Robust Beamforming for Wireless Information and Power Transmission

In this letter, we study the robust beamforming problem for the multi-antenna wireless broadcasting system with simultaneous information and power transmission, under the assumption of imperfect channel state information (CSI) at the transmitter. Following the worst-case deterministic model, our objective is to maximize the worst-case harvested energy for the energy receiver while guaranteeing that the rate for the information receiver is above a threshold for all possible channel realizations. Such problem is nonconvex with infinite number of constraints. Using certain transformation techniques, we convert this problem into a relaxed semidefinite programming problem (SDP) which can be solved efficiently. We further show that the solution of the relaxed SDP problem is always rank-one. This indicates that the relaxation is tight and we can get the optimal solution for the original problem. Simulation results are presented to validate the effectiveness of the proposed algorithm.Comment: 4 pages, 3 figures; IEEE Wireless Communications Letters 201

How to Understand LMMSE Transceiver Design for MIMO Systems From Quadratic Matrix Programming

In this paper, a unified linear minimum mean-square-error (LMMSE) transceiver design framework is investigated, which is suitable for a wide range of wireless systems. The unified design is based on an elegant and powerful mathematical programming technology termed as quadratic matrix programming (QMP). Based on QMP it can be observed that for different wireless systems, there are certain common characteristics which can be exploited to design LMMSE transceivers e.g., the quadratic forms. It is also discovered that evolving from a point-to-point MIMO system to various advanced wireless systems such as multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems and so on, the quadratic nature is always kept and the LMMSE transceiver designs can always be carried out via iteratively solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given. The work presented in this paper is likely to be the first shoot for the transceiver design for the future ever-changing wireless systems.Comment: 31 pages, 4 figures, Accepted by IET Communication

Robust Designs of Beamforming and Power Splitting for Distributed Antenna Systems with Wireless Energy Harvesting

In this paper, we investigate a multiuser distributed antenna system with simultaneous wireless information and power transmission under the assumption of imperfect channel state information (CSI). In this system, a distributed antenna port with multiple antennas supports a set of mobile stations who can decode information and harvest energy simultaneously via a power splitter. To design robust transmit beamforming vectors and the power splitting (PS) factors in the presence of CSI errors, we maximize the average worst-case signal-to-interference-plus- noise ratio (SINR) while achieving individual energy harvesting constraint for each mobile station. First, we develop an efficient algorithm to convert the max-min SINR problem to a set of "dual" min-max power balancing problems. Then, motivated by the penalty function method, an iterative algorithm based on semi-definite programming (SDP) is proposed to achieve a local optimal rank-one solution. Also, to reduce the computational complexity, we present another iterative scheme based on the Lagrangian method and the successive convex approximation (SCA) technique to yield a suboptimal solution. Simulation results are shown to validate the robustness and effectiveness of the proposed algorithms.Comment: To appear in IEEE Systems Journal. (10 pages, 6 figures

Secure MIMO Relaying Network: An Artificial Noise Aided Robust Design Approach

Owing to the vulnerability of relay-assisted and device-to-device (D2D) communications, improving wireless security from a physical layer signal processing perspective is attracting increasing interest. Hence we address the problem of secure transmission in a relay-assisted network, where a pair of legitimate user equipments (UEs) communicate with the aid of a multiple-input multiple output (MIMO) relay in the presence of multiple eavesdroppers (eves). Assuming imperfect knowledge of the eves' channels, we jointly optimize the power of the source UE, the amplify-and-forward (AF) relaying matrix and the covariance of the artificial noise (AN) transmitted by the relay, in order to maximize the received signal-to-interference-plus-noise ratio (SINR) at the destination, while imposing a set of robust secrecy constraints. To tackle the resultant nonconvex optimization problem, a globally optimal solution based on a bi-level optimization framework is proposed, but with high complexity. Then a low-complexity sub-optimal method relying on a new penalized difference-of-convex (DC) algorithmic framework is proposed, which is specifically designed for non-convex semidefinite programs (SDPs). We show how this penalized DC framework can be invoked for solving our robust secure relaying problem with proven convergence. Our extensive simulation results show that both proposed solutions are capable of ensuring the secrecy of the relay-aided transmission and significantly improve the robustness towards the eves' channel uncertainties as compared to the non-robust counterparts. It is also demonstrated the penalized DC-based method advocated yields a performance close to the globally optimal solution.Comment: 13 pages, 6 figures, one table and one supplementary documen

Algebraic Solution for Beamforming in Two-Way Relay Systems with Analog Network Coding

We reduce the problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state infomation (CSI) that use analog network coding (ANC) to a pair of algebraic equations in two variables that can be solved inexpensively using numerical methods. The solution has greatly reduced complexity compared to previous exact solutions via semidefinite programming (SDP). Together with the linearized robust solution described in (Aziz and Thron, 2014), it provides a high-performance, low-complexity robust beamforming solution for 2-way relays.Comment: 5 pages, 5 figure

Robust Downlink Beamforming in Multiuser MISO Cognitive Radio Networks

This paper studies the problem of robust downlink beamforming design in a multiuser Multi-Input Single-Output (MISO) Cognitive Radio Network (CR-Net) in which multiple Primary Users (PUs) coexist with multiple Secondary Users (SUs). Unlike conventional designs in CR-Nets, in this paper it is assumed that the Channel State Information (CSI) for all relevant channels is imperfectly known, and the imperfectness of the CSI is modeled using an Euclidean ball-shaped uncertainty set. Our design objective is to minimize the transmit power of the SU-Transmitter (SU-Tx) while simultaneously targeting a lower bound on the received Signal-to-Interference-plus-Noise-Ratio (SINR) for the SU's, and imposing an upper limit on the Interference-Power (IP) at the PUs. The design parameters at the SU-Tx are the beamforming weights, i.e. the precoder matrix. The proposed methodology is based on a worst case design scenario through which the performance metrics of the design are immune to variations in the channels. We propose three approaches based on convex programming for which efficient numerical solutions exist. Finally, simulation results are provided to validate the robustness of the proposed methods.Comment: 23 pages, 4 figures, submitted to IEEE Trans. Wireless Comms., accepted conference version to PIMRC'0

Low-Complexity Robust Adaptive Beamforming Algorithms Based on Shrinkage for Mismatch Estimation

In this paper, we propose low-complexity robust adaptive beamforming (RAB) techniques that based on shrinkage methods. The only prior knowledge required by the proposed algorithms are the angular sector in which the actual steering vector is located and the antenna array geometry. We firstly present a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) algorithm to estimate the desired signal steering vector mismatch, in which the interference-plus-noise covariance (INC) matrix is estimated with Oracle Approximating Shrinkage (OAS) method and the weights are computed with matrix inversions. We then develop low-cost stochastic gradient (SG) recursions to estimate the INC matrix and update the beamforming weights, resulting in the proposed LOCSME-SG algorithm. Simulation results show that both LOCSME and LOCSME-SG achieve very good output signal-to-interference-plus-noise ratio (SINR) compared to previously reported adaptive RAB algorithms.Comment: 8 pages, 2 figures, WSA. arXiv admin note: text overlap with arXiv:1311.233

Simultaneous Wireless Information Power Transfer for MISO Secrecy Channel

This paper investigates simultaneous wireless information and power transfer (SWIPT) for multiuser multiple-input-single-output (MISO) secrecy channel. First, transmit beamfoming without artificial noise (AN) design is considered, where two secrecy rate optimization frameworks (i.e., secrecy rate maximization and harvested energy maximization) are investigated. These two optimization problems are not convex, and cannot be solved directly. For secrecy rate maximization problem, we employ bisection method to optimize the associated power minimization problem, and first-order Taylor series expansion is consider to approximate the energy harvesting (EH) constraint and the harvested energy maximization problem. Moreover, we extend our proposed algorithm to the associated robust schemes by incorporating with channel uncertainties, where two-level method is proposed for the harvested energy maximization problem. Then, transmit beamforming with AN design is studied for the same secrecy rate maximization problem, which are reformulated into semidefinite programming (SDP) based on one-dimensional search and successive convex approximation (SCA), respectively. Moreover, tightness analysis of rank relaxation is provided to show the optimal transmit covariance matrix exactly returns rank-one. Simulation results is provided to validate the performance of the proposed algorithm.Comment: 14 pages, 7 figure

A Robust Design for MISO Physical-Layer Multicasting over Line-of-Sight Channels

This paper studies a robust design problem for far-field line-of-sight (LOS) channels where phase errors are present. Compared with the commonly used additive error model, the phase error model is more suitable for capturing the uncertainty in an LOS channel, as the dominant source of uncertainty lies in the phase. We consider a multiple-input single-output (MISO) multicast scenario, in which our goal is to design a beamformer that minimizes the transmit power while satisfying probabilistic signal-to-noise ratio (SNR) constraints. The probabilistic constraints give rise to a new computational challenge, as they involve random trigonometric forms. In this work, we propose to first approximate the random trigonometric form by its second-order Taylor expansion and then tackle the resulting random quadratic form using a Bernstein-type inequality. The advantage of such an approach is that an approximately optimal beamformer can be obtained using the standard semidefinite relaxation technique. In the simulations, we first show that if a non-robust design (i.e., one that does not take phase errors into account) is used, then the whole system may collapse. We then show that our proposed method is less conservative than the existing robust design based on Gaussian approximation and thus requires a lower power budget.Comment: This manuscript is submitted for possible journal publication on 13-Nov-201

Secure SWIPT for Directional Modulation Aided AF Relaying Networks

Secure wireless information and power transfer based on directional modulation is conceived for amplify-and-forward (AF) relaying networks. Explicitly, we first formulate a secrecy rate maximization (SRM) problem, which can be decomposed into a twin-level optimization problem and solved by a one-dimensional (1D) search and semidefinite relaxation (SDR) technique. Then in order to reduce the search complexity, we formulate an optimization problem based on maximizing the signal-to-leakage-AN-noise-ratio (Max-SLANR) criterion, and transform it into a SDR problem. Additionally, the relaxation is proved to be tight according to the classic Karush-Kuhn-Tucker (KKT) conditions. Finally, to reduce the computational complexity, a successive convex approximation (SCA) scheme is proposed to find a near-optimal solution. The complexity of the SCA scheme is much lower than that of the SRM and the Max-SLANR schemes. Simulation results demonstrate that the performance of the SCA scheme is very close to that of the SRM scheme in terms of its secrecy rate and bit error rate (BER), but much better than that of the zero forcing (ZF) scheme