Secrecy Sum Rate Research Articles

Secrecy Performance of a Multi-NOMA-MIMO System in the UEH Relaying Network Using the PSO Algorithm

In this paper, we investigate the secrecy performance of the nonorthogonal multiple access (NOMA) system in an untrusted relaying energy harvesting (UEH) network with the multiple-input multiple-output (MIMO) architecture using the maximum ratio transmission (MRT) and maximal ratio combining (MRC) techniques. In this network, a source communicates with users with the help of a relaying network composed of multiple untrusted components using the amplify-and-forward (AF) protocol. These untrusted relay nodes are equipped with a single antenna and employ the power-splitting (PS) protocol to harvest energy from received signals. Moreover, to improve the secrecy outage performance and protect the confidential information from the untrusted relaying network, the source acts as the jammer to generate artificial noise (AN). To evaluate the secrecy performance of each user and the overall system, we derive the closed-form expressions of the secrecy outage probability (SOP) over the Rayleigh fading channels and use a Monte Carlo simulation to verify the accuracy of these analytical results. Moreover, to analyze the secrecy data rate, the maximization problem of the sum secrecy rate (SSR) of the system is solved by applying the particle swarm optimization (PSO) algorithm based on power allocation (PA). These results are also validated with the optimal exhaustive search method. Furthermore, we compare the MIMO/NOMA and MIMO/OMA systems and examine the effects of various system parameters to characterize the secrecy effectiveness of both systems.

Optimization of pre-processing filter for time-reversal multi-user secure transmission systems based on artificial noise

Physical layer security is a way to realize the secure transmission of information by employing the characteristics of wireless channels. Thanks to its spatial and temporal focusing property, the time-reversal (TR) transmission can achieve effective secure communications even when the transmitter is only equipped with one antenna. This paper studies the design and optimization of the security scheme based on artificial noise (AN) with or without the eavesdropper's channel state information (ECSI) in a TR multi-user downlink multiple access system. The null-space AN is adopted when ECSI is unavailable, and the corresponding optimization problem is to minimize the signal power under each user's signal-to-interference-plus-noise ratio (SINR) target constraint, so that the power used to send AN is maximized and the interception rate of the eavesdropper is minimized. The problem is solved by transforming it into a semidefinite program (SDP) with semidefinite relaxation (SDR). The pre-processing filter and AN are jointly optimized to maximize the sum secrecy rate when ECSI is available. The problem is solved by transforming it into a convex program by using SDR and the first-order Taylor approximation. Simulation results show that the sum secrecy rate of the proposed scheme is significantly higher than that of the conventional TR transmission system with or without AN.

Optimal rotation angle for finite constellation over additive white Gaussian noise multiple access wiretap channel

The achievable secrecy rate regions of various multi-user channels with Gaussian inputs are well-known in the literature. To gain more practical insights into the achievable rates, it is more useful to consider channels with inputs from finite constellations, such as M-ary quadrature amplitude modulation (M-QAM), M-ary phaseshift keying (MPSK), M-ary amplitude phase-shift keying (M-APSK) etc. The authors study the achievable secrecy rates with a constrained constellation input for a multiple access wiretap channel with an eavesdropper. They also show that if the constellation points are rotated relatively for the two users then the secrecy sum-rate can be improved. They perform Monte–Carlo simulations for computing these secrecy rates for classical modulation schemes including BPSK, quadrature phase-shift keying, M-QAM, M-PSK, M-PAM, and M-APSK. They also derived an approximate function, whose argument of supremum provides an approximately optimal rotation angle for obtaining a maximum secrecy sum-rate. they also show, via simulations, that rotation of constellation is helpful for some range of signal-to-noise ratio only, which is contrary to the results of multiple access channel without security constraint. Finally, they consider a more realistic scenario, where the channel from transmitters to receivers and eavesdroppers is time-varying. They consider the case of complex circularly symmetric Gaussian random channel gains and compute the optimal rotation angle, which will maximise the expected value of an upper bound of the secrecy sum-rate.

Secure performance analysis and optimization for FD-NOMA vehicular communications

Vehicle-to-vehicle (V2V) communication appeals to increasing research interest as a result of its applications to provide safety information as well as infotainment services. The increasing demand of transmit rates and various requirements of quality of services (QoS) in vehicular communication scenarios call for the integration of V2V communication systems and potential techniques in the future wireless communications, such as full duplex (FD) and non-orthogonal multiple access (NOMA) which enhance spectral efficiency and provide massive connectivity. However, the large amount of data transmission and user connectivity give rise to the concern of security issues and personal privacy. In order to analyze the security performance of V2V communications, we introduce a cooperative NOMA V2V system model with an FD relay. This paper focuses on the security performance of the FD-NOMA based V2V system on the physical layer perspective. We first derive several analytical results of the ergodic secrecy capacity. Then, we propose a secrecy sum rate optimization scheme utilizing the instantaneous channel state information (CSI), which is formulated as a non-convex optimization problem. Based on the differential structure of the non-convex constraints, the original problem is approximated and solved by a series of convex optimization problems. Simulation results validate the analytical results and the effectiveness of the secrecy sum rate optimization algorithm.

Secure Hybrid A/D Beamforming for Hardware-Efficient Large-Scale Multiple-Antenna SWIPT Systems

In this work, we investigate the problem of secure communications in a downlink large-scale multi-antenna assisted simultaneous wireless information and power transfer (SWIPT) system, where a base station (BS) transmits signals to serve a number of information decoding (ID) and energy harvesting (EH) users. Considering that the EH users can potentially eavesdrop the ID users' confidential information, we study the robust joint design of the hybrid analog-digital (A/D) beamforming (BF) matrices and of the artificial redundant signal (ARS) covariance matrix at the BS, where the aim is to maximize the worst-case sum secrecy rate for the ID users under a transmit power constraint, a nonlinear EH constraint and a unit-modulus constraint on the entries of the analog BF matrix. The corresponding optimization problem is very challenging due to the nonlinear and nonconvex objective function and constraints. Using innovative optimization techniques, we first transform the original problem into an equivalent but more tractable form, and then develop a novel joint iterative algorithm based on the penalty-concave-convex procedure (CCCP) for solving the resultant problem. We show that the proposed penalty-CCCP based algorithm for ARS-aided robust joint hybrid BF design converges to a Karush-Kuhn-Tucker solution of the original problem, and also analyze its computational complexity. Our simulation results verify that the resultant robust joint hybrid BF design algorithm relying on ARS significantly outperforms the conventional hybrid BF benchmark algorithms and efficiently achieves the performance of the fully-digital BF with reduced number of radio frequency chains and energy consumption.

Secure Degrees of Freedom of MIMO Two-Way Wiretap Channel With no CSI Anywhere

This article considers a two-way multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel with two full-duplex nodes (Alice and Bob) exchanging messages simultaneously and wiretapped by a $ {N}_{ {e}}$ -antennas eavesdropper (Eve). The channel state remains unchanged over a coherence interval T and is unknown to all terminals, including Alice, Bob, and Eve, at the beginning of the coherence interval. We first show the expression of the optimal signal waveform for Alice and Bob, which maximizes the sum secrecy rate, should be the products of independent random diagonal matrices and isotropically distributed unitary matrices. Then, conditioned on large T and small $ {N}_{ {e}}$ , the upper-bound for the secure degree of freedom (s.d.o.f.) of the two-way wiretap channel is derived, and a constant-norm-signaling (CNS) scheme is presented to achieve this theoretical bound. Finally, we formulate an optimization problem of the s.d.o.f. achieved by the CNS scheme for general cases with arbitrary T and $ {N}_{ {e}}$ , and solve this problem by exploring the monotonicity of the achievable s.d.o.f.. Our result shows that the optimal s.d.o.f. can be independent of coherence time T and becomes the product of the numbers of legitimate nodes’s transmitter antennas (NLNTA) for large $ {N}_{ {e}}$ and small NLNTA.

Power Optimization for Enhancing Secrecy of Cooperative User Relaying NOMA Networks

To enhance the secrecy of wireless transmission, we propose a cooperative user relaying NOMA scheme, in which the near user works in full-duplex mode by transmitting jamming signals and receiving desired signals in the first phase, and the base station sends jamming signals in the second phase. Two power allocation (PA) schemes between the legitimate and jamming signals are designed based on different knowledge of the eavesdropping channel state information (ECSI). The first scheme aims to jam the eavesdropping with highest power while meeting rate requirements without ECSI. In the second scheme, the closed-form expressions of secrecy outage probability (SOP) are first derived using the statistical ECSI. Then, the sum secrecy rate is maximized by optimizing the PA and redundant rate with SOP constraints. Simulation results are provided to show the effectiveness of the proposed schemes.

Space–Time Line Code for Enhancing Physical Layer Security of Multiuser MIMO Uplink Transmission

In this article, we investigate a secure uplink multiple-input multiple-output communication system, in which the multiple users transmit information to a legitimate access point (AP) when a passive eavesdropper exists. A secure multiple access method is proposed for single-antenna users by employing space-time line codes (STLCs), which enables noncoherent detection at the legitimate AP without channel state information (CSI) and achieves full spatial diversity. While extending the secure STLC scheme from the single-antenna to two-antenna users by combining the STLC with artificial noise (AN) injection, we design a low-complexity AN signals with the optimal power control scheme. The proposed AN is ensured to be eliminated after STLC decoding at the legitimate AP, while sustained in eavesdropper's received signals as interference. Theoretical sum secrecy rates are derived by considering time-varying fading channels with the uncertainty of CSI at the users, and the numerical results verify that the proposed STLC schemes outperform the existing secure transmission schemes in terms of the sum secrecy rate.

Space-Frequency Increment Index Modulation Approach for Fifth Generation and Beyond Wireless Communication Systems

Unlike the classical modulation, for instance, quadrature amplitude modulation (QAM) and others, where bits are transmitted via symbols particularly from modulation alphabets, in index modulation (IM), extra information bits can be conveyed via the indices of a particular transmit entities during the transmission process. Transmit antenna elements are example of transmit entities in multi-antenna systems which can be used to convey extra information bits. Recently, frequency diverse array (FDA), as a new type of transmit antenna array which differs from the traditional phased-array has been proposed in the literature. In FDA, the element indices has small frequency increment across them. In this paper, space-frequency increment IM is proposed. The proposed scheme utilizes the indices of the activated transmit FDA antennas and their respective corresponding frequency increments $\Delta f$ to convey additional information bits. The proposed scheme is inspired by the principle of quadrature spatial modulation (QSM) and no additional antenna activation is required. Compared with spatial modulation (SM) and QSM, it is shown that, the proposed scheme achieved higher spectral efficiency. Further, the average bit error rate (ABER), secrecy sum rate (SSR) and system capacity are derived and evaluated. Moreover, a low-complexity decoding algorithm is examined. Finally, via numerical results, the proposed scheme shows to be better than the comparative alternatives (QSM/SM), and may offer promising properties in various contexts.

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.

Coordinated Beamforming for Secure Transmission in the Downlink Multicell MIMO Systems

In this paper, we consider secure transmission in the downlink of a multicell multiple-input multiple-output (MIMO) system with M cells; each cell consists of an N-antenna base station (BS) and K single-antenna users. Coordinated beamforming (CBf) is employed for secrecy enhancement. For CBf, the BSs can jointly design their respective beamformers to control intercell interference and information leakage. Based on regularized channel inversion (RCI) precoding structures, we derive the concise formulas for the signal-to-interference-plus-noise ratio (SINR) for the legitimate users and the colluding malicious users and the achievable secrecy sum rate for the CBf. Furthermore, we obtain a novel closed-form expression of the secrecy sum in the large-system regime where N and K tend to infinity with a fixed ratio β=K/N. Based on the large-system regime result, the regularization parameter is optimized to maximize the secrecy sum rate. It shows that the optimal regularization parameter decreases with the signal-to-noise ratio (SNR) and stays constant at high SNR if β>1/M. Compared with single-cell processing (SCP) without BS cooperation, simulation results show that the secrecy performance can be significantly enhanced by exploiting CBf. The analytical results are validated with the finite-size system by simulation.

Ergodic Secrecy Sum Rate Analysis of a Two-Way Relay NOMA System

In this letter, we investigate the ergodic secrecy sum rate of a two-way relay NOMA system. In particular, by considering decode-and-forward signal processing at the relay and selection combining at the eavesdropper, we derive a tight closed-form ergodic secrecy sum rate expression for the considered system. We demonstrate effects of the main link and eavesdropper link on the ergodic secrecy sum rate. The results reveal that the ergodic secrecy sum rate performance degrades when the eavesdropper is closer to one of the users. Numerical and simulation results corroborate our theoretical findings.

Power Allocation for Intelligent Interference Exploitation Aided Physical-Layer Security in OFDM-Based Heterogeneous Cellular Networks

In this paper, we consider an orthogonal frequency division multiplexing (OFDM) based heterogeneous cellular network consisting of a macro cell and a small cell, where a macro-cell base station (MBS) and a small-cell base station (SBS) communicate with respective macro-cell user (MU) and small-cell user (SU) with the existence of a common eavesdropper across different OFDM subcarriers. In order to make full use of the mutual interference between MBS and SBS against eavesdropping, an artificially designed signal is emitted at MBS to cancel out the interference received at MU as well as to interfere with the common eavesdropper at each subcarriers. For the purpose of further improving the secrecy performance, a sum secrecy rate (SSR) of OFDM-based heterogeneous cellular networks is maximized by optimizing the power allocation between MBS and SBS across different OFDM subcarriers when the eavesdropper owns the global instantaneous channel state information (ICSI), thus called ICSI based SSR maximization (ICSI-SSRM). As for the case when the ICSI of wiretap channels is unknown, we propose a statistical CSI based SSR maximization (SCSI-SSRM) scheme, where the statistical characteristics of channels from MBS and SBS to eavesdropper are employed to optimally allocate powers of MBS and SBS across different subcarriers under the constraint of MBS's total transmit power. The formulated ICSI-SSRM and SCSI-SSRM problems are all non-convex due to form of the difference between two-convex (D.C.) functions. Thus, we utilize the D.C. approximation approach to respectively convert original optimization problems into convex problems. Moreover, iterative optimal power allocation algorithms for ICSI-SSRM and SCSI-SSRM schemes are also presented to obtain their respective SSR values. Simulation results illustrate that the ICSI-SSRM and SCSI-SSRM algorithms can converge to their optimal values, which confirms the correctness and validation of the proposed algorithms. In addition, numerical results are also given to show that the ICSI-SSRM and SCSI-SSRM schemes outperform conventional power allocation methods in terms of their SSR performance.

Secrecy sum rate maximisation in multi‐antenna two‐way relay networks

This study investigates the achievable secrecy rate of two-way relay-assisted networks. It is assumed that there is no direct link between transceiver ends and the communication is carried out in two hops through the use of multi-antenna relays in the middle of transmission, where the relays employ amplify-and-forward strategies. To increase the bandwidth efficiency, intending nodes exchange their confidential messages in two hops. First, both nodes simultaneously send their messages to the relay nodes. Then, throughout the second hop, the relays make use of cooperative beamforming to send their incoming information in such a way that the achievable secrecy sum rate is maximised, considering each node is subject to a minimum secrecy rate constraint. Accordingly, two beamforming strategies, named as null-space beamforming and information leakage alignment beamforming are proposed, where their achievable secrecy sum rates are investigated and compared to existing works addressed in the literature.

Butler Matrix Frequency Diverse Retrodirective Array Beamforming: An Energy-Efficient Technique for mmWave Networks

Millimeter-wave (mmWave) networks with the frequency spectrum ranging from 30 GHz (with wavelength 10 mm) to 300 GHz (with wavelength 1 mm), can support massive wireless data in fifth-generation (5G) systems. Importantly, large colocated antenna elements can be exploited at the base station (BS) to facilitate beam-steering synthesis along the users’ directions. This paper proposes the Butler matrix (BM) frequency diverse retrodirective array (BM-FDRA) beamforming network at the BS for multiuser communications in mmWave networks. We utilize the orthogonal feature of the M×M BM with M elements of the FDRA to create directional beams for concurrent transmission towards different users in range-angle locations. The proposed scheme has the following merits: (a) there is beam-steering orthogonality without beam interferences and (b) there is automatic tracking functionality, i.e., the prior knowledge on the user location is not required by the proposed BM-FDRA at the BS. The proposed method can serve multiple users concurrently using the beam-steering orthogonality property. Furthermore, performance metrics such as the multiaccess secrecy sum rate (SSR) model, bit error rate (BER), system capacity, and energy efficiency are examined. The proposed BM-FDRA scheme achievements are highlighted via simulation results.

Robust Directional Modulation Design for Secrecy Rate Maximization in Multiuser Networks

Based on directional modulation (DM), robust beamforming matrix design for sum secrecy rate maximization is investigated in this article in multiuser systems. First, in case of random estimation error of direction angles toward eavesdroppers, a Von Mises distribution-sum secrecy rate maximization (VMD-SSRM) method is proposed to maximize the sum secrecy rate. Semidefinite relaxation and first-order approximation based on Taylor expansion are employed to solve the optimization problem in VMD-SSRM. Then in order to optimize the sum secrecy rate in the case of the worst estimation errors of direction angles, a maximum angle estimation error-SSRM (MAEE-SSRM) method is proposed. The optimization problem is constructed based on the upper and lower bounds of the estimated eavesdropping channel related coefficient and then solved by the change of the variable. Simulation results show that our two proposed methods have better sum secrecy rates than the state-of-the-art methods. Furthermore, when the estimation error of direction angle toward each eavesdropper is random but within a certain range, the secrecy performance of our VMD-SSRM method is better than that of our MAEE-SSRM method. On contrary, when the direction angle estimation error reaches its maximum, our MAEE-SSRM method performs better.

Secure Beamforming for Full-Duplex MIMO Two-Way Untrusted Relay Systems

This paper focuses on a full-duplex multiple-input multiple-output two-way untrusted relay system, and investigates the optimal beamforming design of such system to maximize its secrecy sum rate (SSR) based on the physical layer security technology. We first provide the modeling of SSR under a general beamforming setting as well as the theoretical formulation of the optimal beamforming design problem. Based on the ideal assumption that the full channel state information is available, we then develop a novel theoretical framework to solve the optimal design problem and thus establish an upper bound on SSR, where the techniques of alternate optimization, fractional programming, semi-definite programming and barrier function method are jointly employed. With the consideration of the constraints in practical implementations, we further propose two sub-optimal beamforming design solutions based on either Wiener prediction or asymptotic approximation. The issue of how to reduce the computational complexity in the optimal relay beamforming design is also discussed in this paper. Finally, we present extensive numerical results to illustrate our theoretical findings and to demonstrate the performance of the proposed sub-optimal beamforming design solutions.

Secure Beamforming in Full-Duplex Two-Way Relay Networks With SWIPT for Multimedia Transmission

With the advent of 5G, multimedia services in wireless communication networks will grow dramatically. So far, many researches have focused on improving security, throughput and channel capacity to support multimedia services. In this paper, a new system model of full-duplex (FD) two-way amplify-and-forward (AF) relay network with simultaneous wireless information and power transfer is presented, where two FD legitimate nodes with two single-antenna communicate with each other via energy-constrained AF relay with multiple antennas, and there is a half-duplex node with single antenna who intends to eavesdrop. This paper targets to maximize the secrecy sum rate of the system by designing the transmit beamforming vector of relay under power constraint and zero-forcing constraint, where two energy harvesting protocols, namely, power splitting and time switching are considered. However the maximization problem is a non-convex optimization, and it is very complex to solve. Therefore a linear method is used to find the lower bound of the secrecy sum rate and the non-convex problem is transformed into a convex optimization problem. After that, an iterative algorithm based on difference-of-convex programming is proposed to solve this convex optimization problem. The simulation results show the good convergence of the proposed iterative algorithm and also the superiority of secrecy sum rate of our proposed scheme compared with two traditional schemes.

Coordinated Beamforming and Artificial Noise in the Downlink Secure Multi-cell MIMO Systems under Imperfect CSI

In this letter, we consider the problem of secure communication in the downlink of a multi-cell multiple-input multiple-output (MIMO) system under imperfect channel state information (CSI) at the base stations (BSs). The passive eavesdroppers are considered, whose CSI are unavailable at the BSs. Coordinated Beamforming (CBf) and artificial noise (AN) are employed for secrecy enhancement. Based on regularized channel inversion (RCI) precoding, we derive a novel closed-form expression of secrecy sum-rate in the large-system regime. Based on the result, the regularization parameter and the power allocation ratio between the information signal and AN are optimized. Compared to the perfect CSI case, it shows that the channel estimation error can drastically reduce the secrecy sum-rate, and more power needs to be allocated for AN when the channel estimation error grows larger. The analytical results are validated with the finite-size system by simulation.

Cognitive NOMA for UAV-Enabled Secure Communications: Joint 3D Trajectory Design and Power Allocation

In the paper, we investigate the physical layer security (PLS) of an unmanned aerial vehicle (UAV) enabled communication system that integrates non-orthogonal multiple access (NOMA) with cognitive radio (CR), namely CR-NOMA. Specifically, the secondary UAV transmits confidential information to multiple secondary legitimate receivers with NOMA by sharing the spectrum with the primary networks, while an eavesdropper (Eve) attempts to wiretap the communication. We aim to jointly optimize the three-dimensional (3D) UAV trajectory and power allocation to maximize the worst-case average secrecy sum rate of all secondary receivers (SRs) while keeping the interference to primal receivers (PRs) below a certain threshold. The formulated problem is mixed-binary non-convex and is generally NP-hard. To address this issue, we first equivalently transform the binary variables into continuous ones by introducing tractable inequality constraints. Then, we decompose the optimization problem into two subproblems and develop an efficient iterative algorithm based on the successive convex approximate (SCA) technique, block coordinate descent (BCD) technique, and penalty function method. Numerical results are extensively studied to show that the proposed joint design significantly outperforms the benchmark schemes in terms of secrecy rate.