Individual Relay Power Constraints Research Articles

DC programming and DCA for enhancing physical layer security via relay beamforming strategies

Beside of cryptography-the primary traditional methods for ensuring information security and confidentiality, the appearance of the physical layer security approach plays an important role for not only enabling the data transmission confidentially without relying on higher-layer encryption, but also enhancing confidentiality of the secret key distribution in cryptography. Many techniques are employed in physical layers to improve secure transmission including cooperative relaying and beamforming technique. In this paper, we consider the secrecy rate maximization problems using two techniques mentioned above with two different relaying protocols: Amplify-and-Forward and Decode-and-Forward. The optimization problems with the aim of maximizing secrecy rate subject to total and individual relay power constraints are formulated as nonconvex problems, which can be reformulated as DC (difference of two convex functions) programs and thus can be solved by DC Algorithms (DCA). The special structure of feasible set is exploited which results to an efficient DC decomposition in the sense that it leads to convex subproblems that can be explicitly solved. The numerical results show that the proposed DCA schemes are better than the existing methods in terms of both runtime and secrecy rate.

Secure transmission for wireless collaborative systems based on second‐order channel statistics

AbstractIn this article, we investigate the maximum secrecy rates (SRs) and the optimal beamforming schemes for a collaborative wireless network under uncertain channel levels of available second‐order statistics. Both decode‐and‐forward (DF) and amplify‐and‐forward (AF) strategies under the aggregate and individual power constraints are considered. We have derived the maximum SRs and the optimal beamforming vectors under aforementioned conditions and an efficient cooperation paradigm to provide secrecy in a multirelay environment. A closed‐form maximum SR in the DF scheme under aggregate power constraint is presented. Next, the upper and lower bounds for the maximum SR under aggregate power constraint in the AF scheme is derived. The optimization problem in the AF scheme can be converted into a convex semidefinite programming problem, which is efficiently solved by the bisection method. Moreover, the optimal beamforming weights are also obtained to maximize the SRs under both aggregate and individual relay power constraints. Numerical results are provided to demonstrate the effectiveness of proposed algorithms.

Robust transmit design for secure AF relay networks with imperfect CSI

This paper studies robust transmit design for secure AF relay networks with imperfect channel state information (CSI). Two CSI error models, deterministically bounded error model and stochastic error model, are considered. In order to use the power at relays more efficiently, a joint cooperative relaying and jamming scheme is considered, where relays cooperate to forward the source signal and simultaneously they cooperate to send jamming signals to confuse the eavesdroppers. In this joint cooperative relaying and jamming framework, we address the robust joint optimization of the relay weights and the input covariance matrix of jamming signals for secrecy rate maximization (SRM), under both total and individual relay power constraints. Specifically, for the case of deterministically bounded error model, where the CSI error can be specified by an uncertainty set, we maximize the worst-case secrecy rate. While for the case of stochastic error model, where the probability distribution of the CSI error is Gaussian, we maximize the outage constrained secrecy rate. The challenge of these considered SRM-based optimizations lies in their non-convexity. This paper shows that such SRM-based optimization can be solved in a convex fashion and via solving a sequence of semidefinite programs (SDPs). Numerical results are presented to show the efficacy of the proposed scheme.

Low-complexity QL-QR decomposition- based beamforming design for two-way MIMO relay networks

In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a two-way amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system, consisting of two source nodes and two relay nodes, is considered, and the linear minimum mean-square-error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain at least a locally optimal solution. The proposed algorithm is developed based on QL, QR, and Choleskey decompositions which differ in complexity and performance. Analytical and simulation results show that the proposed algorithm can significantly reduce computational complexity compared with their existing two-way relay systems and have equivalent bit-error-rate (BER) performance to the singular value decomposition (SVD) based on a regular block diagonal (RBD) scheme.

Robust Transceiver Design for Broadband Multiuser Multi-Relay Networks

In this paper, we study the robust design of the relay beamforming (rBF) and destination equalization (dEQ) filters for broadband multiuser multi-relay networks employing single-carrier frequency-division multiple access (SC-FDMA) and orthogonal frequency-division multiple access (OFDMA). Thereby, we consider the realistic case where only imperfect channel state information is available for rBF and dEQ filter optimization. Our goal is to maximize a lower bound for the weighted achievable bit rate (ABR) of the network, subject to either individual relay power constraints (Ind-PCs) or an aggregate relay power constraint (Agg-PC). We first derive the optimal dEQ filters and the phases of the optimal rBF filter coefficients, which are independent of the power constraints. For the Agg-PC, the amplitude optimization of the rBF filter coefficients is decomposed into two subproblems, which correspond to the optimization of the power allocation across the relays and the power allocation across the users and subcarriers, respectively. We obtain a closed-form structural solution for the first subproblem by fixing the powers across users and subcarriers, and the global optimal solution for the second subproblem. For the Ind-PCs, the corresponding optimization problem is formulated as a reverse-convex problem with convex constraints. Subsequently, the constrained convex concave procedure is applied to approximate the original non-convex problem with a sequence of convex problems, which can be efficiently solved using convex optimization techniques. Simulation results validate the excellent performance of the proposed robust rBF and dEQ filter designs and show their superiority compared to conventional non-robust and naive relaying schemes.

Efficient Solutions to Distributed Beamforming for Two-Way Relay Networks Under Individual Relay Power Constraints

This paper investigates distributed beamforming (DBF) designs for two-way relay networks (TWRNs), where two terminal nodes exchange information through a set of amplify-and-forward (AF) relays. We assume individual relay power constraints and study two important design problems, namely, the max–min fairness (MMF) problem and the weighted sum-rate maximization (WSRM) problem. For the MMF problem, unlike the existing works that usually solve the problem by a bisection method, we propose an efficient optimal solution by solving one convex second-order cone program (SOCP) only. For the WSRM problem, we develop an efficient iterative algorithm based on SOCP reformulation and the successive convex approximation (SCA) technique. For both the MMF and WSRM designs, we further propose a distributed implementation framework where each of the relays can independently compute its beamforming weight using its local channel state information (CSI) and some common parameters broadcasted by a control center. Simulation results are presented to demonstrate the performance advantages of the proposed solutions.

Joint Cooperative Beamforming and Artificial Noise Design for Secrecy Sum Rate Maximization in Two-Way AF Relay Networks

In this letter, a joint design of cooperative beamforming (CB) and artificial noise (AN) is proposed for two-way amplify-and-forward (AF) relay networks to improve the security of the date exchange. Based on secrecy sum rate maximization (SSRM) criterion, such joint design problem under individual relay power constraints is mathematically hard due to the non-convex objective function. By utilizing the semidefinite relaxation (SDR) technique and successive convex approximation (SCA) algorithm, we efficiently develop a stationary point for the original SSRM design problem. Proof is also given to show that SDR is always tight and yields a rank-one solution. Simulations are presented to validate the efficiency and merits of our proposed joint CB and AN design in enhancing the secrecy sum rate.

Distributed relay beamforming based on worst signal‐to‐noise ratio constraints for multiple receivers

Recent studies suggest that relay communications can be a major application to extend the range of wireless communications by forwarding the signal from the sender to the receiver. Although fixed or robust distributed relay schemes for single receiver have been previously investigated, the distributed relay beamforming (DRBF) for multiple receivers is studied here. The authors propose an algorithm to design the DRBF weights for maximising the worst received signal-to-noise ratio subject to two different types of relay power constraints, which are the total relay power constraints and individual relay power constraints. The authors also prove that the proposed algorithm with relay power constraints results in a quadratic programming optimisation problem, which can be optimally solved by using semidefinite relaxation technology. The simulation results demonstrate an effective gain of the proposed optimal scheme over other intuition schemes.

Weighted Sum Rate Maximization for Downlink Multiuser Relay Network with Direct Link

This paper investigates the joint source, relay precoder and receive filters optimization, aiming to maximize the weighted sum rate (WSR) for non-regenerative downlink multiuser MIMO relay network with source-destination direct link. The joint transceiver is developed taking both the direct link and the relay link into consideration with individual source and relay power constraints. Since the WSR problem is generally non-convex and intractable, it's difficult to solve directly. Inspired by the recent results of relationship between the mutual information and the mean-square-error, we reformulate the WSR problem into a weighted sum mean square error minimization problem. An iterative algorithm is developed to solve the WSR problem. Simulation results demonstrate that the proposed algorithm offers significant performance gain over existing methods. In addition, we also propose a modified robust joint transceiver design against the imperfect channel state information.

Cooperative Secure Beamforming for AF Relay Networks With Multiple Eavesdroppers

This letter studies cooperative secure beamforming for amplify-and-forward (AF) relay networks in the presence of multiple eavesdroppers. Under both total and individual relay power constraints, we propose two schemes, namely secrecy rate maximization (SRM) beamforming and null-space beamforming. In the first scheme, our design problem is based on SRM. Using a suboptimal, but convex, technique-semidefinite relaxation (SDR), we show that this problem can be handled by performing a one-dimensional search which involves solving a sequence of semidefinite programs (SDPs). To reduce the complexity, in the second scheme, we instead maximize the information rate at the destination while completely eliminating the information leakage to all eavesdroppers. We prove that this problem can be exactly solved by SDR with one SDP only. Simulation results demonstrate the performance gains of the two proposed designs.

Collaborative Relay Beamforming Strategies for Multiple Destinations with Guaranteed QoS in Wireless Machine-to-Machine Networks

The Machine-to-Machine (M2M) communications allow information exchange between machine devices, which can be carried out without any human interaction. However, there are a large number of small and low-power machine devices in the wireless M2M networks. To guarantee the quality of service (QoS) requirements of the destination devices, we study the amplify-and-forward (AF) relay beamforming, where multiple relay M2M devices can transmit signals from the source M2M device to multiple destination M2M devices. In this paper, we propose two iterative strategies to jointly optimize the source antenna selection and the collaborative relay beamforming weights with the aid of perfect channel state information (CSI). The aim of the proposed strategies is to maximize the worst-case received signal-to-interference-and-noise ratio (SINR) under two different types of relay power constraints, which are the total relay power constraint and individual relay power constraints, respectively. Using the semidefinite relaxation (SDR) technique, the optimization problem of collaborative relay beamforming can be formulated as a semidefinite programming (SDP) problem, which can be optimally solved. Simulation results validate our theoretical analysis and demonstrate that after several iterations, the performance of the proposed iterative strategies can obtain near-optimal performance.

Robust Relaying Schemes for Multiple-Antenna Multi-Relay Networks

The optimal beamforming weight matrix for amplify and forward multiple-antenna multiple-relay network is investigated. It is assumed that the partial first and second hop channel state information (CSI) is available at relays. In order to minimize the mean square error (MSE) at destination, all relay weight matrices must be designed simultaneously under individual relay power constraints. Using the Lagrange dual variables, it is shown that this general vector optimization problem can be converted into a scalar optimization problem whose scalar Lagrange multipliers can be obtained numerically. This is the generalized version of the scheme suggested for complete CSI. The proposed scheme is evaluated through computer simulation with various numbers of relays and antennas to obtain MSE and bit error rate (BER) metrics. It is also shown that the resulting MSE and BER are less than those of the schemes available in the literature by a good margin depending upon the amount of the utilized relay and antennas as well as the estimation error.

Cooperative Amplify-and-Forward Beamforming with Multiple Multi-Antenna Relays

In this paper, we consider beamforming (BF) for cooperative networks with one multi-antenna source, multiple multi-antenna amplify-and-forward (AF) relays, and one single-antenna destination. The source BF vector and the AF-BF matrices at the relays are optimized for maximization of the signal-to-noise ratio (SNR) at the destination under three different power constraints. In particular, we consider individual relay power constraints, a joint relay power constraint, and a joint power constraint for the source and the relays. We solve the associated optimization problems in two stages. In the first stage, we find the optimal AF-BF matrices for a given BF vector at the source. For the cases of individual and joint relay power constraints, closed-form solutions for the AF-BF matrices are provided, respectively. Furthermore, for the case of a joint source-relay power constraint, the AF-BF matrices are obtained in closed form up to a scalar power allocation factor and an efficient numerical algorithm for the power allocation between the source and the relays is given. In the second stage, the optimal source BF vectors are computed. Thereby, we show that for the joint relay and the joint source-relay power constraints, the resulting problem can be transformed into a non-convex polynomial programming problem which allows for an exact solution for small-scale networks. For large-scale networks and networks with individual relay power constraints, we propose efficient suboptimal optimization methods for the source BF vector. Simulation results show the benefits of having multiple antennas at the source and/or multiple multi-antenna relays and illustrate the performance differences introduced by the three different power constraints.

Cooperative Transmission for Relay Networks Based on Second-Order Statistics of Channel State Information

Cooperative beamforming in relay networks is considered, in which a source transmits to its destination with the help of a set of cooperating nodes. The source first transmits locally. The cooperating nodes that receive the source signal retransmit a weighted version of it in an amplify-and-forward (AF) fashion. Assuming knowledge of the second-order statistics of the channel state information, beamforming weights are determined so that the signal-to-noise ratio (SNR) at the destination is maximized subject to two different power constraints, i.e., a total (source and relay) power constraint, and individual relay power constraints. For the former constraint, the original problem is transformed into a problem of one variable, which can be solved via Newton's method. For the latter constraint, the original problem is transformed into a homogeneous quadratically constrained quadratic programming (QCQP) problem. In this case, it is shown that when the number of relays does not exceed three the global solution can always be constructed via semidefinite programming (SDP) relaxation and the matrix rank-one decomposition technique. For the cases in which the SDP relaxation does not generate a rank one solution, two methods are proposed to solve the problem: the first one is based on the coordinate descent method, and the second one transforms the QCQP problem into an infinity norm maximization problem in which a smooth finite norm approximation can lead to the solution using the augmented Lagrangian method.

Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and relay nodes. For such a network, assuming that the second-order statistics of the channel coefficients are available, we study two different beamforming design approaches. As the first approach, we design the beamformer through minimization of the total transmit power subject to the receiver quality of service constraint. We show that this approach yields a closed-form solution. In the second approach, the beamforming weights are obtained through maximizing the receiver signal-to-noise ratio (SNR) subject to two different types of power constraints, namely the total transmit power constraint and individual relay power constraints. We show that the total power constraint leads to a closed-form solution while the individual relay power constraints result in a quadratic programming optimization problem. The later optimization problem does not have a closed-form solution. However, it is shown that using semidefinite relaxation, this problem can be turned into a convex feasibility semidefinite programming (SDP), and therefore, can be efficiently solved using interior point methods. Furthermore, we develop a simplified, thus suboptimal, technique which is computationally more efficient than the SDP approach. In fact, the simplified algorithm provides the beamforming weight vector in a closed form. Our numerical examples show that as the uncertainty in the channel state information is increased, satisfying the quality of service constraint becomes harder, i.e., it takes more power to satisfy these constraints. Also our simulation results show that when compared to the SDP-based method, our simplified technique suffers a 2-dB loss in SNR for low to moderate values of transmit power.

Robust Wireless Relay Networks: Slow Power Allocation With Guaranteed QoS

In wireless networks, power allocation is an effective technique for prolonging network lifetime, achieving better quality-of-service (QoS), and reducing network interference. However, these benefits depend on knowledge of the channel state information (CSI), which is hardly perfect. Therefore, robust algorithms that take into account such CSI uncertainties play an important role in the design of practical systems. In this paper, we develop relay power allocation algorithms for noncoherent and coherent amplify-and-forward (AF) relay networks. The goal is to minimize the total relay transmission power under individual relay power constraints, while satisfying a QoS requirement. To make our algorithms practical and attractive, our power update rate is designed to follow large-scale fading, i.e., in the order of seconds. We show that, in the presence of perfect global CSI, our power optimization problems for noncoherent and coherent AF relay networks can be formulated as a linear program and a second-order cone program (SOCP), respectively. We then introduce robust optimization methodology that accounts for uncertainties in the global CSI. In the presence of ellipsoidal uncertainty sets, the robust counterparts of our optimization problems for noncoherent and coherent AF relay networks are shown to be an SOCP and a semi-definite program, respectively. Our results reveal that ignoring uncertainties associated with global CSI often leads to poor performance. We verify that our proposed algorithms can provide significant power savings over a naive scheme that employs maximum transmission power at each relay node. This work highlights the importance of robust algorithms with practical power update rates in realistic wireless networks.