We consider a cooperative wireless network in the presence of one or more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme, cooperating nodes retransmit a weighted version of the source signal in a decode-and-forward (DF) fashion. In the second scheme, referred to as cooperative jamming (CJ), while the source is transmitting, cooperating nodes transmit weighted noise to confound the eavesdropper. We investigate two objectives: i) maximization of the achievable secrecy rate subject to a total power constraint and ii) minimization of the total power transmit power under a secrecy rate constraint. For the first design objective, we obtain the exact solution for the DF scheme for the case of a single or multiple eavasdroppers, while for the CJ scheme with a single eavesdropper we reduce the multivariate problem to a problem of one variable. For the second design objective, existing work introduces additional constraints in order to reduce the degree of difficulty, thus resulting in suboptimal solutions. Our work raises those constraints, and obtains either an analytical solution for the DF scheme with a single eavesdropper, or reduces the multivariate problem to a problem of one variable for the CJ scheme with a single eavesdropper. Numerical results are presented to illustrate the proposed results and compare them to existing work.
@cite_30: In this work a relay channel with a wire-tapper is studied for both discrete memoryless and Gaussian channels. The wire-tapper receives a physically degraded version of the destination's signal. We find inner and outer bounds for the capacity-equivocation rate region. We also argue that when the destination receives a physically degraded version of the relay's signal, inner and outer bounds meet for some special cases.
@cite_27: Due to the broadcast nature of the wireless medium, wireless communication is susceptible to adversarial eavesdropping. This paper describes how eavesdropping can potentially be defeated by exploiting the superposition nature of the wireless medium. A Gaussian wire-tap channel with a helping interferer (WTC-HI) is considered in which a transmitter sends confidential messages to its intended receiver in the presence of a passive eavesdropper and with the help of an interferer. The interferer, which does not know the confidential message assists the confidential message transmission by sending a signal that is independent of the transmitted message. An achievable secrecy rate and a Sato-type upper bound on the secrecy capacity are given for the Gaussian WTC-HI. Through numerical analysis, it is found that the upper bound is close to the achievable secrecy rate when the interference is weak for symmetric interference channels, and under more general conditions for asymmetric Gaussian interference channels.
@cite_5: The secrecy capacity is developed for a class of relay channels with orthogonal components and a passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multi-antenna channel with a multi-antenna eavesdropper. The outer bounds are shown to be tight for two sub-classes of channels. The first sub-class is one in which the source and relay are clustered and the eavesdropper overhears on only one of the two channels for which the PDF strategy is optimal. The second is a sub-class in which the source does not transmit to the relay for which a noise-forwarding strategy is optimal.
@cite_16: This paper establishes the utility of user cooperation in facilitating secure wireless communications. In particular, the four-terminal relay-eavesdropper channel is introduced and an outer-bound on the optimal rate-equivocation region is derived. Several cooperation strategies are then devised and the corresponding achievable rate-equivocation region are characterized. Of particular interest is the novel noise-forwarding (NF) strategy, where the relay node sends codewords independent of the source message to confuse the eavesdropper. This strategy is used to illustrate the deaf helper phenomenon, where the relay is able to facilitate secure communications while being totally ignorant of the transmitted messages. Furthermore, NF is shown to increase the secrecy capacity in the reversely degraded scenario, where the relay node fails to offer performance gains in the classical setting. The gain offered by the proposed cooperation strategies is then proved theoretically and validated numerically in the additive white Gaussian noise (AWGN) channel.
@cite_13: The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.
A generalization of @cite_13 and @cite_16 was proposed in @cite_27 , in which the helper transmits signals from another source encoder. In @cite_30 , inner and outer bounds on the rate-equivocation region were derived for the four-node model for both discrete memoryless and Gaussian channels. In @cite_5 , the secrecy rate of orthogonal relay and eavesdropper channels was studied.