Physical layer security is an emerging technique to improve the wireless communication security and the corresponding techniques under practical scenarios especially with imperfect channel state information (CSI) need to be taken into consideration. In this paper, we investigate the robust secure transmission for cooperative decode-and-forward (DF) automatic-repeat-request (ARQ) in multiple-input-single-output (MISO) relaying wiretap channels with channel estimation errors. Firstly, the robust transmit covariance matrices and the optimal beamforming weights are obtained using the semi-definite relaxation (SDR) approach to maximize the secrecy rate under power constraint and channel uncertainties. Besides, we further propose a robust design scheme from the secrecy outage-based characterizations for minimizing the secrecy outage probability of legitimate destination. Moreover, a non-robust scheme, in which the designed beamformer refers to the generalized eigenvectors of the channels' matrix pencil, is also considered as a benchmark. Simulation results verify the robustness of the proposed schemes against the estimation errors and shows that the robust design schemes can significantly improve the security performance of the network.
Physical layer security is an emerging technique to improve the wireless communication security and the corresponding techniques under practical scenarios especially with imperfect channel state information (CSI) need to be taken into consideration. In this paper, we investigate the robust secure transmission for cooperative decode-and-forward (DF) automatic-repeat-request (ARQ) in multiple-input-single-output (MISO) relaying wiretap channels with channel estimation errors. Firstly, the robust transmit covariance matrices and the optimal beamforming weights are obtained using the semi-definite relaxation (SDR) approach to maximize the secrecy rate under power constraint and channel uncertainties. Besides, we further propose a robust design scheme from the secrecy outage-based characterizations for minimizing the secrecy outage probability of legitimate destination. Moreover, a non-robust scheme, in which the designed beamformer refers to the generalized eigenvectors of the channels' matrix pencil, is also considered as a benchmark. Simulation results verify the robustness of the proposed schemes against the estimation errors and shows that the robust design schemes can significantly improve the security performance of the network.
In this paper, we investigate the physical layer security of multiple-input single-output single-antenna eavesdropper relaying networks with imperfect channel state information. Different from traditional strategies in relay systems, which would halt the communication if the relay could not decode the signal successfully, we propose a robust secure transmission strategy which switches between cooperative jamming and decoded-and-forward. Our objective is to maximize secrecy rate, given the unavailability of the perfect eavesdropper channel state information, we propose a worst-case robust design based on secrecy rate. In addition, a traditional robust scheme and a non-robust scheme are put forward as benchmarks. Simulation results verify that the proposed scheme based on robust designs can achieve significant security performance gains over other approaches. More interestingly, because of the influence of cooperative jamming, the security performance of non-robust scheme outperforms the traditional robust designs in low transmit power and low channel error coefficient regions.
In this paper, we study robust joint beamforming and cooperative jamming (CJ) in a secure decode-and-forward (DF) relay system in the presence of multiple eavesdroppers, in which a multi-antenna DF relay employs transmit beamforming to help the source deliver information to the destination and simultaneously generates Gaussian artificial noise to confuse these eavesdroppers. We assume that all the channel state information (CSI) is imperfectly known at the relay subject to norm-bounded CSI errors. Our objective is to maximize the achievable secrecy rate at the destination by jointly optimizing the transmit beamforming vector of information signals and the covariance matrix of jamming signals at the relay subject to its total transmit power constraint. Although this problem is non-convex and in general difficult to be solved, we obtain its optimal solution via the technique of semi-definite relaxation (SDR) together with a one-dimensional (1-D) search. Specifically, we prove that the SDR is tight for the problem of our interest. Finally, numerical results are provided to validate our proposed scheme.
In this paper, we investigate the robust secure transmit beamformming design for multiple-input single-output wiretap channels overheard by multiple non-collaborating single-antenna eavesdroppers. Assuming that at the transmitter, the instantaneous legitimate receiver's channel state information (CSI) is imperfect and only the statistical eavesdroppers' CSI is known, we seek to maximize the target secrecy rate R with the total transmit power constraint and the secrecy outage probability constraint. The resulting outage-constrained secrecy rate maximization (O-SRM) is non-convex and difficult to solve. Thus, we develop an efficient algorithm to solve it and determine the robust secure beamforming design. Specifically speaking, we first prove that the original O-SRM problem can be solved by an equivalent outage-constrained power minimization problem (O-PMP), which is easy to perform semi-definite relaxation (SDR) and can be solved by semi-definite program (SDP) consequently. Second, we transform the non-convex secrecy rate outage constraints into deterministic ones by resorting to Bernstein-type inequality II. Finally, by solving the convex approximation of the O-PMP with different Rs and bisection search over R, we convert the original O-SRM problem into a sequence of solvable SDPs. Simulation results are provided to verify the secrecy-rate performance improvement of the proposed robust beamforming compared with the existing worst-case design proposed by Li and Ma and the simple non-robust maximum-ratio transmission.
This paper presents an investigation of the physical layer secrecy outage performance of the cooperative system in the typical four-node (source, relay, destination, and eavesdropper) scenario with imperfect channel state information (CSI). Specifically, we consider the single-input multiple-output wiretap channels, where the source (S) and the relay (R) are equipped with a single antenna, and the destination (D) and the eavesdropper (E) are equipped with multiple antennas. D and E adopt maximal ratio combining to process multiple copies of signals, and the relay adopts decode-and-forward (DF) and randomize-and-forward (RF) schemes to forward the received signal to the destination. E overhears the information transmitted over both the S-R and R-D links. We derive the closed-form and asymptotic expressions for the secrecy outage probability under both the DF and RF schemes with imperfect CSI, respectively, the accuracy of which is verified by simulation results.
Robust quality-of-service (QoS)-based and secrecy rate-based secure transmission designs are investigated for a multiple-input single-output system with multiple eavesdroppers and a cooperative jammer. Two scenarios are considered: (a) eavesdroppers' channel state information (ECSI) is available and (b) ECSI is unavailable. In scenario (a), a QoS-based design is considered to minimize the worst case signal-to-interference-and-noise ratio at the eavesdroppers and to guarantee the QoS of the legitimate receiver. A secrecy rate-based design is also studied where the worst case secrecy rate is maximized. In scenario (b), a QoS-based design is considered to maximize the power of jamming signals under the QoS constraint of the legitimate receiver, and the secrecy rate-based design is not applicable. In all these designs, we jointly optimize the transmit beamforming vector and the covariance matrix of jamming signals under individual power constraints. As the optimization problems are non-convex, we propose an algorithm for each problem through semidefinite relaxation. Our analysis and simulation results show that, even though the linear precoding scheme in our designs is transmit beamforming rather than the general rank transmit covariance, this does not cause any loss of optimality.
This paper studies robust transmit design for secure AF relay networks with imperfect channel state information (CSI). Two CSI error models, deterministically bounded error model and stochastic error model, are considered. In order to use the power at relays more efficiently, a joint cooperative relaying and jamming scheme is considered, where relays cooperate to forward the source signal and simultaneously they cooperate to send jamming signals to confuse the eavesdroppers. In this joint cooperative relaying and jamming framework, we address the robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM), under both total and individual relay power constraints. Specifically, for the case of deterministically bounded error model, where the CSI error can be specified by an uncertainty set, we maximize the worst-case secrecy rate. While for the case of stochastic error model, where the probability distribution of the CSI error is Gaussian, we maximize the outage constrained secrecy rate. The challenge of these considered SRM-based optimizations lies in their non-convexity. This paper shows that such SRM-based optimization can be solved in a convex fashion and via solving a sequence of semidefinite programs (SDPs). Numerical results are presented to show the efficacy of the proposed scheme.