Zheng Chu

Secrecy Rate Optimizations for a MIMO Secrecy Channel With a Cooperative Jammer

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 exploiting S-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 a Stackelberg game where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game, Stackelberg equilibrium 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, the Stackelberg equilibrium solution has been validated through numerical results.

Secrecy Rate Optimizations for a MISO Secrecy Channel with Multiple Multiantenna Eavesdroppers

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.

Simultaneous Wireless Information Power Transfer for MISO Secrecy Channel

This paper investigates simultaneous wireless information and power transfer (SWIPT) for a multiple-input-single-output (MISO) secrecy channel. First, transmit beamforming without artificial noise (AN) is designed to achieve the secrecy rate maximization problem subject to the transmit power and the energy harvesting (EH) constraints. This problem is not convex, but this can be solved by applying a bisection search to a sequence of the associated power minimization problems, each of which can be solved by using a novel relaxation approach. Moreover, we extend our proposed algorithms to the robust case by incorporating channel uncertainties. Then, transmit beamforming with AN is investigated for the secrecy rate maximization problem, where two relaxation approaches are presented, i.e., a two-level optimization algorithm and a successive convex approximation (SCA), to solve the secrecy rate maximization problem. In addition, tightness analyses of rank relaxation are provided to show that the optimal transmit covariance matrix exactly returns rank one. Simulation results are provided to validate the performance of the proposed algorithms.

To Harvest and Jam: A Paradigm of Self-Sustaining Friendly Jammers for Secure AF Relaying

Cooperative jamming has been demonstrated to be an effective means to provide secret wireless communications and yet this is realized at the expense of the power consumption of the friendly jammers. This paper considers the scenario where friendly jammers harvest energy wirelessly from the signal transmitted by the source, and then use only the harvested energy to transmit the jamming signals for improving the secrecy of the communications of the source to the destination. In particular, we investigate the use of multi-antenna harvest-and-jam (HJ) helpers in a multi-antenna amplify-and-forward (AF) relay wiretap channel assuming that the direct link between the source and destination is broken. Our goal is to maximize the achievable secrecy rate at the destination subject to the transmit power constraints of the AF relay and HJ helpers. In the case of perfect channel state information (CSI), the joint optimization of the artificial noise (AN) covariance for jamming and the AF beamforming matrix is presented as well as a suboptimal solution with lower complexity based on semidefinite relaxation (SDR) which is tight in this case. For the practical case where the CSI is imperfect at both the relay and the HJ helpers, we provide the formulation of the robust optimization for maximizing the worst-case secrecy rate. Using SDR techniques, a near-optimal robust scheme is proposed. Numerical results are provided to validate the effectiveness of the HJ protocol.This paper studies the use of multi-antenna harvest-and-jam (HJ) helpers in a multi-antenna amplify-and-forward (AF) relay wiretap channel assuming that the direct link between the source and destination is broken. Our objective is to maximize the secrecy rate at the destination subject to the transmit power constraints of the AF relay and the HJ helpers. In the case of perfect channel state information (CSI), the joint optimization of the artificial noise (AN) covariance matrix for cooperative jamming and the AF beamforming matrix is studied using semidefinite relaxation (SDR) which is tight, while suboptimal solutions are also devised with lower complexity. For the imperfect CSI case, we provide the equivalent reformulation of the worst-case robust optimization to maximize the minimum achievable secrecy rate. Inspired by the optimal solution to the case of perfect CSI, a suboptimal robust scheme is proposed striking a good tradeoff between complexity and performance. Finally, numerical results for various settings are provided to evaluate the proposed schemes.

Robust Outage Secrecy Rate Optimizations for a MIMO Secrecy Channel

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.

Outage Constrained Robust Beamforming for Secure Broadcasting Systems With Energy Harvesting

In this paper, we investigate simultaneous wireless information and power transfer systems for multiuser multiple-input single-output secure broadcasting channels. Considering imperfect channel state information, we introduce a robust secure beamforming design, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. With the aid of Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. Based on a successive convex approximation (SCA) method, we propose a low-complexity approach, which reformulates the original problem as a second-order cone programming problem. Also, we prove the convergence of the SCA-based iterative algorithm. Simulation shows that the proposed scheme outperforms the conventional method with lower complexity.

Robust Optimization for AN-Aided Transmission and Power Splitting for Secure MISO SWIPT System

This letter investigates a multiple-input single-output secrecy channel, where the legitimate user and the eavesdroppers employ a power splitting scheme for information decoding and energy harvesting (EH), simultaneously. An artificial noise is embedded to the information bearing signal to interfere the eavesdroppers and to harvest power by all receivers (i.e., legitimate user and eavesdroppers). We consider the robust secrecy rate maximization problem subject to the transmit power and the EH constraints by incorporating the norm-bounded channel uncertainty. This robust optimization problem is not convex, and thus, it can be reformulated as a convex one along with matrix transformations and convex conic optimization techniques, which is iteratively solved based on constrained concave-convex procedure-based algorithm. Finally, numerical results are provided to validate our proposed algorithm.

Harvest-and-jam: Improving security for wireless energy harvesting cooperative networks

The emerging radio signal enabled simultaneous wireless information and power transfer (SWIPT), has drawn significant attention. To achieve secrecy transmission by cooperative jamming, especially in the upcoming 5G networks with self-sustainable mobile base stations (BSs) and yet not to add extra power consumption, we propose in this paper a new relay protocol, i.e., harvest-and-jam (HJ), in a relay wiretap channel with an additional set of spare helpers. Specifically, in the first transmission phase, a single-antenna transmitter (Tx) transfers signals carrying both information and energy to a multi-antenna amplify-and-forward (AF) relay and a group of multi-antenna helpers; in the second transmission phase, the AF relay processes the information and forwards it to the receiver while each of the helpers generates an artificial noise (AN), the power of which is constrained by its previously harvested energy, to interfere with the eavesdropper. By optimizing the transmit beamforming matrix for the AF relay and the covariance matrix for the AN, we maximize the secrecy rate for the receiver subject to transmit power constraints for the AF relay and all helpers. The formulated problem is shown to be non-convex, for which we propose an iterative algorithm based on alternating optimization. Finally, the performance of the proposed scheme is evaluated by simulations as compared to other heuristic schemes.

Robust transceiver designs in multiuser MISO broadcasting with simultaneous wireless information and power transmission

In this paper, we address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission, where a multi-antenna base station (BS) sends energy and information simultaneously to multiple users equipped with a single antenna. Assuming that perfect channel-state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. Due to the channel uncertainty, the original problem becomes a homogeneous quadratically constrained quadratic problem, which is NP-hard. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Numerical results are provided to validate the robustness of the proposed algorithms.

Joint optimization of AN-aided beamforming and power splitting designs for MISO secrecy channel with SWIPT

In this paper, we study an energy harvesting scheme for a multiple-input-single-output secrecy channel under imperfect channel state information case with either deterministic and statistical channel uncertainties. The system consists of one multi-antenna transmitter, several multi-antenna energy receivers (ERs) and one single-antenna co-located receiver (CR) who adopts a power splitter to decode information and harvest power simultaneously. We consider the artificial noise (AN) embedded information-bearing signal to interfere potential eavesdroppers (i.e., ERs) and capture the harvested power. We perform joint optimization for the masked beamforming matrix, the AN covariance matrix and the power splitting ratio, such that the transmit power is minimized to satisfy the target secrecy rate of the CR, the total transmit power and the energy harvesting constraints for the CR and the ERs. By incorporating norm-bounded channel uncertainty model, we propose a robust joint design method to obtain the optimal solution. Also, a suboptimal algorithm for the outage constrained robust optimization problem is proposed by adopting the Bernstein-type inequality. Furthermore, the tightness of the relaxation for the proposed schemes are verified by showing that the optimal solution of the relaxed problem is rank-one. Finally, simulation results are presented to validate the performance of our proposed schemes.