Null Space Beamforming Research Articles

Enhanced MIMO CSI Estimation Using ACCPM with Limited Feedback.

Multiple Input and Multiple Output (MIMO) is a promising technology to enable spatial multiplexing and improve throughput in wireless communication networks. To obtain the full benefits of MIMO systems, the Channel State Information (CSI) should be acquired correctly at the transmitter side for optimal beamforming design. The analytical centre-cutting plane method (ACCPM) has shown to be an appealing way to obtain the CSI at the transmitter side. This paper adopts ACCPM to learn down-link CSI in both single-user and multi-user scenarios. In particular, during the learning phase, it uses the null space beamforming vector of the estimated CSI to reduce the power usage, which approaches zero when the learned CSI approaches the optimal solution. Simulation results show our proposed method converges and outperforms previous studies. The effectiveness of the proposed method was corroborated by applying it to the scattering channel and winner II channel models.

Minimum secrecy rate maximization for multiple peer-to-peer communications in two-way relaying networks

We investigate physical layer security for multi-user peer-to-peer relay networks, where a secure user pair and other unclassified users exchange information only through a multi-antenna relay in the presence of a multi-antenna eavesdropper. Our aim is to obtain the optimal values for variables of user transmit power and the relay beamforming matrix by solving the minimum secrecy rate maximization problem under specific constraints. We assume scenarios in which the eavesdropper’s channel state information is and is not available. Mathematically, the optimization problem raised in the first scenario is nonlinear and non-convex. The relay adopts a null space beamforming technique to facilitate the problem and guarantee secrecy. Also, we decouple it into two subproblems and solve them using inequality semi-definite programming and nonlinear optimization techniques to find solutions for variables. Also, the complexity of the proposed algorithms is analyzed and its convergency is proved by simulation. In the second scenario, we utilize an artificial noise-aided secure relay beamforming scheme. The problem is equivalent to the problem of assigning maximum power to the artificial noise evaluated by the secrecy outage probability concept. Finally, simulations demonstrate the validity of the proposed methods.

Enabling joint transmitter-receiver spatial modulation with RF mirrors: A low-cost and highly-flexible perspective

Joint transmitter and receiver modulation (JSM) is a promising spatial-domain modulation scheme, which is capable of enhancing the spatial diversity, as well as the spatial multiplexing gain for the modulated multiple-input multiple-output (MIMO) systems. In this piece of paper, in order to generalize the JSM for arbitrary size MIMOs, we propose and investigate a novel joint transmit and receive spatial pattern grouping based JSM (SPG-JSM), which is enabled by RF mirrors configured around transmit antennas. To provide the proposed SPG-JSM with further enhanced spatial diversity, a SPG associated alternative null-space beamforming (ANB) strategy is introduced for accomplishing the transmitter preprocessing. In addition to the classical maximum-likelihood detection (MLD), we design a ratio sorting assisted low-complexity detection (RS-LCD) scheme to decrease the implementation cost at the receiver. Furthermore, we analyze the capacity, error performance, and the spatial diversity achievable by the proposed SPG-JSM, provided that the MLD is exploited at the receiver. Simulation outcomes are characterized to demonstrate the advantages of our novel SPG-JSM, and to validate the analytical performance derivations.

Jammer-Assisted Secure Precoding and Feedback Design for MIMO IoT Networks

Great concerns on the Internet of Things (IoT) security are raised as IoT becomes an emerging paradigm to achieve ubiquitous connectivity. This article studies low-complexity secure transceiver and feedback design with the assistance of a jammer for physical-layer security in multiantenna IoT systems. We consider the general setting where a legitimate multiantenna controller broadcasts confidential messages to multiple multiantenna IoT devices in the presence of a passive external multiantenna eavesdropper. Moreover, there is only quantized downlink channel state information (CSI) at the controller and the jammer through feedback channels. We introduce several secure transceivers for different system setups, all of which employ block-diagonal precoding at the controller and null-space beamforming at the jammer but are with the different receivers at each IoT device. Considering the practical setup of IoT and for the tractability of analysis, we study the secrecy performance of the transceiver with an arbitrarily selected receive matrix independent of the channels of all devices. We derive an approximate lower bound on the ergodic secrecy rate (ESR) of each device <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> assuming any asymptotes for system parameters. The obtained result can also be viewed as a lower bound on the ESR performance of any other transceivers. We also optimize this bound to find an adaptive feedback bit allocation to the two feedback channels of each legitimate device. Numerical results are shown to illustrate the obtained analytical ESR lower bound, the feedback bit allocation algorithm, and significant ESR performance gain that results from the proposed feedback bit allocation.

Artificial Noise Aided Secure Communications for Cooperative NOMA Networks

Non-orthogonal multiple access (NOMA) has been envisioned as a promising multiple access technique to improve spectral efficiency and provide massive connectivity in future wireless networks. However, the inherited security issues with NOMA should be carefully addressed to further exploit its potential benefits in NOMA enabled wireless networks. As such, we consider a cooperative NOMA network, where a source uses the NOMA to simultaneously communicate with a multi-antenna near-user and a far-user. While directly communicating with the near-user, the source employs multiple full-duplex (FD) decode-and forward (DF) relays to establish communication with the far-user in the presence of a passive eavesdropper. To address the eavesdropping in this cooperative NOMA network, we propose a new two-phase FD-based artificial noise (AN) scheme with different relay selection techniques. In the first phase, the selected FD relay emits AN to confuse the eavesdropper while receiving the superimposed signal from the source. In the second phase, the selected relay performs exclusive OR (XOR) operation on both the message intended to the far-user and the AN before broadcasting the resulting mixed signal. By utilizing null-space beamforming, self-interference cancellation techniques and DF-XOR cooperative protocol, the AN in the proposed scheme can be efficiently eliminated at the near-user and far-user as well as at the selected relay. However, the AN cannot be suppressed at the eavesdropper which serves the purpose of AN through degrading the decoding capability of the eavesdropper. We evaluate the performance of the proposed scheme in terms of security-reliability trade-off (SRT). For the AN-aided scheme with max-min and partial relay selection techniques, we theoretically derive the exact and asymptotic closed-form expressions of the outage probability and intercept probability. Numerical results have been provided to validate the derivations. In addition, the results reveal that the SRT of the near-user and far-user can be improved by increasing the number of antennas at the near-user and the number of relays.

User power allocation and relay beamforming design for secrecy sum rate maximization in two-way relay networks

In this paper, we investigate the physical-layer security (PLS) for multiple peer-to-peer communications in a two-way relaying networks involving 2 L single-antenna users, an N R -antenna relay, and an N E -antenna eavesdropper. Only a pair of peer-to-peer users demand security to exchange messages because the eavesdropper intends to wiretap them in both transmission phases. Our goal is to maximize the achievable secrecy sum rate (SSR) of specific peer-to-peer users, provided that restrictive constraints are satisfied. We endorse a null space beamforming technique at the relay to simplify the optimization problem and exclude private information leakage. The main problem is still very complicated due to coupled variables of the user transmit power with the relay beamforming matrix. Therefore, we convert the main problem into two subproblems, one in terms of the relay beamforming matrix and the other in terms of the user transmit power. To find a locally optimal solution for the relay beamforming, we turn the main problem into a difference of convex (DC) programming problem and for user power allocation, we drive the main problem into a constrained nonlinear optimization problem. Finally, simulations are performed to evaluate the performance benefits of the proposed method.

Total transmit power minimization with physical layer security in multiuser peer-to-peer two-way relay networks

In this paper, we investigate a multiuser peer-to-peer (MUP2P) two-way relay network (TWRN) in the presence of an eavesdropper. In this network, only the k∗th pair of users demand secure communication. Also, a multi-antenna eavesdropper aim to wiretap the confidential data of the k∗th pair in both cooperative phases. Our goal is to minimize the total transmit power provided that the secrecy rate for two secure users and the quality of service constraints of each user are met. For simplifying the problem and also omitting the confidential information leakage in the second phase, a null space beamforming (NSBF) scheme is employed. Despite this, the problem is still non-convex. We divided the problem into two subproblems to solve beamforming and users’ power formulated in two iterations, respectively. Three different methods are proposed to solve the first subproblem, semi-definite programming (SDP), second-order cone programming (SOCP), and sequential quadratic programming (SQP). We employ a sequential parametric convex approximation (SPCA) method to convert the users’ power subproblem into inequality form a linear programming (LP) problem to solve it. In the following, we evaluate the computational complexity of these methods. Simulation results confirmed the validity of the proposed methods.

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.

Self-Interference Cancellation Scheme for Secure AF Satellite Communication Based on FH-MWFRFT

This letter focuses on the self-interference cancellation problem for a secure two-way amplify-and-forward (AF) satellite communication system with eavesdropper at both the transmitter and the receiver. Several multi-antenna earth stations (ESs) aim to exchange messages through a multi-antenna satellite in two hops. We apply the frequency hopping multiple-term weighted fractional fourier transform (FH-MWFRFT) with different transform orders at the earth stations in the first hop to eliminate the self-interference existing in the two-way communication and enhance the security. The second hop of the communication is secured by null space beamforming, which steer the signal to the null space of the eavesdroppers’ channel. We demonstrate the improvement in secrecy capacity brought by the self-interference cancellation scheme via various simulation results and discussions. The simulations are carried out under the conditions of perfect channel state information (CSI) and imperfect CSI to verify the robustness of the proposed scheme.

Secure transmission in AF satellite system based on FH‐MWFRFT and null space beamforming

This study investigates the information security problem in amplify-and-forward (AF) satellite transmission with eavesdroppers at both the transmitter and the receiver. Two multi-antenna earth stations aim to exchange messages through a multi-antenna satellite in two hops. The satellite channels (both uplink and downlink) are assumed to be shadowed-Rician fading. In the first hop, the multiple term weighted fractional Fourier transform (MWFRFT) is adopted to secure the messages from the eavesdropper at the transmitter. To overcome the simplicity of parameters in MWFRFT, the authors enhance the MWFRFT with frequency hopping and propose the frequency hopping multiple term weighted fractional Fourier transform (FH-MWFRFT) to improve the secrecy. In the second hop, the satellite broadcasts the signal to the receiver after null space beamforming (NSBF). Since the energy at the satellite is confined, the NSBF is simplified by applying the singular value decompose to avoid the complicate optimisation calculations at the satellite. The one-way and two-way transmission scenarios with full channel state information (CSI) and statistic CSI are both considered in this study. Simulation results demonstrate the proposed method could achieve a better security at the transmitter while maintain a similar secrecy performance to the optimisation method at the legitimate receiver.

Secure Transmission Schemes for Two-Way Relay Networks

We investigate the physical-layer security problems of two-way relay networks in this paper. The whole network consists of two legitimate users and one eavesdropper, where the legal users need the help of some intermediate nodes to exchange information. We propose joint jamming and relaying mechanism, where a jamming node is selected from all intermediate nodes, to create interference upon eavesdropper, while other nodes are used to relay data for two users. All intermediate nodes are subjected to per-node power constraints. Based on null-space beamforming, we propose two different transmission schemes when the number of relay nodes is large enough. One scheme is designed to maximize the secrecy sum rate (MSSR) of the network, and the other is designed to maximize the minimum secrecy rate (MMSR) between two users. In the MMSR scheme, a series of semi-definite programming problems with a rank-1 constraint needs to be solved. We prove that this rank-1 constraint does not affect the solutions of original problems. In addition, we propose two modified secure transmission schemes when the number of relay nodes is less abundant. In short, no matter how many intermediate nodes in the communication networks, one can find suitable transmission schemes to ensure communication security.

A Secure Hybrid Satellite-Terrestrial Communication Network With AF/DF and Relay Selection

This paper makes research on a secure hybrid satellite-terrestrial communication network with eavesdroppers at the primary and secondary receivers. To secure the transmitted messages, we adopt the null space beamforming to the amplified-and-forward (AF) relay protocol and weighted fractional data carrying artificial noise (WFDCAN) to the decoded-and-forward (DF) relay protocol at the satellite. Considering the time delay may be brought by the WFDCAN, we introduce a parameter θ to indicate the delay severity. The secrecy capacity is combined with θ to derive the maximum secrecy delay constrain. The secrecy capacity, the ASER of the up-link channel and the delay constrain of the down-link channel are applied as factors for a three level relay protocol selection scheme. To simplify the analyses and expressions, the models of the AF protocol and the DF protocol are integrated to form a new transmission model. Furthermore, the secrecy performance at the destination receiver is considered for terrestrial relay selection to enhance the security performance. We also apply the columns of the frequency hopping based multi-term weighted fractional fourier transform (FH-MWFRFT) matrix as signal processing vector to the base station of the terrestrial network to minimize the interference it brings to the terrestrial relays. The simulation results demonstrate that the proposed system could maintain the security at the relays and the secondary receiver while reducing the delay at the satellite in some conditions.

Nonlinear-Precoded Multiuser Secure Transmission With Cooperative Jamming and Adaptive Limited Feedback

This paper studies secure transceiver design for multiuser multiantenna systems with an external passive eavesdropper and a cooperative jamming helper. Due to the finite-rate constraint of feedback channels, only quantized channel state information (CSI) of the legitimate users is available at the transmitter and the helper. A nonlinear-precoded secure transmission strategy is proposed using Tomlinson–Harashima precoding at the transmitter and null-space beamforming at the helper based on the quantized CSI. The accurate closed-form expression of an approximation for the ergodic rate of each legitimate user is obtained using quantization cell approximation for random vector quantization of the channels. Assuming the quantized CSI of the legitimate channels and the helper's channel at the eavesdropper, closed-form expression of an upper bound of the ergodic rate of each user's message at the eavesdropper is also derived. Then, a closed-form expression of an approximation for the worst-case ergodic secrecy sum rate follows. We also theoretically show that, besides the advantage in ergodic rate over the linear precoding scheme, when the quantized CSI is not available at the eavesdropper, Tomlinson–Harashima precoding is also more effective in degrading the received signal quality at the eavesdropper, and, thus, is more capable to enhance the secrecy of the systems compared with the linear precoding scheme. Given the total bandwidth constraint of CSI-feedback channels, an adaptive feedback bit allocation algorithm is proposed for each legitimate user to optimize the ergodic secrecy rate performance. Numerical results illustrate that the proposed nonlinear-precoded secure transmission strategy outperforms the corresponding linear precoding scheme, and significant advantage can be achieved by adaptively allocating the total available feedback bits.

Efficient algorithms for physical layer security in two-way relay systems

In this paper, we study the physical layer security in a two-way relay system (TWRS) consisting of two transceivers, one eavesdropper, and multiple relays. The channel state information (CSI) of the eavesdropper is assumed to be known. We consider the problem of maximizing the secrecy sum rate by optimizing the relay beamforming vector and the transceivers’ powers under total power constraint. The optimization problem of the beamforming vector has been formulated in the literature as a product of three Rayleigh quotients which is very difficult to solve, and the best proposed solution was a suboptimal solution to the null space beamforming. Here, we propose two approaches: (1) Optimal solution to the null space beamforming approach, and (2) Ignoring one Rayleigh quotient (IORQ) approach (which has not been proposed before). In the first approach, we convert the nonconvex product of two Rayleigh quotients to a quadratically constrained quadratic program (QCQP) and then to a convex problem with one dimensional search using semidefinite programming (SDP). Then we significantly simplify the problem by providing a new approach that uses the generalized eigenvalues. This new approach can be used to solve all QCQPs with positive definite objective function and two trace constraints. In the second proposed approach, we look for a beamforming vector that does not eliminate the complete information signal at the eavesdropper aiming to increase the whole secrecy sum rate. This approach provides a substantial contribution in improving the secrecy sum especially when the number of relays is low. Numerical results show that the proposed algorithms provide higher secrecy sum rates than the existing algorithms.11This Work is a part of the MSc thesis of the first author (Obeed, 2016 [1]).

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.

Maximising the minimum achievable secrecy rate of two‐way relay networks using the null space beamforming method

This paper concerns maximizing the minimum achievable secrecy rate of a two-way relay network in the presence of an eavesdropper, in which two nodes aim to exchange messages in two hops, using a multi-antenna relay. Throughout the first hop, the two nodes simultaneously transmit their messages to the relay. In the second hop, the relay broadcasts a combination of the received information to the users such that the transmitted signal lies in the null space of the eavesdropper's channel; this is called null space beamforming (NSBF). The best NSBF matrix for maximizing the minimum achievable secrecy rate is studied, showing that the problem is not convex in general. To address this issue, the problem is divided into three sub-problems: a close-to-optimal solution is derived by using the semi-definite relaxation (SDR) technique. Simulation results demonstrate the superiority of the proposed method w.r.t. the most well-known method addressed in the literature.

Beamforming strategies for multi‐antenna relay‐assisted networks

Physical layer security has received considerable attentions in recent years. Moreover, cooperative communications using some nodes of network as relays make use of the benefit of multi-antenna systems such as increasing the secrecy capacity. This study studies a communication network incorporating some multi-input–multi-output amplify and forward relays in the presence of some eavesdroppers. The objective persuaded in the current work is to find the beamforming matrices at the relays to maximise the achievable secrecy rate under either individual or total power constraint at these nodes. Accordingly, three main approaches including general rank beamforming (GRBF), rank-1 beamforming (RBF) and null-space beamforming (NSBF) are developed. For the NSBF under the total power constraint, a closed-form solution is obtained, while for the remaining scenarios the corresponding optimisation problem is expressed as a semi-definite programming problem. Numerical results indicate that the RBF and NSBF methods follow GRBF in some cases and degraded from GRBF in the others. However, it is shown that these two methods have much lower complexity than GRBF.

Achievable secrecy rate of wiretap channels incorporating multi‐input–multi‐output amplify and forward relaying

This study discusses the secrecy rate of two-hop relay-assisted cooperative wiretap channels, incorporating multi-antenna amplify and forward relaying in the middle of transmission. In this regard, under the Gaussian code book assumption, three main scenarios including null-space beamforming (NSBF), rank-1 beamforming (RBF), and the so-called general rank beamforming (GRBF) are proposed to be employed at the relay where their achievable secrecy rates are studied. Accordingly, for NSBF, a closed-form solution is derived, whereas the corresponding optimisation problems are formulated for the remaining cases as a standard semi-definite programming problem. Though GRBF ranks the first in terms of the achievable secrecy rate, RBF exhibits favourable results with a much lower complexity, as the corresponding optimisation problem runs over a reduced dimension. Moreover, NSBF has a much lower complexity, as it provides an analytical solution at the expense of a decrease in the secrecy rate, and interestingly, it performs quite well when the number of eavesdroppers is less than that of the relay antennas.

Cooperative beamforming design for physical-layer security of multi-hop MIMO communications

The security issue is critically important for wireless communications, especially for multi-hop communications. In this paper, we propose a cooperative secrecy beamforming scheme for a multi-hop MIMO communication network, in which there is a single-antenna source, multiple multi-antenna relays and a single-antenna destination. Moreover, two types of eavesdroppers exist in the network, one of which has known channel state information (CSI), while the other not. To achieve security communications, in our work null-space beamforming and artificial noise beamforming are jointly optimized to improve the secrecy rate of the multi-hop network. In nature, the joint optimization is nonconvex and challenging. Exploiting its structure, the considered optimization problem is decoupled into a series of subproblems that can be efficiently solved based on convex optimization theory. Finally, some numerical experiment results are provided to assess the performance of the proposed secrecy beamforming design.

Joint Beamforming and Power Allocation for Secrecy in Peer-to-Peer Relay Networks

This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.