In this letter, we study energy-efficient precoder design in a three-node MIMO wiretap channel. Different from previous works in this area that mainly focus on secrecy rate maximization or power minimization problems, here, we aim to maximize the energy efficiency (EE) of the system subject to the secret rate and transmit power constraints, which is a nonconvex optimization and hard to tackle. To solve it, we first transform it into an equivalent parameterized polynomial subtractive form and then approximate the nonconvex equivalent problem into a convex optimization problem by means of Taylor series expansion. Based on that, an iterative algorithm with proved convergence is proposed, and this algorithm is also extended to an imperfect-channel-state-information case. Numerical results show that the proposed algorithm outperforms traditional design methods in terms of EE.
In this letter, we study energy-efficient precoder design in a three-node MIMO wiretap channel. Different from previous works in this area that mainly focus on secrecy rate maximization or power minimization problems, here, we aim to maximize the energy efficiency (EE) of the system subject to the secret rate and transmit power constraints, which is a nonconvex optimization and hard to tackle. To solve it, we first transform it into an equivalent parameterized polynomial subtractive form and then approximate the nonconvex equivalent problem into a convex optimization problem by means of Taylor series expansion. Based on that, an iterative algorithm with proved convergence is proposed, and this algorithm is also extended to an imperfect-channel-state-information case. Numerical results show that the proposed algorithm outperforms traditional design methods in terms of EE.
This letter studies transmit optimization in three-node multiple-input-multiple-output wiretap channels with simultaneous wireless information and power transfer. In particular, we address the transmit covariance optimization for the energy-harvesting maximization (EHM) problem under the constraint of secrecy rate and transmit power. The problem is nonconvex and hard to tackle. To circumvent it, we first resort to the Taylor series expansion to convert the problem into a convex optimization problem. Then, based on the analysis of its dual problem, an iterative algorithm, which includes a semiclosed-form solution, is proposed to handle this EHM problem. The scenario of imperfect channel state information of an energy receiver (the potential eavesdropper) is also considered. In this scenario, a Bernstein-type inequality-based iterative algorithm is proposed to deal with the challenging outage-constrained EHM problem. Simulation results demonstrate the efficiency of our proposed designs.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.
In this paper, we study the precoding problem for physical layer security in a general multiple-input multiple-output (MIMO) wiretap channel. Since the resultant secrecy capacity maximization (SCM) problem is nonconvex in general, we solve it by employing a successive convex approximation method, where the nonconvex part of the formulated problem is approximated by its first-order Taylor expansion. Thus, the SCM problem can be iteratively solved through convex programming of its convexified version. Finally, an iterative precoding algorithm with provable convergence is presented. Numerical simulations are also provided to verify the proposed algorithm.
In this paper, we study the precoder design problem for secrecy rate maximization in a decode-and-forward (DF)-based multiple-input multiple-output (MIMO) relay network. The system model considered here consists of a source, a trusted relay, a legitimate receiver and an eavesdropper, all mounted with multiple antennas. Our objective is to maximize the achievable secrecy rate of this DF-based MIMO relay wiretap system subject to a total transmit power constraint. Since the formulated secrecy rate maximization (SRM) problem is nonconvex in general, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the formulated problem is linearized to its first-order Taylor expansion. Then, the nonconvex SRM problem can be iteratively solved through successive convex programming of its convexified version, and thus an iterative precoding algorithm is developed. Moreover, the theoretical result is further extended to the case when multiple eavesdroppers are simultaneously present. Finally, numerical simulations are provided to evaluate the performance of the proposed algorithm. Results show that our algorithm can converge fast to a near-optimal solution.
In this letter, we investigate the energy efficiency optimization for simultaneous wireless information and power transfer in multiple-input-multiple-output wiretapping systems, which consist of one transmitter, multiple desired receivers (DRs), and multiple eavesdroppers. Specifically, considering non-linear energy harvesting model, we aim to maximize the ratio of the total harvested power at the DRs to the total power consumption at the transmitter, e.g., the harvested power efficiency, by jointly designing the transmit precoding matrix, the artificial noise covariance and the power splitting ratios, subject to the secrecy rate constraint. To solve the formulated highly non-convex non-linear single-ratio problem, we propose a successive convex approximation and constrained concave convex procedure-based iterative algorithm. Finally, our proposed algorithm is validated by some representative numerical results.
This paper studies different secrecy rate optimization problems for a multiple-input–multiple-output (MIMO) secrecy channel. In particular, we consider a scenario where a communication through a MIMO channel is overheard by a multiple-antenna eavesdropper. In this secrecy network, we first investigate two secrecy rate optimization problems: 1) power minimization and 2) secrecy rate maximization. These optimization problems are not convex due to the nonconvex secrecy rate constraint. However, by approximating this secrecy rate constraint based on Taylor series expansion, we propose iterative algorithms to solve these secrecy rate optimization problems. In addition, we provide the convergence analysis for the proposed algorithms. These iterative optimization approaches are developed under the assumption that the transmitter has perfect channel state information. However, there are practical difficulties in having perfect channel state information at the transmitter. Hence, robust secrecy rate optimization techniques based on the worst-case secrecy rate are considered by incorporating channel uncertainties. By exploiting theS-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming at low signal-to-noise ratios (SNRs). Simulation results have been provided to validate the convergence of the proposed algorithms. In addition, numerical results show that the proposed robust optimization techniques outperform the nonrobust schemes in terms of the worst-case secrecy rates and the achieved secrecy rates.