This paper studies a wire-tap channel in which a source node wants to communicate securely to a destination node in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay operating in full-duplex (FD) mode. The residual self-interference due to FD transmission is explicitly taken into account. The secrecy capacity and the respective optimal power allocation schemes for this system are examined under both individual and joint power constraints. At first, the related optimization problems are shown to be quasi-concave. As such, the globally optimal solution exists and is unique. Due to the non-linearity of the derivative, we apply a simple bisection method for root finding and obtain a simple expression for the optimal power allocation scheme. To further provide some insight on the solutions, we apply the method of dominant balance to analyze the capacity and power allocations in different high power regions. It is then demonstrated that full relay power is only needed when the power at the relay is sufficiently small compared to the power at the source. Comparisons with half-duplex (HD) relaying also revealed that FD can achieve a significantly higher secrecy capacity. Finally, numerical results are presented to confirm the optimality of the solutions.
This paper studies a wire-tap channel in which a source node wants to communicate securely to a destination node in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay operating in full-duplex (FD) mode. The residual self-interference due to FD transmission is explicitly taken into account. The secrecy capacity and the respective optimal power allocation schemes for this system are examined under both individual and joint power constraints. At first, the related optimization problems are shown to be quasi-concave. As such, the globally optimal solution exists and is unique. Due to the non-linearity of the derivative, we apply a simple bisection method for root finding and obtain a simple expression for the optimal power allocation scheme. To further provide some insight on the solutions, we apply the method of dominant balance to analyze the capacity and power allocations in different high power regions. It is then demonstrated that full relay power is only needed when the power at the relay is sufficiently small compared to the power at the source. Comparisons with half-duplex (HD) relaying also revealed that FD can achieve a significantly higher secrecy capacity. Finally, numerical results are presented to confirm the optimality of the solutions.
In this research work, we investigate the secrecy rate and optimal power allocation schemes for a half-duplex (HD) wire-tap Rayleigh fading channel in which a source wishes to communicate securely to a destination in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay. The secrecy capacity and the corresponding optimal power allocation schemes are examined under both individual and joint power constraints. Due to the absence of an insightful expression of the secrecy rate for a given power allocation scheme, determining such secrecy capacity is challenging. To overcome this issue, we first propose a novel method to calculate the expectation of an exponentially distributed random variable using the exponential integral function. By exploiting this calculation, we then establish the average secrecy rate of the considered AF relay channel in closed-form. By examining the quasi-concavity of the optimal power allocation problem, it is then concluded that the problem is quasi-concave. As such, the globally optimal solution exists and is unique for both individual and joint power constraints. A simple root finding method then can be applied into the derived close-formed formula to approximately calculate the optimal power allocation scheme to achieve the secrecy capacity. Numerical results are then provided to confirm the accuracy of the derived formula and the optimality of the proposed power allocation.
This paper considers the wire-tap channel in which a source node communicates to a destination node with the help of a single amplify-and-forward (AF) relay and in the presence of an eavesdropper. The secrecy capacity and respective optimal power allocation scheme at the source and relay are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered. These include combinations of dual-hop, orthogonal AF and direct transmission schemes. To deal with the non-concave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes' rule of signs. It is then shown that the power allocation strategies that maximize the secrecy rates can be obtained in closed form. Simulation results are finally provided to verify the optimality of the proposed schemes.
In this paper, we examine the use of a friendly full-duplex (FD) relay to increase the secrecy rate over a fading channel between the legitimate source and the destination in the presence of residual self-interference (SI) and eavesdropper. In particular, we consider two different protocols based on the FD capability of relay: 1) FD transmission (FDT), in which the FD-Relay receives and sends data concurrently; 2) FD-Relay with jamming (FDJ), where first, the FD-Relay simultaneously receives data and sends jamming to the eavesdropper; then, it forwards the data, while the source jams the eavesdropper. We first develop the secrecy rate expressions for half-duplex transmission (HDT), half-duplex with jamming (HDJ), FDT, and FDJ relaying protocols, and then use them to derive their performance properties in terms of the channel gains between nodes, eavesdropper types, and more importantly, the SI level in FD-Relay. We further investigate the non-convex power allocation problems for the developed FDT and FDJ to maximize the secrecy rate under the power constraints. In particular, we develop an efficient iterative algorithm based on the difference-of-two-concave-functions programming. Analytical and simulation results show the strong influence of SI level on the achieved secrecy rate of the FDT and the FDJ. For sufficiently low SI, FDT achieves a much higher secrecy rate than FDJ, HDJ, and HDT. However, for higher SI, FDJ becomes more effective in enhancing the achieved secrecy rate. The results also indicate that adaptive power allocation can significantly improve the performance and confirm that the proposed FDT and FDJ outperform the HDT and the HDJ.
This thesis studies the secrecy rate and respective optimal power allocation schemes to maximize the secrecy rate of a full-duplex (FD) relay wiretap channel.The FD relay is assumed to operate in decode-and-forward (DF) mode to support a secured communication from a source to a destination under the presence of an eavesdropper.Both slowly varying fading and ergodic fading channels where the channel gains are assumed to be available at the receivers but not the transmitters are considered.The residual self-interference due to FD transmission is taken into account in formulating the secrecy rate and the optimal power allocation schemes.The first part of the thesis establishes closed-form expressions of the secrecy rates for a given power allocation scheme at the source and the relay.For a slowly varying fading environment, the channel conditions for which a positive secrecy rate is attained are identified.In the case of ergodic fading, we first propose a simple method to calculate the expectation of an exponentially distributed random variable using the exponential integral function.Using this result, the ergodic secrecy rates of the considered FD relay channel are then established in closed-form.The proposed method provides a simple yet effective way to compute the secrecy rates without the need of lengthy Monte Carlo simulations.iii I am grateful to my advisor, Dr. Nghi H. Tran, for the kindness he showed me, his understanding to my situation and his knowledgeable and experienced guidance throughout this masters.This work could not have been possible without my loving, sweet and generous husband, Abdo, who supported and encouraged me in every step of the way and was the light that guided me through my darkest
This paper considers the use of a friendly full-duplex (FD) relay to increase the secrecy rate over a fading channel between the legitimate source and destination in the presence of a naive or informed eavesdropper. Naive eavesdropper can only decode the received signals either from the source or from the relay, while informed eavesdropper can overhear signals transmitted from both the source and relay. Accordingly, we compare the achievable secrecy rates of FD relay with traditional half-duplex (HD) relay in terms of the channel state information (CSI) between nodes, eavesdropper types, and the self-interference (SI) in FD-Relay. We consider the non-convex power allocation problems for the developed FD-relay to maximize the secrecy rate under the power constraints and develop an efficient iterative algorithm based on the difference-of-two-concave-functions (DC) programming. The analytical and simulation results confirm that FD relay offers significant improvements in the secrecy rate over the HD-Relay.
This paper considers the wiretap channel in which a source node communicates with a destination node with the aid of a single helper and in the presence of an eavesdropper. The helper can apply either amplify-and-forward (AF) relaying or jamming. The secrecy capacity and respective optimal power allocation schemes at the source and the helper are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered for relaying. To deal with the related nonconcave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes' rule of signs. Using this approach, optimal power allocation strategies are derived for some relay topologies and for the jamming system. Insights into the proposed schemes for different transmission power ranges and comparisons to the optimal information rate power allocations are also discussed. Simulation results are finally provided to quantify the optimality of the proposed schemes.