Robust Beamforming Research Articles

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System.

In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach’s algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.

Robust Beamforming Design in C-RAN With Sigmoidal Utility and Capacity-Limited Backhaul

In this paper, we study the robust beamforming design in cloud radio access networks, where remote radio heads (RRHs) are connected to a cloud server that performs signal processing and resource allocation in a centralized manner. Different from traditional approaches adopting a concave increasing function to model the utility of a user, we model the utility by a sigmoidal function of the signal-to-interference-plus-noise ratio (SINR) to capture the diminishing utility returns for very small and very large SINRs in real-time applications (e.g., video streaming). Our objective is to maximize the aggregate utility of the users while considering the imperfection of channel state information (CSI), limited backhaul capacity, and minimum quality of service requirements. Because of the sigmoidal utility function and some of the constraints, the formulated problem is non-convex. To efficiently solve the problem, we introduce a maximum interference constraint, transform the CSI uncertainty constraints into linear matrix inequalities, employ convex relaxation to handle the backhaul capacity constraints, and exploit the sum-of-ratios form of the objective function. This leads to an efficient resource allocation algorithm, which outperforms several baseline schemes, and closely approaches a performance upper bound for large CSI uncertainty or large number of RRHs.

Robust Beamforming Techniques for Non-Orthogonal Multiple Access Systems with Bounded Channel Uncertainties

In this letter, we propose a robust beamforming design for non-orthogonal multiple access (NOMA) based multiple-input single-output (MISO) downlink systems. In particular, the robust power minimization problem is studied with imperfect channel state information (CSI), where the beamformers are designed by incorporating norm-bounded channel uncertainties to provide the required quality of service at each user. This robust scheme is developed based on the worst-case performance optimization framework. In terms of beamforming vectors, the original robust design is not convex and therefore, the robust beamformers cannot be obtained directly. To circumvent this non-convex issue, the original intractable problem is reformulated into a convex problem, where the non-convex constraint is converted into a linear matrix inequality (LMI) by exploiting S-Procedure. Finally, simulation results are provided to demonstrate the effectiveness of the proposed robust design.

Distributionally Robust Collaborative Beamforming in D2D Relay Networks With Interference Constraints

In this paper, we consider a device-to-device (D2D) network underlying a cellular system wherein the densely deployed D2D user devices can act as wireless relays for a distant transceiver pair. We aim to devise a beamforming strategy for the relays that maximizes the data rate of the distant transceiver while satisfying interference constraints at the cellular receivers. Towards that end, we first formulate a beamforming problem whose solution is robust against the channel uncertainties in the relay-destination hop. Motivated by practical observations, we assume that the random channels in this hop follow unimodal distributions and propose a novel unimodal distributionally robust model to capture the channel uncertainties. Then, we extend the formulation so that it can also guard against the channel uncertainty in the source-relay hop under the worst case robust model. The resulting robust beamforming problem is generally non-convex and intractable. Therefore, we design an iterative algorithm, which is based on solving semidefinite programs, to find an approximate solution to it. Simulation results show that under mild conditions, our robust model significantly improves the throughput of D2D relay transmissions when compared with the conventional robust models that merely rely on the channels’ moment information. It also outperforms the Bernstein-type inequality-based convex approximation, which assumes that the channel follows a Gaussian distribution.

Performance investigation of robust concentric circular antenna array beamformer in the presence of look direction disparity

This paper presents the performance of a Concentric Circular Antenna Array (CCAA) with robust optimal diagonal loading (ODL) technique. Because of the symmetrical configuration of a CCAA geometry, it enables the antenna array to scan azimuthally with minimal changes in its beam width and side-lobe levels. The performance of CCAA system is degraded in the presence of disparity between the original signal direction and the steering direction of the beamformer. This performance degradation problem due to look direction disparity can be improved by using robust techniques. This paper proposes the ODL technique for CCAA system and compare the performance of proposed robust CCAA processor with the existing CCAA processors. The proposed robust CCAA beamformer enhances the output power 28.12dB and 8.624dB at 2° disparity angle compared to the existing CCAA processor (Hossain et al., 2016) and robust CCAA beamformer (Reza et al., 2016) respectively. Numerical examples are presented to analyze the performance of proposed robust beamformer in different scenarios.

Probabilistic-constrained robust secure transmission for energy harvesting over MISO channels

In this paper, we consider a system supporting simultaneous wireless information and power transfer (SWIPT),where the transmitter delivers private message to a destination receiver (DR) and powers to multipleenergy receivers (ERs) with multiple single-antenna external eavesdroppers (Eves). We study secure robust beamformer and powersplitting (PS) design under imperfect channel state information (CSI).The artificial noise (AN) scheme is further utilized at the transmitter to provide strong wireless security.We aim at maximizing the energy harvested by ERs subject to the transmission power constraint, a range of outageconstraints concerning the signal-to-interference-plus-noise ratio (SINR) recorded at the DR and the Eves, as well as concerningthe energy harvested at the DR. The energy harvesting maximization (EHM) problem is challenging to directly solve,we resort to Bernstein-type inequality restriction technique to reformulatethe original problem as a tractable approximated version. Numerical results show that our robust beamforming schemeoutperforms the beamforming scheme relying on the worst-case design philosophy.

A robust beamforming approach for early detection of readiness potential with application to brain-computer interface systems.

Early detection of intention to move, at self-paced voluntary movements from the activities of neural current sources on the motor cortex, can be an effective approach to brain-computer interface (BCI) systems. Achieving high sensitivity and pre-movement negative latency are important issues for increasing the speed of BCI and other rehabilitation and neurofeedback systems used by disabled and stroke patients and helps enhance their movement abilities. Therefore, developing high-performance extractors or beamformers is a necessary task in this regard. In this paper, for the sake of improving the beamforming performance in well reconstruction of sources of readiness potential, related to hand movement, one kind of surface spatial filter (spherical spline derivative on electrode space) and the linearly constrained minimum variance (LCMV) beamformer are utilized jointly. Moreover, in order to achieve better results, the real head model of each subject was created, using individual head MRI, and was used in beamformer algorithm. Also, few optimizations were done on reconstructed source signal powers to help our template matching classifier with detection of movement onset for five healthy subjects. Our classification results show an average true positive rate (TPR) of 77.1% and 73.1%, false positive rate (FPR) of 28.96% and 28.74% and latency of -512.426 ±396. 7ms and - 360.29 ±252. 16 ms from signals of current sources of motor cortex and sensor space respectively. It can be seen that the proposed method has reliable sensitivity and is faster in prediction of movement onset and more reliable to be used for online BCI in future.

Robust Minimum Variance Beamforming Based on Signal Power Maximization

Conventional beamformers are very sensitive to steering vector mismatches and their performance degrades in the presence of array mismatches. This paper proposes a robust minimum variance beamforming algorithm based on signal power maximization. In the proposed algorithm, the beamforming vector is determined by maximizing the signal power while minimizing the output power of the beamformer, with the signal distortionless response constrained to be unity. Numerical results show that the proposed beamformer is robust to the steering vector mismatch, and achieves better SINR performance than other robust beamforming algorithms when the mismatch in the signal look direction is large.

Joint cooperative beamforming and artificial noise design for secure AF relay networks with energy-harvesting eavesdroppers

In this paper, we investigate physical layer security for simultaneous wireless information and power transfer in amplify-and-forward relay networks. We propose a joint robust cooperative beamforming and artificial noise scheme for secure communication and efficient wireless energy transfer. Specifically, by treating the energy receiver as a potential eavesdropper and assuming that only imperfect channel state information can be obtained, we formulate an optimization problem to maximize the worst-case secrecy rate between the source and the legitimate information receiver under both the power constraint at the relays and the wireless power harvest constraint at the energy receiver. Since such a problem is non-convex and hard to tackle, we propose a two-level optimization approach which involves a one-dimensional search and semidefinite relaxation. Simulation results show that the proposed robust scheme achieves better worst-case secrecy rate performance than other schemes.

User clustering and robust beamforming design in multicell MIMO-NOMA system for 5G communications

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) – non-orthogonal multiple access (NOMA) downlink system for 5G wireless communications. This work consider the imperfect channel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beamforming design which establishes on majorization minimization (MM) technique to find the optimal transmit beamforming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.

Robust minimum dispersion distortionless response beamforming against fast-moving interferences

The recently proposed minimum dispersion distortionless response (MDDR) beamformer is able to improve the reception of non-Gaussian signals over the minimum variance distortionless response (MVDR) beamformer. However, the performance of the MDDR beamformer degrades in the presence of fast-moving interferences. To suppress such an interference, a robust beamformer against fast-moving interferences based on the minimum dispersion (MD) criterion is proposed, which provides a continuous deep null sector over a predefined range of dynamic angle-of-arrival (AOA). The designed beamformer ensures that the output is minimized in terms of dispersion and the average power over the dynamic AOA is zero via a quadratic constraint. In order to reduce the computational load, the optimization problem with a quadratic constraint is relaxed to its counterpart with a linear constraint. This allows us to devise an efficient beamforming approach, namely, gradient projection algorithm. Numerical results are provided to demonstrate that the developed beamformer can suppress the strong fast-moving interferences effectively.

Optimal beamforming using higher order statistics for passive acoustic mapping

Passive Acoustic Mapping (PAM) of sources of nonlinear acoustic emissions has been extensively investigated for monitoring ultrasound therapies. Optimal data-adaptive beamforming algorithms, such as Robust Capon Beamformer (RCB), were readily proposed as a means of improving source localization, accounting simultaneously for array configuration and calibration errors. RCB, however, assumes that signal samples follow a Gaussian distribution. Aiming at improving the spatial resolution of PAM, especially in the axial direction with respect to the array, we propose an alternative beamforming approach, Robust Beamforming by Linear Programming (RLPB). This method makes no assumptions on the statistical distribution of the received signals, and exploits not only the variance but also higher-order-statistics (HOS) of the received signals. Performance evaluation on simulated and in vitro experimental data suggests improvement in spatial resolution on the order of 20% and 15% in the axial and transverse directions respectively. This facilitates real-time mapping of disjoint cavitating regions over biologically relevant lengthscales on the order of 2 mm in the axial direction. It is expected that the proposed beamforming approach will provide the necessary improvement in PAM spatial resolution required in several clinically relevant situations, where a single array is used and the ratio of depth to aperture becomes large.

Fully Quaternion-Valued Adaptive Beamforming Based on Crossed-Dipole Arrays

Based on crossed-dipole antenna arrays, quaternion-valued data models have been developed for both direction of arrival estimation and beamforming in the past. However, for almost all the models, and especially for adaptive beamforming, the desired signal is still complex-valued as in the quaternion-valued Capon beamformer. Since the complex-valued desired signal only has two components, while there are four components in a quaternion, only two components of the quaternion-valued beamformer output are used and the remaining two are simply discarded, leading to significant redundancy in its implementation. In this work, we consider a quaternion-valued desired signal and develop a fully quaternion-valued Capon beamformer which has a better performance and a much lower complexity. Furthermore, based on this full quaternion model, the robust beamforming problem is also studied in the presence of steering vector errors and a worst-case-based robust beamformer is developed. The performance of the proposed methods is verified by computer simulations.

Low-Complexity Robust MISO Downlink Precoder Design With Per-Antenna Power Constraints

This paper considers the design of the beamformers for a multiple-input single-output (MISO) downlink system that seeks to mitigate the impact of the imperfections in the channel state information (CSI) that is available at the base station (BS). The goal of the design is to minimize the outage probability of specified signal-to-interference-and-noise ratio (SINR) targets, while satisfying per-antenna power constraints (PAPCs), and to do so at a low computational cost. Based on insights from the offset maximization technique for robust beamforming, and observations regarding the structure of the optimality conditions, low-complexity iterative algorithms that involve the evaluation of closed-form expressions are developed. To further reduce the computational cost, algorithms are developed for per-antenna power-constrained variants of the zero-forcing (ZF) and maximum ratio transmission (MRT) beamforming directions. In the MRT case, our low-complexity version for systems with a large number of antennas may be of independent interest. The proposed algorithms are extended to systems with both PAPCs and a total power constraint. Simulation results show that the proposed robust designs can provide substantial gains in the outage probability while satisfying the PAPCs.

Robust Secure Transmission of Using Main-Lobe-Integration-Based Leakage Beamforming in Directional Modulation MU-MIMO Systems

In the paper, we make an investigation of robust beamforming for secure directional modulation in the multi-user multiple-input and multiple output (MU-MIMO) systems in the presence of direction angle measurement errors. When statistical knowledge of direction angle measurement errors is unavailable, a novel robust beamforming scheme of combining main-lobe-integration (MLI) and leakage is proposed to simultaneously transmit multiple different independent parallel confidential message streams to the associated multiple distinct desired users. The proposed scheme includes two steps: designing the beamforming vectors of the useful confidential messages and constructing artificial noise (AN) projection matrix. Here, in its first step, the beamforming vectors for the useful confidential messages of desired user k are given by minimizing the useful signal power leakage from main-lobe of desired user k to the sum of main-lobes of the remaining desired directions plus main-lobes of all eavesdropper directions. In its second step, the AN projection matrix is constructed by simultaneously maximizing the AN power leakage to all eavesdropper directions such that all eavesdroppers are disrupted seriously, where AN is viewed by the transmitter as a useful signal for eavedroppers. Due to independent beamforming vectors for different desired users, a more secure transmission is achieved. Compared with conventional non-robust methods, the proposed method can provide a significant improvement in bit error rate along the desired directions and secrecy-sum-rate towards multiple desired users without needing statistical property or distribution of angle measurement errors.

Iterative regularization method in generalized inverse beamforming

Beamforming based on microphone array is a method to identify sound sources. It can visualize the sound field of the source plane and reveal interesting acoustic information. Generalized inverse beamforming (GIB) is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency. However, in real testing situation, errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy. As an inverse problem, the stability of GIB can be improved with regularization methods. We proposed a new iterative regularization method for GIB by iteratively redefining the form of regularization matrix and calculating the corresponding solution. Moreover, the new method is applied to functional beamforming and double-layer antenna beamforming respectively. Numerical simulations and experiments are implemented. The results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications.

Design of robust high-order superdirectivity for circular arrays with sensor gain and phase errors

Though the high-order superdirectivity theory proposed in recent years is attractive, it is hard to implement in practice due to its poor robustness to small random array errors. Hence, in this paper, we present two robust designs of high-order superdirectivity for circular arrays with gain and phase errors. Firstly, we study on the sensitivity function of the high-order superdirectivity and give an alternative solution for a robust superdirective beamformer based on sensitivity function constraint. This method could achieve an arbitrary compromise between directivity and robustness, so it is more flexible and applicable than the existing higher-order truncation method. Although it does not improve on computational complexity or performance with respect to the second-order cone programming obviously, it could lay the foundation for the following robust design method. Then, considering the fact that different eigenbeams correspond to different eigenvalues, we study the method of diagonal loading with variable factors in detail, and further improve the performance of the former sensitivity function constrained method by loading variable factors to different eigenbeams, which results in better performance and greater flexibility in making a compromise. We also show that this proposed loading variable factors method can achieve an equivalent result to the higher-order truncation method by setting proper factors. Simulation results demonstrate the robustness and effectiveness of the above two methods, especially the performance improvement of the loading variable factors method.

Robust Adaptive Beamforming With Precise Main Beam Control

Many efforts have been recently devoted to robust adaptive beamforming with main beam control such that sufficient robustness against large look direction mismatches can be achieved by flexibly adjusting the beamwidth and response ripple. However, most of the existing approaches inherently rely on assuming an exactly known array manifold, but have not yet addressed the issue of robust beamforming with precise main beam control in the presence of arbitrary steering vector uncertainties. This motivates us to develop a robust beamforming approach that is capable of accurately controlling the array main beam. Unlike the conventional methods, steering vector uncertainties are taken into account in the magnitude response constraints of the adaptive beamformer. This allows us to control the main beam as prescribed. As the resultant nonconvex problem has a more complicated formulation than that of the existing methods, techniques developed for solving the problem of robust beamforming with magnitude response constraints cannot be employed directly. To tackle this problem, the lower and upper norm bounds of the beamformer weight vector are derived. The semidefinite relaxation technique is then employed as approximate solver, ending up with iterative, grid search, and linearization solutions. Simulation results show that the proposed methods are able to precisely control the main beam magnitude response in the presence of steering vector uncertainties.

Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization

Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program) problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.

Energy-Efficient Transmission for Cognitive Vehicular Networks

A robust energy-efficient key for Multiple-Input-Multiple-Output (MIMO) transmissions is described in cognitive vehicular networks. An optimal MIMO beam forming is designed for Secondary Users (SUs) by considering defective interference Channel State Information (CSI). Specifically, Energy Efficiency (EE) of SUs gets optimized by using the transmission power constraint; therefore the robust interference power constraint and the minimum transmission rate are satisfied. The uncertainty of state information derived by bounding it in a Frobenius-norm-based region and then consistently transfer the robust interference constraint to a linear matrix variation which is categorized by solving the optimization crisis; besides, a sufficient gradient direction approach is proposed to reduce the optimization crisis into a linear chronological constraint semi-definite program, which leads to a disseminated iterative optimization algorithm for deriving the robust and optimal beam-forming.