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International Conference on Communications and Electronics (ICCE)

Optimal power allocation schemes for single-relay af wire-tap channels

Leonardo Jimenez Rodriguez, Nghi Huu Tran, Tho Le‐Ngoc

Published Jul 1, 2014• 4 citations
Publisher

Abstract

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.

DOI
10.1109/cce.2014.6916683

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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.
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.
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 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 paper, we consider secure communications of one source-destination pair in wireless multi-hop decode-and-forward (DF) relay networks. In the presence of an eavesdropper, we derive an optimal power allocation strategy to maximize achievable secrecy rates under an overall transmit power constraint assuming that a single relay is located at each individual hop. We demonstrate that the optimal power allocation is obtained when the overall power constraint and the DF-relaying constraints necessary to guarantee that each DF relay correctly decodes the information signals hold with equality, which rely on channel conditions between the source, relays, and destination. The channel conditions for the eavesdropper are shown to only influence relays that may be inactive for secrecy rate maximization. We also consider multiple cooperative relays at each hop to perform cooperative beamforming in the presence of multiple eavesdroppers. To improve the secrecy rate in multi-hop relay networks, which include more than two hops, we propose an iterative cooperative beamformer design and transmit power allocation scheme with relay selection. Numerical results are presented to investigate the secrecy capacity obtained by the optimal power allocation in multi-hop DF relay networks and to confirm the secrecy rate enhancement of the proposed cooperative beamforming scheme.
The problem of secure unicast communication over multihop wireless relay networks with directed links in the presence of an eavesdropper is considered. In the existing literature this problem has been considered in one or both of the following two scenarios: (A) relay nodes employ relaying schemes, such as Decode-and-Forward (DF), (B) the source communicates with the destination over a two-hop relay network. We argue that computationally complex relaying schemes such as DF render end-to-end performance characterization intractable, without providing any performance guarantee in general channel and network scenarios. Therefore, we consider one of the simplest relaying scheme: Amplify-and-Forward (AF) that allows us to provide guarantees on the optimal performance over a wide range of channel conditions. A node performing AF-relaying scales and forwards the signal received at its input. Further, with AF-relaying the end-to-end performance characterization problem remains tractable for much larger class of networks than those that can be considered with other relaying schemes. The key contribution of this work is twofold. We first provide the optimal vector of scaling factors that maximizes the achievable AF secrecy rate, no matter which relay the eavesdropper listens to. Further, we prove that in high-SNR regime, the optimal AF secrecy rate thus achieved is within a constant gap from the cutset upper bound on the secrecy capacity.
A MIMO secure two-hop wireless communication system is considered in this paper. In this model, there are no direct links between the source-destination and the source-eavesdropper. The problem is maximizing the secrecy capacity of the system over all possible amplify and forward (AF) relay strategies, such that the power consumption at the source node and the relay node is limited. When all the nodes are equipped with single antenna, this non-convex optimization problem is fully characterized. When all the nodes (except the intended receiver) are equipped with multiple antennas, the optimization problem is characterized based on the generalized eigenvalues-eigenvectors of the channel gain matrices.