This paper considers an energy-efficient transmit design in a multiple-input single-output (MISO) wiretap channel. In particular, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from multiple external single-antenna eavesdroppers. Assuming statistical eavesdroppers' channel state information (ECSI) at the transmitter, we aim to design the transmit beamformer, such that the outage secrecy energy efficiency (SEE) is maximized, subject to the outage-constrained secrecy rate and transmit power constraints. The resultant problem is intractable to solve even after introducing a semidefinite relaxation (SDR) reformulation. To handle it, an equivalent parametric reformulation, based on the fractional programming and difference-of-concave programming theories, is proposed to recast this problem as a convex problem. By this means, the maximum outage SEE can be found in an iterative fashion. Moreover, we also give an approach to constructing a rank-one covariance matrix from our proposed method, implying the feasibility of transmit beamforming to achieve the obtained SEE performance. Numerical results are presented to show the effectiveness of our proposed method.
This paper considers an energy-efficient transmit design in a multiple-input single-output (MISO) wiretap channel. In particular, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from multiple external single-antenna eavesdroppers. Assuming statistical eavesdroppers' channel state information (ECSI) at the transmitter, we aim to design the transmit beamformer, such that the outage secrecy energy efficiency (SEE) is maximized, subject to the outage-constrained secrecy rate and transmit power constraints. The resultant problem is intractable to solve even after introducing a semidefinite relaxation (SDR) reformulation. To handle it, an equivalent parametric reformulation, based on the fractional programming and difference-of-concave programming theories, is proposed to recast this problem as a convex problem. By this means, the maximum outage SEE can be found in an iterative fashion. Moreover, we also give an approach to constructing a rank-one covariance matrix from our proposed method, implying the feasibility of transmit beamforming to achieve the obtained SEE performance. Numerical results are presented to show the effectiveness of our proposed method.
This paper considers an energy-efficient transmit design in a general multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from several external multi-antenna eavesdroppers. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input transmit covariance, such that the worst-case secrecy energy efficiency (WC-SEE) is maximized, subject to the quality of service (QoS) and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum WC-SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the optimality of transmit beamforming to achieve the maximum WC-SEE. Numerical results are presented to verify the efficacy of our proposed method.
This paper considers an energy-efficient transmit design in a multiple-input single-output (MISO) wiretap channel. In particular, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from multiple external eavesdroppers. Assuming partial eavesdroppers' channel state information (ECSI) at the transmitter, we aim to design the transmit beamformer such that the outage secrecy energy efficiency (SEE) is maximized. Two ECSI uncertainty scenarios are studied, i.e., statistical ECSI and imperfect ECSI. For the statistical ECSI case, only the distribution of ECSI is available at the transmitter. The SEE outage constraint admits a closed-form expression in this case, and an approximate solution can be obtained by solving a sequence of convex optimization problems. However, this does not apply to the imperfect ECSI case, where the channel lies in some uncertainty set centered at the true channel. We show that a conservative transmit scheme can be derived by invoking the Bernstein-type inequality. It is proved that our proposed methods always yield a solution of rank one, with either statistical or imperfect CSI. Numerical results are finally presented to confirm the efficacy of our proposed methods.
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.
In this letter, we investigate the simultaneous wireless information and power transfer in a multiple-input-single-output downlink system which consists of one multi-antenna transmitter, one single-antenna desired receiver, and multiple single-antenna eavesdroppers. Specifically, we investigate the outage-constrained secrecy rate maximization by jointly designing the transmit beamforming vector and the power splitting ratio with statistical channel uncertainties. To handle the formulated non-convex problem, we resort to semi-definite relaxation (SDR) and the Bernstein-type inequality to transform the outage constraints into a deterministic form. Then, the original problem can be efficiently solved by alternately optimizing two convex subproblems. In addition, we testify that the SDR can obtain the rank-one optimal solution. Finally, our proposed algorithm is validated by some representative numerical results.
This paper considers an energy-efficient transmit design in a three-node MISO wiretap channel in the eyes of service integration. Specifically, we combine two sorts of services, and serve them simultaneously: one multicast message intended for both receivers and one confidential message intended for only one authorized receiver. The confidential message must be kept perfectly secure from the unauthorized receiver. Our goal is to jointly design the input covariance matrices of the multicast message and confidential message such that the secrecy energy efficiency (SEE) is maximized, subject to the multicast rate, secrecy rate and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the feasibility of transmit beamforming to achieve the maximum SEE. Numerical results are finally presented to verify the efficacy of our proposed method.
Physical layer security has recently emerged as a promising approach to provide secure wireless communications. Physical layer security technology is the key means to achieve security and communication integration. The built-in security mechanism based on the characteristics of wireless channel provides a feasible idea for the realization of “one secret at a time”. It has important application prospects in integrity protection of service data, Internet of things (IoT) lightweight encryption and blockchain wireless security technology. In this paper, we consider the scenario of a unicast multiuser multiple-input single-output (MISO) downlink system in the presence of multiple single-antenna passive eavesdroppers. Instead of assuming perfect channel state information (CSI), we investigate the artificial noise (AN)-aided robust transmit beamforming scheme with imperfect CSI on legitimate receivers and no CSI regarding eavesdroppers at the transmitter. Under the fixed total transmit power, the information symbol and the AN are transmitted concurrently. We aim to guarantee each legitimate receiver's signal-to-interference-and-noise ratio(SINR) outage probability below a preset level with minimum power. Hence, as much power as possible can be allocated to AN to confuse the eavesdroppers. In order to reduce the negative impact on the legitimate receivers, the AN is transmitted in the null space of the estimated legitimate channels. To deal with this nonconvex optimization problem, a rank relaxed formulation is obtained by employing semidefinite relaxation (SDR). Then we propose two approaches by using Bernstein-type inequality and S-procedure, respectively, to transform the probabilistic constraints into deterministic constraints. The optimization problem is reformulated as a convex semidefinite program (SDP). Simulation results show that the proposed approaches have better performances than the non-robust approach.