Secure communications using physical layer characteristics has attracted many attentions in recent years. Secrecy capacity of communication systems can be increased by using multiple-antenna nodes. In this paper, we concentrate on the cooperative wiretap channel in which confidential messages are sent from a source to a legitimate receiver with the help of a relay in the presence of an eavesdropper. We study the secrecy capacity of Amplify and Forward (AF) relaying under peak power constraint at the relay node. To this end, we first evaluate an achievable secrecy rate for Gaussian input by solving a nonconvex optimization problem. Then, we prove the converse by using the secrecy capacity of genie-aided channel as an upper bound of the secrecy capacity of interested channel. We show that this upper bound is achievable and equal to achievable secrecy rate of Gaussian input.
Secure communications using physical layer characteristics has attracted many attentions in recent years. Secrecy capacity of communication systems can be increased by using multiple-antenna nodes. In this paper, we concentrate on the cooperative wiretap channel in which confidential messages are sent from a source to a legitimate receiver with the help of a relay in the presence of an eavesdropper. We study the secrecy capacity of Amplify and Forward (AF) relaying under peak power constraint at the relay node. To this end, we first evaluate an achievable secrecy rate for Gaussian input by solving a nonconvex optimization problem. Then, we prove the converse by using the secrecy capacity of genie-aided channel as an upper bound of the secrecy capacity of interested channel. We show that this upper bound is achievable and equal to achievable secrecy rate of Gaussian input.
Physical layer security has attracted a great deal of attentions in recent years. This is achieved through using the physical layer characteristics to help sender to transfer data reliably with perfect secrecy. Using multiple-antenna relay node can improve the secrecy capacity of such channel. In this paper, we study the cooperative wiretap channel in which secure data transmission is achieved with the help of a MIMO Amplify and Forward (AF) relay. In such network, it is assumed multiple eavesdroppers attempt to listen to the relay transmitted signal and try to decode the source message. We assume the relay makes use of separated transmit/receive beamforming vectors, dubbed rank-one beamforming matrix. The beamforming vectors are computed such that the achievable secrecy rate is maximized, assuming the relay is subject to a maximum transmit power constraint. Accordingly, it is shown that the problem of finding proper receive beamforming vector can be translated into a scalar optimization problem, where using that the transmit beamforming vector can be obtained through solving a Semi-Definite Programming (SDP) problem.
We investigate the problem of physical layer security in a wireless cooperative network, where communication is assisted by the untrusted relay. It is impossible for the amplify-and-forward protocol to convey a confidential message from the source to the destination without the help of other nodes, where only an untrusted relay is available. Nonetheless, our results are quite optimistic when there are multiple untrusted relays, which amplify the received signal and forward it to the destination. We treat the untrusted relay nodes as eavesdroppers, despite the fact that they are the enablers of communication. First of all, we prove that a positive secrecy rate can always be ensured regardless of the transmit power and the channel condition of the untrusted relays, as long as there exists a sufficient number of untrusted relays. Furthermore, a closed-form solution to the upper bound of secrecy rate is obtained. Finally, a practical approach is proposed to acquire a positive secrecy rate, which brings nearly no extra communication cost. Simulations are conducted to demonstrate the validity of the proposed approach.
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.
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.
We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped withMandNantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rateRN. The relationship between the average secrecy capacityCˉNof Gaussian wiretap channel and the average secrecy rateRˉNachieved by the null-space jamming scheme is investigated, and we prove thatRˉN≤CˉN≤RˉN+1. Based on this inequality and the derived lower and upper bounds onRN, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that whenN>M, the average secrecy capacity increases linearly with the total transmit power; while whenN≤M−1, there exists a performance ceiling on it.
The prominence of the wireless communication has been urging the monotonically increasing demand of security and privacy. In wireless systems, the notion of perfect secrecy of information with respect to illegitimate nodes can be ensured via physical layer security (PLS) techniques. Unfortunately, they can be made less effective if source- eavesdropper wiretap channel is better than the main source-receiver channel. The various node cooperation schemes can be employed to combat this limitation where a relay node assists the communication to improve the performance significantly. In this paper, a four node wireless communication system consisting of a source, a destination, a relay and an eavesdropper as wire-tapper has been considered. The performance of the traditional cooperation schemes in terms of secrecy rate has been investigated with a different scenario where relay node helps the eavesdropper to deteriorate the secrecy rate. In addition, since legitimate receiver can overhear the transmission of relay, it favours the achievable secrecy rate. We formulate an analytical expression of conditional secrecy outage probability for the investigated system. From the obtained simulation results, it has been observed that secrecy rate is monotonically increases with path loss index. Furthermore, the proper selection of the system parameters leads to enhance the secrecy performance of the system even if relay pertains to degrade the performance. Amplify-and-forward, cooperation, decode-and-Forward, secrecy rate, relay.