Robust Beamforming Research Articles

Robust Transmit Beamforming for SWIPT-Enabled Cooperative NOMA With Channel Uncertainties

In this paper, we study the robust beamforming design for a simultaneous wireless information and power transfer (SWIPT) enabled system, with cooperative non-orthogonal multiple access (NOMA) protocol applied. A novel cooperative NOMA scheme is proposed, where the strong user with better channel conditions adopts power splitting (PS) scheme and acts as an energy-harvesting relay to transmit information to the weak user. The presence of channel uncertainties is considered and incorporated in our formulations to improve the design robustness and communication reliability. Specifically, only imperfect channel state information is assumed to be available at the base station (BS), due to the reason that the BS is far away from both users and suffers serious feedback delay. To comprehensively address the channel uncertainties, two major design criteria are adopted, which are the outage-based constraint design and the worst-case-based optimization. Then, our aim is to maximize the strong user’s data rate, by optimally designing the robust transmit beamforming and PS ratio, while guaranteeing the correct decoding of the weak user. With two different channel uncertainty models respectively incorporated, the proposed formulations yield to challenging nonconvex optimization problems. For the outage-based constrained optimization, we first conservatively approximate the probabilistic constraints with the Bernstein-type inequalities, which are then globally solved by 2-D exhaustive search. To further reduce the complexity, an efficient low-complexity algorithm is then proposed with the aid of successive convex approximation (SCA). For the worst-case-based scenario, we first apply the semidefinite relaxation method to relax the quadratic terms and prove the rank-one optimality. Then the nonconvex max-min optimization problem is readily transformed into convex approximations based on ${S}$ -procedure and SCA. Simulation results show that for both channel uncertainty models, the proposed algorithms can converge within a few iterations, and the proposed SWIPT-enabled robust cooperative NOMA system achieves better system performance than the existing protocols.

Full-Duplex Secure Relay Beamforming Design for Systems With Perfect and Partial CSI

Considering that wireless unidirectional full-duplex (FD) transmission is one of the FD transmissions over 5G mobile wireless networks, this paper proposes a joint receive and transmit relay beamformer design for systems consisting of a source, a FD relay, an intended destination, and an eavesdropper. The source and destination are single-antenna nodes, whereas the FD relay is a multi-antenna node. Assuming that full channel state information (CSI) is available and the eavesdropper processes two blocks of received data at a time, the joint optimization problem is reformulated as a semidefinite relaxation (SDR) problem (in terms of relay transmit beamformer), which is tight in the sense that the rank-one beamformer can always be recovered from the SDR solution. In order to significantly minimize the computational cost of the SDR implementation, a novel semi-analytical approach based on dual optimization is proposed to obtain the optimum transmit beamformer. When the number of data blocks is arbitrary, we propose a successive convex approximation approach for solving the original non-convex optimization problem and show that a stationary solution can be efficiently obtained. We then propose a distributionally robust beamformer design for the case of an arbitrary number of blocks, assuming that the means and covariance matrices of the eavesdropper's channels are known. Computer simulations show that the proposed semi-analytical solution matches with that obtained from numerical optimization of the SDR problem, the FD scheme significantly outperforms its half-duplex counterpart, and the proposed robust design provides robustness against CSI uncertainty.

Quadratic Matrix Inequality Approach to Robust Adaptive Beamforming for General-Rank Signal Model

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been well studied in the literature. Different from the existing literature, herein however the original beamforming problem is tackled. Resorting to the strong duality of linear conic programming, the robust adaptive beamforming problem for general-rank signal model is reformulated into an equivalent quadratic matrix inequality (QMI) problem. By employing a linear matrix inequality (LMI) relaxation technique, the QMI problem is turned into a convex semidefinite programming problem. Using the fact that there is often a positive gap between the QMI problem and its LMI relaxation, an approximate algorithm is proposed to solve the robust adaptive beamforming in the QMI form. Besides, several sufficient optimality conditions for the nonconvex QMI problem are built. To validate our results, simulation examples are presented, which also demonstrate the improved performance of the new robust beamformer in terms of the output signal-to-interference-plus-noise ratio.

Worst case fair beamforming for multiple multicast groups in multicell networks

The design problem associated with robust downlink beamforming in multicast, multigroup, multicell wireless systems is addressed. The channel state information (CSI) of users is assumed to be imperfect and the uncertainty of CSI is modelled using the Frobenius norm. The objective is to optimise the signal-to-interference-plus-noise ratio over all users with a constraint on the maximum total transmitted power. This was achieved through a robust solution using the successive convex approximation (SCA) method. The beamforming problem is treated as a bi-convex problem, which is solved using the iterate-alternative convex technique. Here, the CSI uncertainty is addressed using a convex package through the non-monotone spectral projected gradient method and the beamforming vector is extracted using the SCA method. Also, the authors offer the required condition to extract the beamform vector using the SCA method through a suboptimal solution that always addressed before using different beamforming methods. Their simulation results examine all proposed system parameters in order to show convergence and feasibility of the solution. They also compare the solution with a suboptimal solution and the quality of service method for imperfect CSI in downlink beamforming. Numerical results show that the robust solution achieves the best power efficiency for practical solutions.

Corrigendum: Iterative adaptive approach to interference covariance matrix reconstruction for robust adaptive beamforming

Corrigendum: Iterative adaptive approach to interference covariance matrix reconstruction for robust adaptive beamforming

Outage Constrained Robust Multigroup Multicast Beamforming for Multi-Beam Satellite Communication Systems

We investigate outage constrained robust multigroup multicast beamforming for multi-beam satellite communication systems with full frequency reuse. Based on a satellite downlink beam domain channel model with channel phase uncertainty taken into account, we first investigate robust multigroup multicast beamforming with the aim to maximize the worst-case outage signal-to-interference-plus-noise ratio under the outage and the per-beam power constraints. We then cast the outage constrained robust beamforming design into the convex optimization framework with some approximation techniques. Simulation results show that the proposed robust multigroup multicast beamformer can provide significant performance gains in terms of multicast rate and outage probability over the conventional approach.

Joint Base Station Activation and Coordinated Downlink Beamforming for HetNets: Efficient Optimal and Suboptimal Algorithms

In cellular heterogeneous networks (HetNets), a number of distributed base stations cooperatively provide services to multiple mobile users. This paper addresses joint base-station activation and coordinated beamforming design for downlink transmission in HetNets. To this end, a mixed integer program is formulated to optimize the total power consumption of a HetNet. A novel approach based on Benders' decomposition is then put forth to obtain the optimal solution for the problem of interest with guaranteed convergence. Building on our new formulation, a dual-subgradient algorithm is also proposed to find an approximate solution in polynomial time. The proposed approaches can be generalized to more general setups, including robust beamforming designs under channel uncertainty, and coordinated beamforming for multi-cell scenarios.

Robust beamforming and spatial precoding for quasi-OSTBC massive MIMO communications

This paper considers the problem of massive multiple-input-multiple-output (MIMO) wireless communication systems with quasi-orthogonal space-time block code (QOSTBC) transmission in the presence of spatial correlation effect (SCE) and mutual coupling effect (MCE). Conventional MIMO channels with QOSTBC transmission suffer from several drawbacks. The number of transmit antennas is restricted to a few in order to achieve full transmission rate. Therefore, it is difficult to make a quasi-orthogonal space time block coded massive MIMO system to achieve full transmission rate. Moreover, MIMO channel with QOSTBC transmission is usually considered for the case where the number of user equipments (UEs) is one. We present a joint beamforming and spatial precoding method to deal with the above drawbacks. The proposed method incorporates a beamforming scheme and spatial precoding to formulate an appropriate optimization process to effectively alleviate the considered problems. The resulting optimization problem will be solved by using a cooperative coevolutionary particle swarm optimization algorithm under two proposed fitness functions. During the optimization process, the proposed method finds the optimal beamforming coefficients of the precoding matrix, the optimal normalized positions of transmit and receive antenna elements for the case of using linear antenna arrays, and the optimal angle differences of transmit and receive antenna elements for the case of using circular arrays. Based on the proposed method, we are able to cure the performance degradation of a quasi-orthogonal space time block coded massive MIMO system due to the SCE and MCE. Moreover, the proposed method makes QOSTBC MIMO communications with full transmission rate for any number of transmit antennas achievable. Several simulation examples are presented to show the superior bit error rate (BER) performances of QOSTBC wireless MIMO scenarios with linear as well as circular antenna arrays by using the proposed method as compared to the existing methods.

Joint Robust Beamforming and Power-Splitting Ratio Design in SWIPT-Based Cooperative NOMA Systems With CSI Uncertainty

This paper investigates the effect of imperfect channel state information on the performance of the cooperative non-orthogonal multiple access (NOMA) transmission scheme, in which the cell-center user acts as a decode-and-forward relay to assist the information transmission. The cell-center user adopts a simultaneous wireless information and power transfer (SWIPT) technique to harvest energy for information forwarding. Based on two channel error models, a maximization problem is formulated to jointly design the robust beamforming and the power splitting ratio while satisfying the minimum data rate for the far user and the successfully decoding requirement for the information of the far user at the near user. For the worst case design under the deterministic error model, the successive convex approximation and the semidefinite relaxation technique are utilized to approximate the non-convex problem to an iterative convex problem. For the outage-constrained design under the stochastic error model, Bernstein-type inequality-based and large deviation inequality-based approaches are used to safely approximate the probabilistic constraints of the inner-level problem to the deterministic constraints, and a golden section search algorithm is employed to find out the optimal single variable of the outer-level problem. Furthermore, the rank proof is provided to prove that the relaxation is tight.

Worst-Case Robust Beamforming Design for Wireless Powered Multirelay Multiuser Network With a Nonlinear EH Model

This paper studies joint source and relay beamforming for a wireless powered downlink multirelay multiuser network. Considering nonlinear energy harvesting and imperfect channel state information, we aim to minimize the total transmit power at the base station by jointly optimizing the source beamforming and the relay beamforming weights under the energy causality constraints at the relays and the signal-to-noise ratio constraints at the users. The formulated problem is highly nonconvex, and thus, it is difficult to solve. To solve the problem, we first transform it into a worst-case optimization, and then, an iterative algorithm is developed to solve this worst-case optimization. Numerical results show the advantage of the proposed robust scheme.

Robust Beamforming and Power Allocation in CR MISO Networks with SWIPT to Maximize the Minimum Achievable Rate

In this paper, a new method is presented to maximize the minimum achievable rate of the users in a cognitive radio multiple input single output network. The secondary system provides simultaneous wireless information and power transfer (SWIPT) for energy harvesting receivers. Considering random Gaussian vector for the estimation error of the channel state information (CSI), we impose some outage constraints to guarantee the quality of service of the network. Outage constraints on the received power and the information leakage at the energy harvesting users are imposed to assure SWIPT. We introduce new convex inequalities to replace the original non-convex constraints and write the objective function as the minimization of the maximum of some fractional functions. This new objective function and convex inequalities result in a new quasi-convex general fractional programming problem. The new quasi-convex optimization problem is written in such a way that the computational costs to solve this problem are as low as possible. We develop an algorithm to obtain the optimal beamforming weights and artificial noise covariance matrix. All stochastic constraints are rewritten for the special case that the covariance matrices of error in the estimation of CSI are a factor of identity matrix. This reformulation results in less computation costs to obtain optimal beamforming weights and AN covariance matrix. Simulation results confirm that, all stochastic constraints are satisfied with certain probability. In comparison with the previous robust related work, the proposed method achieves higher rates which confirms superiority of our method.

Robust Beamforming Design for Ultra-Dense User-Centric C-RAN in the Face of Realistic Pilot Contamination and Limited Feedback

The ultra-dense cloud radio access network (UD-CRAN), in which remote radio heads are densely deployed in the network, is considered. To reduce the channel estimation overhead, we focus on the design of robust transmit beamforming for user-centric frequency division duplex UD-CRANs, where only limited channel state information (CSI) is available. Specifically, we conceive a complete procedure for acquiring the CSI that includes two key steps: channel estimation and channel quantization. The phase ambiguity (PA) is also quantized for coherent cooperative transmission. Based on the imperfect CSI, we aim to optimize the beamforming vectors in order to minimize the total transmit power subject to the users' rate requirements and fronthaul capacity constraints. We derive the closed-form expression of the achievable data rate by exploiting the statistical properties of multiple uncertain terms. Then, we propose a low-complexity iterative algorithm for solving this problem based on the successive convex approximation technique. In each iteration, the Lagrange dual-decomposition method is employed for obtaining the optimal beamforming vector. Furthermore, a pair of low-complexity user selection algorithms is provided to guarantee the feasibility of the problem. The simulation results confirm the accuracy of our robust algorithm in terms of meeting the rate requirements. Finally, our simulation results verify that using a single bit for quantizing the PA achieves good performance.

Real-valued robust DOA estimation method for uniform circular acoustic vector sensor arrays based on worst-case performance optimization

The minimum variance distortionless response (MVDR) method suffers performance degradation when the considerable ambient noise and the steering vector mismatch exist. Therefore, this paper proposes a real-valued robust beamforming for the uniform circular acoustic vector sensor array (UCAVSA) based on worst-case performance optimization. The paper first extends the phase-mode transformation into the UCAVSA, and the relationship between the transformation matrices of the UCAVSA and the circular pressure sensor array is derived. The paper then utilizes the spatial correlation characteristic between the acoustic pressure and particle velocity to construct a cross-covariance matrix to eliminate the isotropic noise, and then transforms the cross-covariance matrix into a real-valued one by the unitary transformation. Finally, the paper derives the real-valued robust beamforming algorithm via optimizing the worst-case performance. Theoretical analyses and simulation results indicate that the proposed method is superior over previous methods under scenarios such as low signal-to-noise (SNR), steering vector mismatch and coherent sources. Moreover, the proposed method has a lower computational cost than the complex-valued operation in calculating the weight vector. The experiment results verify the effectiveness of the proposed method.

Robust Beamforming Design in a NOMA Cognitive Radio Network Relying on SWIPT

This paper studies a multiple-input single-output non-orthogonal multiple access cognitive radio network relying on simultaneous wireless information and power transfer. A realistic non-linear energy harvesting model is applied and a power splitting architecture is adopted at each secondary user (SU). Since it is difficult to obtain perfect channel state information (CSI) in practice, instead either a bounded or Gaussian CSI error model is considered. Our robust beamforming and power splitting ratio are jointly designed for two problems with different objectives, namely, that of minimizing the transmission power of the cognitive base station and that of maximizing the total harvested energy of the SUs, respectively. The optimization problems are challenging to solve, mainly because of the non-linear structure of the energy harvesting and CSI errors models. We converted them into convex forms by using semi-definite relaxation. For the minimum transmission power problem, we obtain the rank-2 solution under the bounded CSI error model, while for the maximum energy harvesting problem, a two-loop procedure using a 1-D search is proposed. Our simulation results show that the proposed scheme significantly outperforms its traditional orthogonal multiple access counterpart. Furthermore, the performance using the Gaussian CSI error model is generally better than that using the bounded CSI error model.

Multi-User Analog Beamforming in Millimeter Wave MIMO Systems Based on Path Angle Information

We aim to design an analog-only beamforming scheme for downlink multi-user mm-wave systems to optimize the beamforming gain and the inter-user interference at the same time. Traditional analog beamforming schemes, such as the beam selection method, use the array response vector corresponding to the strongest path of the channel to generate a beam pointing to the user. In multi-user systems, such schemes will lead to large inter-user interference, especially when the users are closely located. In this paper, we formulate a multi-objective problem to strike a balance between the beamforming gain and the inter-user interference. To solve the problem, we first use the weighted-sum method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the analog beamforming with constant-magnitude constraints tractable. Furthermore, to alleviate the effects of the channel estimation and feedback quantization errors, we design a robust beamforming scheme to provide robustness against imperfect channel information. We first develop a channel error model for the scattering clustered channel model, which can serve as a general channel error model for the mm-wave channels. Then, we formulate a multi-objective problem using the stochastic approach to suppress the interference and enhance the beamforming gain at the same time. The simulation results show that our proposed non-robust multi-user analog beamformer outperforms the traditional analog beamforming method when the SNR is high and our proposed robust beamformer can provide up to 109% improvement in the sum-rate compared with the beam selection method.

Robust Beamforming and User Clustering for Guaranteed Fairness in Downlink NOMA With Partial Feedback

In this paper, a downlink multiuser non-orthogonal multiple access (NOMA) with full and partial channel state information (CSI) feedback is considered. We investigate beam design and user clustering from the throughput-fairness trade-off perspective. To enhance this trade-off, two proportional fairness (PF) based scheduling algorithms are proposed, each has two stages. The first algorithm is based on integrating the maximum product of effective channel gains and the maximum signal to interference ratio with the PF principle (PF-MPECG-SIR), to select the strong users in the first stage and the weak users in the second stage. This algorithm is designed to maximize the throughput with moderate fairness enhancement. Whereas, in the second algorithm, the MPECG and the maximum correlation are combined within the PF selection criterion (PF-MPECG-CORR) in order to maximize the fairness with a slight degradation in the total throughput. In addition, we present an optimal power allocation that can achieve a high data rate for the overall system without sacrificing the sum-rate of weak users under full and partial CSI. Simulation results show that the proposed PF-MPECG-CORR can significantly improve the fairness up to 50.82% and 44.90% with only 0.42% and 1.13% degradation in the total throughput, for full and partial CSI, respectively. All these performance gains are achieved without increasing the computational complexity.

A Robust Capon Beamforming Approach for Sparse Array Based on Importance Resampling Compressive Covariance Sensing

Reconstructing the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix is a good method for calculating the adaptive beamforming coefficients. However, when the directions-of-arrival (DOAs) and the number of the interferences are unknown and the steering vector has an error, the reconstructed interference-plus-noise covariance matrix might not be accurate, which degrades the performance of adaptive beamforming. Here, we propose a robust Capon beamforming approach, which is suited to the sparse array with the array steering error and the unknown interference DOAs. In particular, by drawing a modified optimization problem and the mean shift model of the interference covariance matrix, we propose the robust beamforming with the importance resampling based compressive covariance sensing, which is shown to outperform the classical beamforming method based on reconstructing the interference-plus-noise covariance matrix. The key to our approach is the new solution of the reconstructing method and the important functions. The excellent performance of the proposed approach for interference suppression is demonstrated via a number of numerical examples.

Legitimate Monitoring via Cooperative Relay and Proactive Jamming

With the development of communication technologies, many suspicious communication technologies have also been greatly improved. Therefore, one single monitor may not be able to afford in a monitoring process. In this paper, we propose a wireless communication system using two legitimate monitors for cooperative monitoring program, in which the signals sent by two monitors are respectively designed. One monitor is used as the cooperative relay, which is mainly used to improve the overall information transmission rate. The other monitor, which simultaneously receiving suspicious information and sending jamming signals, is used to ensure the successful eavesdropping process. Our purpose is to obtain the maximum eavesdropping rate by jointly design the transmit beamforming of two monitors. Two cases that the channel state information (CSI) is perfectly and imperfectly known by the monitors are considered. For the perfect CSI, several cases corresponding to the different conditions about the CSI from the suspicious transmitter to two monitors are discussed. In each case, a closed-form solution of the appropriate sending strategy is obtained, in which the physical meaning is also proposed. Then, for the imperfect CSI case, by employing the S-procedure method, we reformulate the robust beamforming design problem and solve it optimally. Finally, in the simulation results, the comparison between the cooperative monitoring scheme and the single monitoring scheme demonstrates that the proposed scheme is better in terms of eavesdropping rate.

Robust Beamforming Design for Secure DM-Based Relay Networks With Self-Sustained Jammers

In this paper, we propose to use self-sustained jammers to generate artificial noise with the aim of enhancing the physical layer security of a directional modulation (DM) relay system. To this end, we specifically tackle an optimization problem of designing beamforming vectors at the source, relay, and jammers to maximize a lower bound on the average secrecy rate of the considered system. Due to that the optimization problem is non-convex and the optimization variables are coupled, and so we cannot directly solve this problem. As such, we first develop a centralized scheme to achieve the near-optimal beamforming vectors with the aid of semidefinite relaxation, successive convex approximation, and an alternating iterative algorithm. The tightness of the incurred relaxation and the convergence of the involved algorithm are proved. To reduce the overhead and complexity of the centralized scheme, we also develop two decentralized schemes with partial cooperation and without cooperation among devices to obtain suboptimal beamforming vectors. Our examination shows that the developed centralized scheme can achieve similar performance as the optimal beamforming vectors, which can only be obtained through exhaustive numerical search. Our examination also specifies the conditions under which the decentralized schemes can achieve similar or significantly worse performance relative to the centralized scheme. Furthermore, our examination demonstrates that the developed three schemes are robust to the angle estimation errors in practical DM systems.

Robust Multigroup Multicast Beamforming Design for Backhaul-Limited Cloud Radio Access Network

This letter investigates the robust beamforming design for multigroup multicast in a backhaul-limited cloud radio access network. Users requesting the same content form a multicast group, served by remote radio heads (RRHs) cooperatively. Each RRH acquires the requested contents from baseband unit via backhaul links. We first formulate the robust beamforming design as maximizing the sum of the minimum rate of users in each multicast group under the transmission power and backhaul constraints. Due to the introduction of the channel estimation error and inter-user interference, the considered problem becomes more complex and difficult to address directly. To overcome these difficulties, convex approximation methods are adopted to transform the original problem into convex one. Then, an effective optimization algorithm is developed to address the resulting problem. Numerical results demonstrate the effectiveness of the proposed robust beamforming design of multigroup multicast transmission.