Robust Beamforming Research Articles

A Novel Robust Adaptive Beamforming Algorithm Based on Total Least Squares and Compressed Sensing

A Novel Robust Adaptive Beamforming Algorithm Based on Total Least Squares and Compressed Sensing

Probabilistic Robust Secure Beamforming in MISO Channels With Imperfect LCSI and Statistical ECSI

In this paper, we investigate the robust secure transmit beamformming design for multiple-input single-output wiretap channels overheard by multiple non-collaborating single-antenna eavesdroppers. Assuming that at the transmitter, the instantaneous legitimate receiver’s channel state information (CSI) is imperfect and only the statistical eavesdroppers’ CSI is known, we seek to maximize the target secrecy rate $R$ with the total transmit power constraint and the secrecy outage probability constraint. The resulting outage-constrained secrecy rate maximization (O-SRM) is non-convex and difficult to solve. Thus, we develop an efficient algorithm to solve it and determine the robust secure beamforming design. Specifically speaking, we first prove that the original O-SRM problem can be solved by an equivalent outage-constrained power minimization problem (O-PMP), which is easy to perform semi-definite relaxation (SDR) and can be solved by semi-definite program (SDP) consequently. Second, we transform the non-convex secrecy rate outage constraints into deterministic ones by resorting to Bernstein-type inequality II. Finally, by solving the convex approximation of the O-PMP with different $R\text{s}$ and bisection search over $R$ , we convert the original O-SRM problem into a sequence of solvable SDPs. Simulation results are provided to verify the secrecy-rate performance improvement of the proposed robust beamforming compared with the existing worst-case design proposed by Li and Ma and the simple non-robust maximum-ratio transmission.

Optimal and Robust Beamforming for Secure Transmission in MISO Visible-Light Communication Links

This work considers secure downlink transmission in indoor multiple-input, single-output visible-light communication (VLC) links. In particular, we study the design of transmit beamformers that maximize the achievable secrecy rate subject to amplitude constraints imposed by the limited dynamic range of the light-emitting diodes (LEDs). Such constraints render the design problem nonconvex and difficult to solve. We show, however, that this nonconvex problem can be transformed into a solvable quasiconvex line search problem. We also consider the more realistic case of imperfect channel information regarding the receiver's and eavesdropper's links. We tackle the worst-case secrecy rate maximization problem, again subject to amplitude constraints. In our treatment, uncertainty in the receiver's channel is due to limited feedback, and is modeled by spherical sets. On the other hand, there is no feedback from the eavesdropper, and the transmitter shall utilize the line-of-sight channel gain equation to map the eavesdropper's nominal location and orientation into an estimate of the channel gain. Thus, we derive uncertainty sets based on inaccurate information regarding the eavesdropper's location and orientation, as well as the emission pattern of the LEDs. We also consider channel mismatches caused by the uncertain non-line-of-sight components. We provide numerical examples to demonstrate the performance gain of the optimal beamformer compared with the suboptimal schemes, and the robust beamformer compared with its nonrobust counterparts. We also evaluate the worst-case secrecy rate performance of the robust beamformer in a typical VLC scenario along with the aforementioned uncertainty sources.

Robust Beamforming for Nonorthogonal Multiple-Access Systems in MISO Channels

Nonorthogonal multiple access (NOMA) is a promising technology in future mobile communication systems. In this paper, considering that the base station knows imperfect channel state information (CSI), we investigate the robust beamforming design problem for NOMA systems in multiple-input-single-output (MISO) channels. Modeling channel uncertainties by the worst-case model, we aim at maximizing the worst-case achievable sum rate subject to the transmit power constraint at the base station. We propose to decouple the nonconvex optimization problem into four optimization problems and employ an alternating optimization algorithm to solve the problem. Simulation results demonstrate that our proposed robust beamforming scheme outperforms the orthogonal multiple-access scheme.

Robust adaptive beamforming against large DOA mismatch with linear phase and magnitude constraints for multiple‐input–multiple‐output radar

In this study, a robust adaptive beamformer against large direction-of-arrival (DOA) mismatch for multiple-input–multiple-output radar is proposed with linear phase and magnitude constraints on main lobe. First, the full-dimensional weight vector (WV) is expressed as the Kronecker product of the transmit and receive array WVs based on the WV separable principle. For the transmit array WV, the authors find an interesting property that the Fourier spectrum of its conjugate inverse arrangement is equal to its array response function within a phase factor. This property also exists in the receive array WV. Using this property, the phase response of the transmit and receive array, respectively, is set to be linear based on designing a finite impulse response filter. Then, a bi-quadratic cost function with respect to the transmit and receive WVs is established by only constraining the real magnitude response and it is effectively solved by the bi-iterative algorithm. The proposed beamformer has lower computational complexity and faster sample convergence rate, compared with the traditional magnitude response constraints beamformers with full degrees of freedom. Moreover, it can provide good robustness against large DOA mismatch. Numerical experiments are provided to demonstrate the effectiveness of the proposal.

Robust Adaptive Beamforming Based on Conjugate Gradient Algorithms

The mismatches of signal and array geometry will seriously degrade the performance of adaptive beamformer. In this paper, we propose two methods for robust adaptive beamforming based on the conjugate gradient (CG) algorithm. The proposed beamformers offer a significant improvement in the computational complexity while providing the same performance of the best robust beamformers at present. The first method belongs to the diagonal loading technique. We derive a diagonal loading CGLS algorithm (CG applied to normal equations) and propose a simple method to choose the loading level based on a coarse estimation of the desired signal power. This parameter-free method can effectively reduce the signal self-cancellation at high signal-to-noise ratio. The second method belongs to the regularization technique. Since the CG algorithm has a regularizing effect with iteration number being the regularization parameter, the stopping criterion plays an important role on the robustness. We develop three fast stopping criteria for CG iteration, which reduce the stopping complexity from $O(N)$ or $O(N^2)$ to $O(1)$ . The former two are the fast versions of existing methods and the later one is new. Moreover, the new criterion based on fast Ritz value estimation has better performance than others.

Outage Constrained Robust Beamforming for Secure Broadcasting Systems With Energy Harvesting

In this paper, we investigate simultaneous wireless information and power transfer systems for multiuser multiple-input single-output secure broadcasting channels. Considering imperfect channel state information, we introduce a robust secure beamforming design, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. With the aid of Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. Based on a successive convex approximation (SCA) method, we propose a low-complexity approach, which reformulates the original problem as a second-order cone programming problem. Also, we prove the convergence of the SCA-based iterative algorithm. Simulation shows that the proposed scheme outperforms the conventional method with lower complexity.

Low complexity robust adaptive beamforming for general-rank signal model with positive semidefinite constraint

We propose a low complexity robust beamforming method for the general-rank signal model, to combat against mismatches of the desired signal array response and the received signal covariance matrix. The proposed beamformer not only considers the norm bounded uncertainties in the desired and received signal covariance matrices, but also includes an additional positive semidefinite constraint on the desired signal covariance matrix. Based on the worst-case performance optimization criterion, a computationally simple closed-form weight vector is obtained. Simulation results verify the validity and robustness of the proposed beamforming method.

Multiuser Detection Using Blind Robust Beamforming in Multipath Environment for LTE System

This paper presents a new, efficient data detection for coherent signals in the uplink direction of Long Term Evolution (LTE) system for multiuser in multipath environment through adaptive processing of antenna arrays at the base station. The proposed algorithm at the receiver depends on a robust beamforming based Direction of Arrival (DOA) estimation to extract each path of coherent signals for each user separately, after that combining those estimated signals coherently for maximizing the received power and output signal to noise ratio. The proposed approach depends first on implementation of Re-iterative Superresolution (RISR) DOA algorithm. The RISR is applied here at the receiver for each sub-channel separately after the process of subcarrier demapping, that a signal is processed at each element of antenna array at the receiver. By applying this process the elements of antenna array are required to be only more than the number of received signals for each user (sub-channel), not more than the total signals. Multiple constrained minimum variance (MCMV) beamforming is then applied for purpose of paths extraction of each user exploiting the estimated signal's DOA, the extracted signals are combined coherently after time delay estimation and alignment of signals, finally the data is detected. The simulation results demonstrate the effectiveness of the proposed algorithm in multiuser multipath mobile environment with different modulation schemes.

Robust beamforming and artificial noise design in interference networks with wireless information and power transfer

In this paper, the robust beamforming and artificial noise design is investigated in two-user interference networks with wireless information and power transfer. Specifically, we focus on the secure communication of the two pairs in the presence of an energy receiver (ER) which acts as the potential eavesdropper and intends to wiretap the confidential message transmitted to one of the information receivers (IRs). With only imperfect eavesdropper’s channel state information (ECSI) at the transmitters, our goal is to minimize the total transmit power, while guaranteeing the worst-case secrecy rate requirement at the wiretapped IR, the signal-to-interference-plus-noise ratio requirement at the wiretap-free IR and the energy harvesting requirement at the ER. In particular, we first model the imperfect ECSI in the sense of ellipsoidal uncertainties. Then, our design goal can be further reformulated as a two-stage optimization problem. With the help of rank relaxation and one-dimensional line search, the considered two-stage problem can be solved efficiently. Simulation results verify the effectiveness of the proposed design in different scenarios.

Joint transceiver designs for full-duplex MIMO SWIPT systems based on MSE criterion

For the simultaneous wireless information and power transfer (SWIPT), the full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean-square-error (MSE) criterion, the optimization problem of joint transceiver design with transmitting power constraint and energy harvesting constraint is formulated. Next, by semidefinite relaxation (SDR) and randomization method, the SDR-based scheme is proposed. In order to reduce the complexity, the closed-form scheme is presented with some simplified measures. Robust beamforming is then studied considering the practical condition. The simulation results such as MSE versus signal-noise-ratio (SNR), MSE versus the iteration number, well prove the performance of the proposed schemes for the system model.

Robust Rank-Two Multicast Beamforming Under a Unified CSI Uncertainty Model

We study a beamformed Alamouti coding scheme for a multigroup multicast downlink system. In this letter, we take into account imperfect channel state information (CSI) at the base station, where the CSI uncertainty region is formed by the intersection of multiple ellipsoids. This unified CSI uncertainty model leads to a challenging robust rank-two multicast beamforming problem. We first develop a conservative approximation method to handle the intractable constraints in the formulated robust beamforming problem under the considered CSI uncertainty region. Then, we apply the semidefinite relaxation (SDR) technique to approximately solve this problem. Our rank-profile analysis shows that the SDR is tight when there are at most two users in each multicast group and the CSI uncertainty region is not too large. Finally, we carry out simulations to validate the effectiveness of the proposed conservative approximation method. The simulation results coincide with the rank-profile analysis.

Robust beamforming design for multiple‐input–single‐output secrecy multicasting systems with simultaneous wireless information and power transmission

In this study, the authors study simultaneous wireless information and power transfer for multiuser multiple-input–single-output secure multicasting channels with imperfect channel state information. First, a robust secure beamforming design is considered, where the transmit power is minimised subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. By utilising Bernstein-type inequalities, the authors transform the outage constraints into the deterministic forms. In order to identify a local optimal rank-one solution, the authors propose an efficient approach based on a constrained concave convex procedure method to convert the original problem into a sequence of convex programming problems. Finally, simulation results are provided to validate the performance of the proposed design methods.

Robust adaptive beamforming based on sparse reconstruction using a non‐convex optimisation algorithm

A novel robust adaptive beamforming technique is proposed to solve the problem of performance degradation with one single snapshot. A sparse signal recovery model under the non-convex optimisation framework is first established, which dispenses with the mismatched sample covariance matrix, an indispensable part of most existing beamformers. Then, an iterative algorithm is designed to solve the optimisation problem by using the p-shrinkage operator and the alternating direction method of multipliers. The iteration steps are closed form and convenient to apply in practice. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.

Robust beamforming designs for nonregenerative multipair two-way relaying systems

In this paper, we consider nonregenerative multipair two-way relaying systems, where a relay node supports $K$ pairs of two-way communications in the presence of imperfect channel state information (CSI). We employ a stochastic approach to model the channel uncertainties and study a robust beamforming design at the relay. It is shown that the proposed beamformer provides a reduction in the computational complexity, as well as good robustness against channel errors, compared with conventional designs. To reduce the estimation overhead at the users, we also suggest an efficient downlink training method to inform the users of the channel-dependent self-interference cancellation (SIC) parameters. With the training method, the additive noise may incur a malfunction of the SIC. To address this issue, we develop an intelligent selection criterion that decides whether the SIC should be adopted or not. Finally, from simulation results, we demonstrate the efficiency of our proposed schemes.

Quadratically Constrained Quadratic Optimal Problem in Robust Relay Networks

The paper investigates the problem of a distributed robust relay beamforming in one-way relay networks with imperfect channel state information. The aim is to maximize the SNR (signal-to-noise ratio) of the receiver with the constraint of the total transmits power of relays is less than a certain predefined threshold. Because the channel is imperfect and the objective function is fractional quadratic form, the optimal problem is a non-convex problem which is hard to be solved. We first change the fractional problem into a non-fractional one. Second, we consider the semi-definite programming (SDP) method efficiently by exploiting S-procedure theorem and relaxing the rank-one constrain to obtain the robust beamforming vector. The paper gives the schematic total algorithm too. Numerical results show that the proposed algorithm can solve the maximum problem with robust features efficiently and obtain satisfactory results.

Robust Beamforming for Simultaneous Wireless Information and Power Transfer in MISO Interference Channels

Taking the channel uncertainty into account, we investigate the robust beamforming design for simultaneous wireless information and power transfer in multiple-input single-output interference channels, where multiple multi-antenna transmitters communicate with their targeted single-antenna receivers and simultaneously interfere with all other receivers. Under quality-of-service and energy harvesting constraints at the receivers which adopt power splitting scheme, we aim to minimize the total transmit power at the transmitters when the channel uncertainty is modeled as the norm-bounded. The robust optimization is non-convex and the global optimal solution is challenging. With the help of the extension of the S-Procedure and rank-one relaxation, the robust beamforming is transformed into a semidefinite programming . We develop an novel method to recover a rank-one feasible and locally optimal solution, which is based on difference of convex programming and sequential parametric convex approximation method. Simulations show that our proposed algorithm outperforms the well-known Gaussian randomization method and has much lower computational complexity.

Effects of phase aberration correction methods on the minimum variance beamformer.

The minimum variance (MV) beamformer is a method that has the potential to enhance the resolution and contrast of ultrasound images. However, it suffers from sensitivity to speed of sound errors and aberration. Although there have been several studies on the application of phase aberration correction (PAC) methods to conventional delay-and-sum (DAS) beamforming, the benefits of PAC methods in mitigating the effects of phase aberration in MV beamformed images are not well understood. A study of this type would be helpful in designing a robust beamformer based on PAC knowledge present in the literature. This study analyzes three PAC algorithms (multi-lag cross-correlation, Rigby's beamsum and scaled covariance matrix) and their impact on the performance of the MV beamformer in the presence of second order phase aberrations. The PAC methods in combination with the MV beamformer were tested on simulated and experimental data corrupted with an electronically created near field phase aberrator. It is shown that all gains in performance of the MV beamformer with respect to DAS is lost at high aberration strengths. For instance, at 60 ns of aberration the lateral resolution of DAS degrades by 22% while MV degrades by 600%. It is also shown that basic PAC methods improve the aberrated MV beamformer. PAC methods reduces degradation in lateral resolution from 600% to 5%. Similar improvements are observed in peak sidelobe level (96% to 27%), contrast (88% to 49% for the simulations and 43% to 15% for experiments) and contrast-to-noise ratio (86% to 42% for the simulations and 68% to 55% for experiments). These enhancements allow the MV beamformer to outperform DAS even in the strongest aberration case.

Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction

In this paper, a novel subspace method is proposed to reconstruct the interference-plus-noise covariance matrix (IPNCM) according to its definition, which can fundamentally eliminate the signal of interest (SOI) component from the sample covariance matrix (SCM). The central ideal is that each interference steering vector (SV) is estimated by the vector lying within the intersection of two subspaces while its power obtained by using the Capon spectral estimator. The first subspace is the interference subspace and it is obtained from each interference covariance matrix term calculated by integrating over each interference angular sector. The second one is the signal-interference subspace got from the SCM. Then a more precise IPNCM is reconstructed based on these accurate estimations. Meanwhile the signal covariance matrix is calculated by integrating over the SOI angular sector so that a new SV estimation of SOI can be obtained from its prime eigenvector. Finally, based on the new IPNCM and the SV of SOI, a novel robust beamformer is formulated to improve the robustness against array model mismatches. Simulation results demonstrate that the proposed beamformer outperforms other existing reconstruction-based beamformers and almost attains the optimal performance in both low and high input signal-to-noise ratio (SNR) cases.

Sum-rate maximization and robust beamforming design for MIMO two-way relay networks with reciprocal and imperfect CSI

In this paper, we investigate the robust relay beamforming design for a multi-input multi-output (MIMO) two-way relay networks (TWRN) by considering imperfect and reciprocal channel state informations (CSIs). In order to maximize the sum-rate (SR) subject to the individual relay power constraint, we first equivalently convert the objective problem into a sum of the inverse of the signal-to-residual-interference-plus-noise ratio (SI-SRINR) problem. The SI-SRINR problem can be reformulated as a biconvex semi-definite programming (SDP) which employs bounded channel uncertainties as the worst-case model. Then, we convert residual-interference-plus-noise (RIN) and relay power constraints into linear matrix inequalities (LMIs). By this way, the objective problem can be tackled by the proposed efficient iterative algorithm. The analysis demonstrates the procedures of the proposed SI-SRINR robust design.