This letter investigates robust secrecy rate optimization techniques for a multiple-input-multiple-output (MIMO) wiretap channel in the presence of a multiantenna eavesdropper. In particular, two robust secrecy rate optimization problems are studied: robust power minimization with an outage secrecy rate constraint and robust secrecy rate maximization subject to the outage secrecy rate and transmit power constraints. Here, it is assumed that the legitimate transmitter has perfect channel state information (CSI) of the legitimate receiver and imperfect CSI of the eavesdropper. Both robust problems are not convex in terms of transmit covariance matrix and the outage secrecy rate constraint. Hence, we propose a conservative approximation approach to reformulate this outage secrecy rate constraint by exploiting the Bernstein-type inequality to obtain a tractable solution for these two robust problems. Numerical results have been provided to validate the convergence and the performance of the proposed robust algorithms.
This letter investigates robust secrecy rate optimization techniques for a multiple-input-multiple-output (MIMO) wiretap channel in the presence of a multiantenna eavesdropper. In particular, two robust secrecy rate optimization problems are studied: robust power minimization with an outage secrecy rate constraint and robust secrecy rate maximization subject to the outage secrecy rate and transmit power constraints. Here, it is assumed that the legitimate transmitter has perfect channel state information (CSI) of the legitimate receiver and imperfect CSI of the eavesdropper. Both robust problems are not convex in terms of transmit covariance matrix and the outage secrecy rate constraint. Hence, we propose a conservative approximation approach to reformulate this outage secrecy rate constraint by exploiting the Bernstein-type inequality to obtain a tractable solution for these two robust problems. Numerical results have been provided to validate the convergence and the performance of the proposed robust algorithms.
Consider a multi-input multi-output (MIMO) channel wiretapped by multiple multi-antenna eavesdroppers. Assuming imperfect eavesdroppers' channel state information (CSI) at the transmitter, an outage-constrained secrecy rate maximization (OC-SRM) problem is considered. Specifically, we aim to design the transmit covariance matrix such that the outage secrecy rate is maximized for a given outage probability. The OC-SRM problem is challenging, and as a compromise, we resort to a recently developed Bernstein-type inequality approach to obtain a safe (conservative) approximate solution for OC-SRM. The merit of the proposed safe design lies in its tractability. In particular, a safe solution can be efficiently computed by alternately solving two convex conic optimization problems. The efficacy of the proposed design is demonstrated by simulations.
This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.
A multiple-input multiple-output (MIMO) wiretap channel in the presence of one multiple-antenna eavesdropper is considered. We assume that imperfect channel state information (CSI) on the legitimate link and only statistical CSI of the eavesdropper channel are available at the transmitter. This paper addresses the issue of optimal input covariance matrix design that maximizes the secrecy rate subject to the total power constraint. The secrecy rate maximization (SRM) is studied under a relaxed assumption on the perfect CSI.We reformulate the SRM problem and propose an alternating optimization (AO) algorithm to find the optimal input covariance matrix. Simulation results are presented to validate the effectiveness of the proposed approach. The impact of the channel estimation error is investigated.
In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploitingS-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into aStackelberggame where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game,Stackelbergequilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, theStackelbergequilibrium solution has been validated through numerical results.
In this letter, we investigate a robust transmit optimization design based on an artificial noise (AN)-aided precoding scheme for maximizing secrecy rate in a multiple-input multiple-output multiple-eavesdropper multicast network where a transmitter sends confidential information to multiple intended users and provides energy for multiple idle nodes while multiple passive eavesdroppers try to overhear the secret information. Supposing Gaussian CSI uncertainties, the proposed outage-constrained secrecy rate maximization (OC-SRM) problem is nonconvex and its analytical analysis is more challenging than several existing OC-SRM schemes. Technically, to circumvent this mathematically intractable secrecy problem, we resort to low SNR approximation and some conservative approximations (e.g., Bernstein-type inequality and sphere bounding) to reformulate the OC-SRM problem into two convex subproblems which can be efficiently solved by the off-the-shelf optimization solver. Simulation results are provided to validate the security performance of the robust AN-aided precoding design.
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: a) power minimization, b) secrecy rate maximization. These optimization problems are not convex due to the non-convex 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 the perfect channel state information. However, there are practical difficulties to have the perfect channel state information at the transmitter. Hence, robust secrecy rate optimization techniques based on the worstcase secrecy rate are considered by incorporating the channel uncertainties. By exploiting the S-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.