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.
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.
Physical (PHY) layer security approaches for wireless communications can prevent eavesdropping without upper layer data encryption. However, they are hampered by wireless channel conditions: absent feedback, they are typically feasible only when the source-destination channel is better than the source-eavesdropper channel. Node cooperation is a means to overcome this challenge and improve the performance of secure wireless communications. This paper addresses secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers. Three cooperative schemes are considered: decode-and-forward (DF), amplify-and-forward (AF), and cooperative jamming (CJ). For these schemes, the relays transmit a weighted version of a reencoded noise-free message signal (for DF), a received noisy source signal (for AF), or a common jamming signal (for CJ). Novel system designs are proposed, consisting of the determination of relay weights and the allocation of transmit power, that maximize the achievable secrecy rate subject to a transmit power constraint, or, minimize the transmit power subject to a secrecy rate constraint. For DF in the presence of one eavesdropper, closed-form optimal solutions are derived for the relay weights. For other problems, since the optimal relay weights are difficult to obtain, several criteria are considered leading to suboptimal but simple solutions, i.e., the complete nulling of the message signals at all eavesdroppers (for DF and AF), or the complete nulling of jamming signal at the destination (for CJ). Based on the designed relay weights, for DF in the presence of multiple eavesdroppers, and for CJ in the presence of one eavesdropper, the optimal power allocation is obtained in closed-form; in all other cases the optimal power allocation is obtained via iterative algorithms. Numerical evaluation of the obtained secrecy rate and transmit power results show that the proposed design can significantly improve the performance of secure wireless communications.
In this paper, we consider confidential multicasting in multi-hop multi-antenna decode-and-forward (DF) relay networks, where a source sends a secure common message to multiple destinations in the presence of multiple eavesdroppers with the help of a multi-antenna DF relay located at each hop. Under an overall power constraint, we first show that the optimization problem for relay beamformer design and power allocation to maximize the achievable multicast secrecy rate in a two-hop multi-antenna relay network can be solved by using semidefinite relaxation and bisection technique. Further, we also propose a suboptimal iterative sequential update scheme for a multi-hop relay network including more than two hops. At each iteration, the relay beamformer at each hop is updated sequentially by solving an extended generalized eigenvector problem for a multiple-destination multiple-eavesdropper case, and the power allocation is updated by using the bisection technique with the feasibility problem of linear programming. Numerical results are presented to verify the multicast secrecy rates achieved by the proposed schemes in multi-hop multi-antenna DF relay networks.
Relying on physical layer security is an attractive alternative of utilizing cryptographic algorithms at upper layers of protocol stack for secure communications. In this paper, we consider a two-hop wireless relay network in the presence of an eavesdropper. Our scenario of interest spans over a four-node network model including a source, a destination, a trusted relay, and an untrusted eavesdropper in which the relay forwards the source message in a decode-and-forward (DF) fashion. The source and relay are allowed to use some of their available power to transmit jamming signals in order to create interference at the eavesdropper. The relay and destination are assumed to have the knowledge of the jamming signals. An important question is how to allocate the transmission power of the message signal and that of the jamming signal. First, we propose an optimal power allocation solution in which the knowledge of global channel state information (CSI) is required. To facilitate practical system design, two simple yet sub-optimal power allocation solutions are proposed which do not rely on eavesdropper's channels. For the purpose of performance comparisons, power allocation problems for two benchmark schemes without jamming are also analyzed.
This paper addresses the physical layer security of a two-hop decode-and-forward (DF) wireless relay network in the presence of several eavesdroppers. The wiretap channel model consists of a source, several eavesdroppers, couples of trusted relays and a destination. For this DF based cooperative relay scheme, the relays use different code words independent of the source code words to transmit a weighted version of the recoded messages as with the source messages to the legitimate receiver and jam the eavesdropper. We fix the transmit power of the source ( Ps ) to obtain the weights for secrecy rate maximization, assuming that global channel state information (CSI) is available. The maximization problem can be made to a generalized eigenvector problem, and it is easy to obtain the corresponding eigenvector that is the optimal relay weight vector by using the matrix computations. The closed-form optimal solution is derived for the relay weights that maximize the achievable secrecy rate.
We address a robust beamforming design and power allocation problem for a one-way multi-antenna relay network, where the multi-antenna source implements communication with the multi-antenna destination via a decode-and-forward (DF) relay in the presence of the multiple single-antenna eavesdroppers. The eavesdroppers can only overhear the information flowed from the relay to the destination in the second hop. We aim to maximize the worst-case secrecy rate in the condition that the global channel state information (CSI) is imperfect. To this end, we propose the joint beamforming and power allocation design for the worst-case secrecy rate maximization. However, our proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect CSI. To make the problem more tractable, we approximate the problem into several tractablesemidefinite programs by semidefinite relaxation, successive convex approximation, and S-procedure techniques, and we propose an iterative algorithm to solve the problem. Furthermore, we show that the proposed algorithm is also applicable for the case the Gaussian wiretap model, where only the eavesdroppers' CSI is imperfect. Simulation results validate the effectiveness of the proposed algorithm.
We study secrecy communication for a multi-pair decode-and-forward (DF) relay network (MP-DFRN), where one of the singe-antenna sources is wiretapped by a single-antenna eavesdropper. In particular, we aim to maximize the secrecy rate of the secure source while guaranteeing the quality of service (QoS) at the destinations with a total power constraint. The optimization requires a joint beamforming and power allocation at the multi-antenna relay, and this problem turns out to be non-convex. To this end, an efficient algorithm is proposed by using the techniques of successive convex approximation and constrained concave convex procedure. Following a similar optimization framework, we further investigate the transmit power minimization problem with secrecy and QoS constraints. Our study suggests a new and efficient framework to achieve secrecy communication in the MP-DFRN, and also reveals the interplay between the achievable secrecy rate and the total power budget.