Worst-case Secrecy Rate Maximization Research Articles

Robust 3D-Trajectory and Time Switching Optimization for Dual-UAV-Enabled Secure Communications

This paper investigates a dual-unmanned aerial vehicle (UAV)-enabled secure communication system, in which, a UAV moves around to send confidential messages to a mobile user while another cooperative UAV transmits artificial noise signals to confuse malicious eavesdroppers. Both UAVs have energy constraints and the location information of eavesdroppers is imperfect. We consider a worst-case secrecy rate maximization problem of the mobile user over all time slots. This optimization problem is solved by jointly designing the three-dimensional (3D) trajectory of UAVs and the time allocation (recharging and service or jamming) under practical constraints including maximum UAV speed, UAV collision avoidance, UAV positioning error, and UAV energy harvesting. Specifically, we adopt a more practical UAV-ground channel model with both large-scale and small-scale fading components. Due to the non-convex feasible region constructed by the complicated constraints, directly finding the optimal solution of the original problem is intractable. To address this issue, we decouple the original optimization problem into three subproblems and develop an iterative algorithm to find its suboptimal solution by using the block coordinate descent technique. To solve each subproblem, certain advanced optimization tools, such as integer relaxation, S-procedure, and successive convex approximation techniques, are utilized. Numerical simulation results are provided to corroborate the theoretical derivations and to evaluate the performance of the proposed algorithm. Additionally, the numerical results assist to draw new insights on the 3D UAV trajectory by comparing the performance with conventional two-dimensional (2D) schemes.

Secure Millimeter Wave Cloud Radio Access Networks Relying on Microwave Multicast Fronthaul

In this paper, we investigate the downlink secure beamforming (BF) design problem of cloud radio access networks (C-RANs) relying on multicast fronthaul, where millimeter-wave and microwave carriers are used for the access links and fronthaul links, respectively. The base stations (BSs) jointly serve users through cooperating hybrid analog/digital BF. We first develop an analog BF for cooperating BSs. On this basis, we formulate a secrecy rate maximization (SRM) problem subject both to a realistic limited fronthaul capacity and to the total BS transmit power constraint. Due to the intractability of the non-convex problem formulated, advanced convex approximated techniques, constrained concave convex procedures and semi-definite programming (SDP) relaxation are applied to transform it into a convex one. Subsequently, an iterative algorithm of jointly optimizing multicast BF, cooperative digital BF and the artificial noise (AN) covariance is proposed. Next, we construct the solution of the original problem by exploiting both the primal and the dual optimal solution of the SDP-relaxed problem. Furthermore, a per-BS transmit power constraint is considered, necessitating the reformulation of the SRM problem, which can be solved by an efficient iterative algorithm. We then eliminate the idealized simplifying assumption of having perfect channel state information (CSI) for the eavesdropper links and invoke realistic imperfect CSI. Furthermore, a worst-case SRM problem is investigated. Finally, by combining the so-called $\mathcal {S}$ -Procedure and convex approximated techniques, we design an efficient iterative algorithm to solve it. Simulation results are presented to evaluate the secrecy rate and demonstrate the effectiveness of the proposed algorithms.

Energy-Constrained UAV-Assisted Secure Communications With Position Optimization and Cooperative Jamming

In this paper, we consider an energy-constrained unmanned aerial vehicle (UAV)-enabled mobile relay assisted secure communication system in the presence of a legitimate source-destination pair and multiple eavesdroppers with imperfect locations. The energy-constrained UAV employs the power splitting (PS) scheme to simultaneously receive information and harvest energy from the source, and then exploits the time switching (TS) protocol to perform information relaying. Furthermore, we consider a full-duplex destination node which can simultaneously receive confidential signals from the UAV and cooperatively transmit artificial noise (AN) signals to confuse malicious eavesdroppers. To further enhance the reliability and security of this system, we formulate a worst case secrecy rate maximization problem, which jointly optimizes the position of the UAV, the AN transmit power, as well as the PS and TS ratios. The formulated problem is non-convex and generally intractable. In order to circumvent the non-convexity, we decouple the original optimization problem into three subproblems; this facilitates the design of a suboptimal iterative algorithm. In each iteration, we propose a multi-dimensional search and numerical method to handle the subproblem. Numerical simulation results are provided to demonstrate the effectiveness and superior performance of the proposed joint design versus the conventional schemes in the literature.

Robust Secure Beamforming in MIMO Wiretap Channels With Deterministically Bounded Channel Errors

In this paper, a multiple-input multiple-output wiretap channel model is studied, where the information packet sent from the transmitter to the desired receiver is wiretapped by a potential eavesdropper. When ideal channel state information (CSI) is available, we design the secure beamforming using a proposed iterative closed-form updating scheme based on majorization–minimization approach. Numerical results demonstrate that the proposed scheme acquires the same secrecy rate as the existing algorithms whereas it has much lower complexity. When ideal CSI is not available and channel errors are modeled by deterministically bounded model, we investigate robust secure beamforming (RSB) optimization problem whose goal is worst-case secrecy rate maximization. In the formulated optimization problem, the objective function includes the expression of a logarithm of a determinant ( $\log \det$ ) minus $\log \det$ . Instead of approximating the $\log \det$ expression as a trace, we propose to linearize two $\log \det$ terms. After linearization, epigraph reformulation is used to deal with deterministically bounded channel errors and semi-infinite constraints are recast as linear matrix inequalities. Finally, an alternating optimization algorithm is utilized to find the RSB design. After obtaining the RSB design, we derive the worst-case secrecy rate. Numerical results illustrate that the proposed RSB design is superior to the nonrobust one.

Robust AN-Aided Secure Beamforming and Power Splitting in Wireless-Powered AF Relay Networks

In this letter, we investigate the secrecy design in a wireless-powered amplify-and-forward relay network, where the relay is energy constrained and powered by the signal from the transmitter. Specifically, by adopting the power splitting (PS) scheme at the relay, we investigate the worst-case secrecy rate maximization by jointly designing the relay beamforming matrix, artificial noise covariance, and the PS ratio. However, the formulated problem is highly nonconvex due to the secrecy rate function and the dynamic relay power constraint. By exploiting the hidden convexity, we transform the original problem to a solvable reformulation via the successive convex approximation and constrained concave–convex procedure, which can provide a high-level approximated beamforming solution. Then, an iterative algorithm is proposed to obtain the solution. Numerical results showed the effectiveness of the proposed robust scheme.

Optimal and Robust Beamforming for Secure Transmission in MISO Visible-Light Communication Links

This work considers secure downlink transmission in indoor multiple-input, single-output visible-light communication (VLC) links. In particular, we study the design of transmit beamformers that maximize the achievable secrecy rate subject to amplitude constraints imposed by the limited dynamic range of the light-emitting diodes (LEDs). Such constraints render the design problem nonconvex and difficult to solve. We show, however, that this nonconvex problem can be transformed into a solvable quasiconvex line search problem. We also consider the more realistic case of imperfect channel information regarding the receiver's and eavesdropper's links. We tackle the worst-case secrecy rate maximization problem, again subject to amplitude constraints. In our treatment, uncertainty in the receiver's channel is due to limited feedback, and is modeled by spherical sets. On the other hand, there is no feedback from the eavesdropper, and the transmitter shall utilize the line-of-sight channel gain equation to map the eavesdropper's nominal location and orientation into an estimate of the channel gain. Thus, we derive uncertainty sets based on inaccurate information regarding the eavesdropper's location and orientation, as well as the emission pattern of the LEDs. We also consider channel mismatches caused by the uncertain non-line-of-sight components. We provide numerical examples to demonstrate the performance gain of the optimal beamformer compared with the suboptimal schemes, and the robust beamformer compared with its nonrobust counterparts. We also evaluate the worst-case secrecy rate performance of the robust beamformer in a typical VLC scenario along with the aforementioned uncertainty sources.

Secure Beamforming for Multiple-Antenna Amplify-and-Forward Relay Networks

In this paper, we investigate the secure relay beamforming problems for the amplify-and-forward (AF) relay network, where the transmitter sends the information to the receiver with the help of a multiple-antenna relay in the presence of an eavesdropper. We first study the secrecy rate maximization (SRM) problem in the case of complete channel state information (CSI). The rank-1 relay beamformer, which has been solved in our previous work in “Secure relay beamforming with imperfect channel side information,” IEEE Trans. Veh. Technol., vol. 62, no. 5, pp. 2140–2155, June 2013, is rigorously proved to be globally optimal. Then, we turn to the case of partial eavesdropper’s CSI (ECSI), where the uncertainty of ECSI is characterized as a bounded region, and study the worst-case secrecy rate maximization (WCSRM) problem. Different from the common spherical uncertainty region, the uncertainty region adopted in our paper imposes independent constraints on the channel gain and direction. With the proposed uncertainty region, we give an in-depth analysis of the WCSRM problem. We solve the rank-1 relay beamformer in an explicit form and move a step further by establishing the sufficient conditions for the global optimality of the rank-1 solution. Besides, the rank-2 relay beamformer with a special singular value decomposition (SVD) structure is also considered. By reducing the optimization variables into single variable, we show that the proposed rank-2 solution can be solved by simple line search. The asymptotic optimality of the proposed rank-2 relay beamformer in the high relay power region is also proved under mild conditions. Finally, numerical results are presented to verify the analysis in the paper.

Robust Beamforming and Power Allocation for Secrecy in DF Relay Networks With Imperfect Channel State Information

We address a robust beamforming design and power allocation problem for a one-way multi-antenna relay network, where the multi-antenna source implements communication with the multi-antenna destination via a decode-and-forward (DF) relay in the presence of the multiple single-antenna eavesdroppers. The eavesdroppers can only overhear the information flowed from the relay to the destination in the second hop. We aim to maximize the worst-case secrecy rate in the condition that the global channel state information (CSI) is imperfect. To this end, we propose the joint beamforming and power allocation design for the worst-case secrecy rate maximization. However, our proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect CSI. To make the problem more tractable, we approximate the problem into several tractablesemidefinite programs by semidefinite relaxation, successive convex approximation, and S-procedure techniques, and we propose an iterative algorithm to solve the problem. Furthermore, we show that the proposed algorithm is also applicable for the case the Gaussian wiretap model, where only the eavesdroppers' CSI is imperfect. Simulation results validate the effectiveness of the proposed algorithm.

Robust Joint Beamforming and Jamming for Secure AF Networks: Low-Complexity Design

This paper investigates the physical-layer security issue of an amplify-and-forward (AF) relay network. We propose a joint cooperative beamforming (CB) and cooperative jamming (CJ) design that is robust to the imperfect channel state information (CSI) of the multiple multiantenna eavesdroppers. The objective is the worst-case secrecy rate maximization (WCSRM). Based on the inner convex approximation and semidefinite relaxation (SDR) technique, the original nonconvex problem is transformed into a sequence of approximate convex problems, which can be solved conveniently. The proposed robust design guarantees to converge to a Karush–Kuhn–Tucker (KKT) solution and is efficient in computational complexity. Furthermore, we prove that SDR always has a rank-1 solution, which identifies that SDR is tight. Simulations demonstrate the validity of the proposed strategy.

Robust Artificial Noise Aided Transmit Design for MISO Wiretap Channels with Channel Uncertainty

In this letter, we study the robust artificial noise (AN) aided transmit design for a multiple-input single-output (MISO) wiretap channel with a single-antenna eavesdropper. We consider two uncertainty models for the imperfect channel state information (CSI) on the main and eavesdropper's channels at the transmitter. For the deterministic uncertainty model, we solve the worst-case secrecy rate maximization (WC-SRM) problem via semidefinite program (SDP). For the stochastic uncertainty model, we propose a suboptimal solution to the outage probability constrained secrecy rate maximization (OP-SRM) problem based on the robust design for the WC-SRM problem. The simulation results demonstrate performance improvement of the proposed worst case robust design as compared to that based on the worst case method without usage of AN.

Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the nonconvex maximin optimization problem can be transformed into a quasi-convex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied. We also investigate the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at the eavesdropper in the presence of channel mismatches between the transmitters and the eavesdropper.