Sum Secrecy Rate Maximization Problem Research Articles

A Robust Scheme for RIS-Assisted UAV Secure Communication in IoT

Reconfigurable intelligent surface (RIS)-assisted unmanned aerial vehicles (UAV) have been extensively studied on the Internet of Things (IoT) systems to improve communication performance. In this paper, we aimed to counter simultaneous jamming and eavesdropping attacks by jointly designing an active beamforming vector at the base station (BS) and reflect phase shifts at the RIS. Specifically, considering imperfect angular channel state information (CSI), the sum secrecy rate maximization problem in the worst case could be formulated, which is NP-hard and non-convex. To address this problem, we improved the robust enhanced signal-to-leakage-and-noise ratio (E-SLNR) beamforming to reduce the computational complexity and mitigate the impact of interference, eavesdropping and jamming. Furthermore, a genetic algorithm with a tabu search (GA-TS) method was proposed to efficiently obtain an approximate optimal solution. The simulation results demonstrated that the proposed GA-TS method converged faster with better results than conventional GA, while the proposed robust scheme could achieve higher sum secrecy rates than the zero-forcing (ZF) and SLNR schemes.

IRS-Assisted Physical Layer Security in MIMO-NOMA Networks

In this letter, we propose deploying the intelligent reflecting surface (IRS) to enhance the physical layer security in non-orthogonal multiple access (NOMA). The secrecy sum-rate of IRS-assisted multiple-input multiple-output (MIMO) NOMA is maximized in the presence of an eavesdropper. Because of the discrete unit-modulus constraint and the nonconvex property, the secrecy sum-rate maximization problem is hard to solve. We reformulate the original problem into an equivalent parameterized optimization using rotation matrices and apply the particle swarm algorithm for global optimization. Simulation results verify that the performance of the proposed algorithm is close to the secrecy capacity of the channel, realized by exhaustive search, and outperforms other methods like alternating optimization and zero-forcing in terms of complexity and achievable rates.

Secure Transmission for Hierarchical Information Accessibility in Downlink MU-MIMO

Physical layer security is a useful tool to prevent illegal wiretapping to confidential information. In this paper, we consider a generalized model of conventional physical layer security, referred as hierarchical information accessibility (HIA). A main feature of the HIA model is that a network has a hierarchy in information access, wherein decoding feasibility is determined by each user’s priority. Under this HIA model, we formulate a sum secrecy rate maximization problem with regard to precoding vectors. This problem is challenging since multiple non-smooth functions are involved into the secrecy rate to fulfill the HIA conditions and also the problem is non-convex. To address the challenges, we approximate the minimum function by using the LogSumExp technique, thereafter obtain the first-order optimality condition. One key observation is that the derived condition is cast as a functional eigenvalue problem, where the eigenvalue is equivalent to the approximated objective function of the formulated problem. Accordingly, we show that finding a principal eigenvector is equivalent to finding a local optimal solution. To this end, we develop a novel method called generalized power iteration for HIA (GPI-HIA). Simulations demonstrate that the GPI-HIA significantly outperforms other baseline methods in terms of the secrecy rate.

Secure Transmission in NOMA-Aided Multiuser Visible Light Communication Broadcasting Network With Cooperative Precoding Design

In this paper, we study the secrecy performance of non-orthogonal multiple access (NOMA) enabled visible light communication (VLC) broadcast channels in the presence of an active eavesdropper (Eve). The considered VLC system consists of multiple separately distributed light-emitting diodes arrays and multiple randomly located users (UEs) in an indoor room. User clustering is conducted to reduce the implementation complexity of successive interference cancellations. Two cooperative precoding strategies based on zero-forcing (ZF) and maximum ratio transmission (MRT) are designed using the effective channel of each cluster. Based on each precoding strategy, a sum secrecy rate maximization problem is developed to obtain the near-optimal power allocation (PA) to strengthen UEs’ confidential transmission and degrade Eve’s reception under minimum secrecy rate requirement, peak amplitude, non-negativity, and power constraints. To tackle the challenging non-convex problem for each precoding strategy, equivalent transformations and arithmetic-geometric mean approximation are conducted to convert the original problem into a series of geometric programming (GP) problems. Based on the reformulated problems, iterative algorithms are proposed to obtain near-optimal solutions by solving the GP problems through successive convex approximations. The convergence and complexity analysis of the proposed algorithms are studied. Simulation results show that the sum security performance of the proposed PA approach outperforms the conventional PA approaches in both ZF-based and MRT-based precoder schemes. The effectiveness of applying NOMA compared with the orthogonal multiple access-based scheme is also validated for the proposed system.

Robust Secure Beamforming and Power Splitting for Millimeter-Wave Cognitive Satellite–Terrestrial Networks With SWIPT

In this article, we investigate robust secure beamforming and power splitting for multiuser secondary terrestrial networks with simultaneous wireless information and power transfer, which coexist with primary satellite networks in the same millimeter-wave bands. In particular, a base station is equipped with a uniform planar array, and a secondary user (SU) employs a power-splitting-type receiver. Under an angle-based channel state information (CSI) error model, we formulate an optimization problem with the aim to maximize the minimal worst-case achievable secrecy rate among all SUs, while satisfying the quality-of-service (QoS) constraints for each SU, the interference limit for a primary satellite earth station, and the power consumption limit for the base station. To handle the intractable problem, we propose an iterative algorithm based on a series of approximations and a concept of the convex hull. Specifically, the former is for jointly designing secure beamformers and power splitting ratios, and the latter is for ensuring robustness to the angle-based CSI uncertainty. Furthermore, we analyze the computational complexity of this algorithm and extend the proposed scheme for solving a weighted sum secrecy rate maximization problem. Numerical results validate the effectiveness and superiority of the proposed scheme compared to the existing approaches, and obtain an insight into different robust designs.

Sum secrecy rate maximization for multi-carrier MIMOME systems with full-duplex jamming

In this work we study the sum secrecy rate maximization problem for a multi-carrier and multiple-input-multiple-output multiple-antenna eavesdropper (MIMOME) communication system. We consider the setup that the receiver is capable of full-duplex (FD) operation and simultaneously sends jamming signal to a potential eavesdropper. In particular, we intend to achieve a higher security level in the physical layer by simultaneously utilizing the spatial and frequency diversity of the FD-enabled system. In order to deal with the non-convex nature of the problem, we reformulate the problem as a separately convex program and propose an iterative algorithm. The iterative solution has a guaranteed convergence based on block coordinate descent method. Furthermore, for a simplified scenario where the transmitter is only equipped with a single antenna, the system is mitigated to a transmit power allocation problem. We obtain an optimal solution analytically with the assumption of a known jamming strategy. We also study an FD bidirectional secure communication system, where both transceivers are capable of FD operation. The numerical evaluations indicate the gain of an optimized jamming strategy for an FD multi-carrier system.

Optimization for Maximizing Sum Secrecy Rate in MU-MISO SWIPT Systems

In this paper, we consider the sum secrecy rate maximization problem in multiuser multiple-input single-output (MU-MISO) systems in the presence of multiple energy harvesters (EHs) which also have potential to wire-tap the information users (IUs). To facilitate delivering secure information to the IUs and increase the total harvested energy by the EHs simultaneously, we optimize the transmit beamforming vectors to direct the information signals toward the IUs and artificial noise (AN) toward the EHs. We assume that each EH relies on itself to decode the information signal intended for an individual IU. Therefore, the corresponding problem is to maximize the worst-case sum secrecy rate under transmit power and energy harvesting constraints. The problem is optimally solved by transforming it into a convex iterative program using a change of variables, semi-definite relaxation (SDR), and linearization of quadratic terms. We prove that rank-one optimal solutions for the IUs beamforming covariance matrices can be obtained from the optimal relaxed unconstrained solution. Also, we provide three suboptimal solutions based on null space projection and power control of the beamforming vectors for the low and high harvested energy constrained regions. A special case of cooperative EHs in which the EHs can collaboratively cancel the signal of all IUs except the one they intend to eavesdrop is also investigated, and the optimal solution is derived in a comparable way as in noncooperative EHs case. Our simulation results reveal an understanding of how the tradeoff between the AN and information signal can jointly improve both the sum secrecy rate and the total harvested energy. We also show that, within the low total harvested energy region, the suboptimal solution in which the AN is projected in the null space of the IUs channels outperforms the suboptimal solution which ignores AN alignment at the IUs, and vice versa over the high total harvested energy region; and the suboptimal solution that combines both of them achieves close to optimal performance.

Secure beamforming for two-way multiantenna relay systems

In two-way multiantenna relay systems, confidential information can be easily intercepted by eavesdroppers. To overcome this problem, two secure beamforming schemes are proposed: secrecy sum rate maximization beamforming (SSRMB) and null space beamforming (NSB). For the SSRMB scheme, the nonconvex secrecy sum rate maximization problem is solved using a successive convex approximation strategy, which is convergent. The obtained beamforming solution is locally optimal to the original problem. For the special scenario where the number of antennas at the relay is more than the number of eavesdroppers, the NSB scheme with a low complexity is proposed. The beamforming solution is obtained by solving a generalized Rayleigh quotient problem. Simulation results demonstrate that the proposed schemes can effectively improve the security performance, and the SSRMB scheme has a fast convergence rate.

Joint resource allocation and artificial noise design for multiuser wiretap OFDM channels

PHY-layer security is one of promising techniques for enhanced security and privacy protection in 5G communications. In this paper, the joint resource allocation and artificial noise (AN) design problem of multiuser wiretap orthogonal frequency-division multiplexing (OFDM) systems is investigated to improve the system secrecy rate and power efficiency, which can help to provide waveform design references for secure 5G communications. In such a multiuser wiretap OFDM system, one legitimate transmitter (Alice), multiple legitimate receivers (Bobs), and one eavesdropper (Eve) are simultaneously considered. The time-domain artificial noise is firstly involved to guarantee the target secrecy rates of multiple Bobs. Then a sum secrecy rate maximization problem with nonconvex integer nonlinear programming is formulated to jointly optimize the power, subcarrier allocation and AN design. To solve this tough problem with low computational complexity, a heuristical sub-optimal subcarrier allocation method is proposed, followed by the Lagrange dual method based joint power allocation and AN design scheme. Moreover, considering that sum secrecy rate maximization may result in unfairness for Bobs with bad channel gains, the transmit power minimization problem that ensures a target secrecy rate for each individual Bob is further addressed. An iterative algorithm is proposed to solve this power minimization problem by updating the subcarrier, power allocation and AN design alternatively. Numerical results demonstrate the effectiveness of the proposed algorithms.

Robust secrecy beamforming for full-duplex two-way relay networks under imperfect channel state information

Consider a two-way amplify-and-forward (AF) relay network where two legitimate nodes communicate through a relay in the presence of an eavesdropper. Assuming full duplexity at the legitimate nodes and the relay, a robust artificial noise (AN)-aided AF scheme is proposed to maximize the worst-case sum secrecy rate under imperfect channel state information (CSI) of the eavesdropper. This robust sum secrecy rate maximization (SSRM) problem is formulated as a max-min semi-infinite problem and is tackled by the semidefinite relaxation (SDR) method. In particular, we first convert the max-min semi-infinite problem into a maximization problem with a finite number of constraints. Then, an efficient two-block alternating difference-of-concave (DC) programming approach is proposed to iteratively solve the SDR problem, with one of the blocks computed in closed form. In addition, a specific robust rank-one solution construction procedure is presented to extract a feasible solution for the original robust SSRM problem from the SDR solution. The efficacy of the proposed method is demonstrated by numerical simulations.

Computing B-Stationary Points of Nonsmooth DC Programs

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc) minimization problem. The contributions of this paper are (i) clarify several kinds of stationary solutions and their relations; (ii) develop and establish the convergence of a novel algorithm for computing a d-stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions; (iii) extend the algorithm in several directions including a randomized choice of the subproblems that could help the practical convergence of the algorithm, a distributed penalty approach for problems whose objective functions are sums of dc functions, and problems with a specially structured (nonconvex) dc constraint. For the latter class of problems, a pointwise Slater constraint qualification is introduced that facilitates the verification and computation of a B(ouligand)-stationary point.

Sum Secrecy Rate Maximization for Full-Duplex Two-Way Relay Networks Using Alamouti-Based Rank-Two Beamforming

Consider a two-way communication scenario where two single-antenna nodes, operating under full-duplex mode, exchange information to one another through the aid of a (full-duplex) multi-antenna relay, and there is another single-antenna node who intends to eavesdrop. The relay employs artificial noise (AN) to interfere the eavesdropper's channel, and amplify-forward (AF) Alamouti-based rank-two beamforming to establish the two-way communication links of the legitimate nodes. Our problem is to optimize the rank-two beamformer and AN covariance for sum secrecy rate maximization (SSRM). This SSRM problem is nonconvex, and we develop an efficient solution approach using semidefinite relaxation (SDR) and minorization-maximization (MM). We prove that SDR is tight for the SSRM problem and thus introduces no loss. Also, we consider an inexact MM method where an approximately but computationally cheap MM solution update is used in place of the exact update in conventional MM. We show that this inexact MM method guarantees convergence to a stationary solution to the SSRM problem. The effectiveness of our proposed approach is further demonstrated by an energy-harvesting scenario extension, and by extensive simulation results.

Secrecy Sum Rates of MIMO Multi-Receiver Wiretap Channels

We consider MIMO multi-receiver wiretap channels where the transmitter sends confidential messages to legitimate receivers in the presence of an external eavesdropper. Since the secrecy sum rate maximization problem is nonconvex, we derive an equivalent alternating optimization problem. We propose an iterative algorithm to find the optimal transmit covariance matrix based on the MIMO BC-MAC duality. We prove that the limit point satisfies the KKT conditions of the original secrecy sum rate maximization problem.

Secrecy Analysis on Network Coding in Bidirectional Multibeam Satellite Communications

Network coding is an efficient means to improve the spectrum efficiency of satellite communications. However, its resilience to eavesdropping attacks is not well understood. This paper studies the confidentiality issue in a bidirectional satellite network consisting of two mobile users who want to exchange message via a multibeam satellite using the XOR network coding protocol. We aim to maximize the sum secrecy rate by designing the optimal beamforming vector along with optimizing the return and forward link time allocation. The problem is non-convex, and we find its optimal solution using semidefinite programming together with a 1-D search. For comparison, we also solve the sum secrecy rate maximization problem for a conventional reference scheme without using network coding. Simulation results using realistic system parameters demonstrate that the bidirectional scheme using network coding provides considerably higher secrecy rate compared to that of the conventional scheme.

Resource Allocation for Secure Multicarrier AF Relay System Under Total Power Constraint

In this letter, we consider an amplify-and-forward-relay-aided secure multicarrier communication between two nodes with an eavesdropper. We solve the sum secrecy rate maximization problem by solving the following two problems: 1) subcarrier usage policy at the source and the relay; and 2) power allocation among subcarriers between the source and the relay under a total system power constraint. We provide a suboptimal closed-form solution to the problem that involves mixed-integer variables and a nonlinear fractional function. The numerical results demonstrate an improved sum rate by the proposed scheme over a scenario without relay.