for the proposed system. They observe that the objective function is a quasi‐concave function at high signal‐to‐noise‐ratio regimes. Based on this OPA strategy, in the first step, the outage probability of the system is investigated. It is investigated for three cases. In the two cases, either of the source or the destination node is equipped with large‐scale antennas, and in the third case, both of them are equipped with large‐scale antenna arrays. In all the cases, the closed‐form expressions are derived. In the second step, they investigate the ergodic secrecy rate and present the closed‐form solutions for all the mentioned cases. Finally, simulation results indicate the accuracy of the derived equations.
This paper investigates the ergodic secrecy capacity (ESC) of multiple-antenna amplify-and-forward relay systems, where one eavesdropper can wiretap the relay. To reveal the capability of the multiple- antenna relay in improving the secrecy performance, we derive new tight closed-form lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. Based on the asymptotic analysis, we optimally allocate the power to the information signal and the artificial noise. Both the analysis and simulation results indicate that, in the moderate-to-high SNR regime, ANP achieves considerable performance gain over EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.
In this paper, the authors deal with secure transmission in two‐hop amplify‐and‐forward network with untrusted relays. To prevent the untrusted relays from intercepting the source message and to achieve positive secrecy rate, the destination‐based cooperative jamming technique is used. The authors propose joint secure best relay selection (BRS) and optimal power allocation (OPA) for uplink transmission of a cellular network when the base station is equipped with very large‐scale antenna arrays. Then, the common performance metrics such as ergodic secrecy rate (ESR) and secrecy outage probability are evaluated for the optimised network. Moreover, the diversity order and diversity‐multiplexing tradeoff of the system are examined. The authors obtain that the diversity order of joint BRS and OPA scenario is equal to number of relays. Finally, some numerical and simulation results are presented to validate the theoretical analysis and to show the advantages offered by the presented systems. They reveal interesting results that, by increasing number of untrusted relay nodes, the system performance improves. For example, for target ESR 2 bits/s/Hz and ten untrusted relay nodes, the optimised network saves about 5 dB for uplink transmission, in comparison with the system applying the BRS and equal power allocation.
By taking a variety of realistic hardware imperfections into consideration, we propose an optimal power allocation (OPA) strategy to maximize the instantaneous secrecy rate of a cooperative wireless network comprised of a source, a destination, and an untrusted amplify-and-forward relay. We assume that either the source or the destination is equipped with a large-scale multiple antennas' system, while the rest are equipped with a single antenna. To prevent the untrusted relay from intercepting the source message, the destination sends an intended jamming noise to the relay, which is referred to as destination-based cooperative jamming. Given this system model, novel closed-form expressions are presented in the high signal-to-noise ratio regime for the ergodic secrecy rate and the secrecy outage probability. We further improve the secrecy performance of the system by optimizing the associated hardware design. The results reveal that by beneficially distributing the tolerable hardware imperfections across the transmission and reception radio-frequency front ends of each node, the system's secrecy rate may be improved. The engineering insight is that equally sharing the total imperfections at the relay between the transmitter and the receiver provides the best secrecy performance. Numerical results illustrate that the proposed OPA together with the most appropriate hardware design significantly increases the secrecy rate.
Abstract—In this paper, the problem of secure transmission in two-hop amplify-and-forward (AF) systems with an untrusted relay is investigated. To prevent the untrusted relay from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming (DBCJ) technique is used. In this method the destination sends an intended jamming signal to the relay. This jamming signal helps protecting the source message from being captured reliably at the untrusted relay, while the destination cancels itself intended jamming signal. The optimal power allocation (OPA) technique is considered for the presented system. It is observed that the objective function is a quasiconcave function at high signal-to-noise-ratio (SNR) regimes. Based on this OPA technique, we study the ergodic secrecy rate (ESR) and the secrecy outage probability (SOP) of the system when the source and relay are equipped with a single antenna while the destination is equipped with largescale antenna arrays (LSA). Using the achieved closed-form expressions, one can evaluate the performance of the secure system easily and fast and also, they provide significant insight for system design. Finally, simulation results indicate the accuracy of the derived expressions.