Adaptive and Robust Beamforming

In contrast with the common delay-and-sum (DAS) beamformer, adaptive beamformers can be used to increase the resolution of acoustic measurement systems without sacrificing sidelobe levels. The non-linear nature of adaptive beamforming methods may cause changes to measured scattered amplitude distributions. For example, large differences in speckle statistics have been observed in some cases when using the adaptive minimum variance distortionless response (MVDR) beamformer in medical ultrasound, unless preventative measures were implemented. Low complexity adaptive (LCA) beamforming techniques have shown similar, but smaller, differences. Recently, experiments have been conducted in the Oslofjord, Norway, to determine whether low-complexity adaptive (LCA) beamforming techniques can improve the performance of bathymetric echosounders. When using LCA with these types of sonar systems, it is important to understand any changes to the backscatter statistics, as these changes may affect, e.g., seafloor classification methods. In this talk we will present comparisons between backscatter statistics estimated using a weighted delay-and-sum beamformer and those estimated using a low complexity adaptive beamformer. We will discuss any differences seen, possible mechanisms causing these differences and potential remedies. [Research supported by The Norwegian Research Council and Kongsberg Maritime. The first author is employed in Kongsberg Maritime.]

This study proposes low-complexity robust adaptive beamforming (RAB) techniques based on shrinkage methods. The authors first review a low-complexity shrinkage-based mismatch estimation batch algorithm to estimate the desired signal steering vector mismatch, in which the interference-plus-noise covariance matrix is also estimated by a recursive matrix shrinkage method. Then they develop low-complexity adaptive recursive versions of stochastic gradient and conjugate gradient to update the beamforming weights, resulting in low-cost robust adaptive algorithms. An analysis of the effect of shrinkage on the estimation procedure is developed along with a computational complexity study of the proposed and existing algorithms. Simulations are conducted in local scattering scenarios and comparisons to existing RAB techniques are provided.

Robust adaptive beamforming (RAB) has became a popular research topic, with various RAB techniques being proposed in the past decades. However, because the sample covariance matrix rather than the interference-plus-noise co-variance matrix is used to calculate the weight vector, the performance of the previously developed RAB techniques is not optimal. In this paper, a novel RAB algorithm, which uses the reconstructed interference-plus-noise covariance matrix, is developed. First, the interference-plus-noise covariance matrix and the desired signal covariance matrix are reconstructed by matched spectrum processing. Then, the weight vector of RAB is directly obtained using the general-rank minimum variance distortionless response method. A significant advantage of the proposed RAB is that only little prior information is required. The imprecise knowledge of the antenna array geometry and the angular sectors (in which the desired signal and interferences are located) is sufficient for the proposed RAB algorithm. Simulation results demonstrate that the proposed method outperforms other previously developed RAB techniques.

The most popular robust adaptive beamforming technique is diagonal loading. However, no clear guidelines can be applied to choose the optimal diagonal loading factor, and beamforming techniques based on the uncertainty set of array steering vector still need to specify the bound of the uncertainty set. In this paper, we develop a novel robust adaptive algorithm. Firstly, we modify covariance fitting criteria (CFC) via replacing the conventional sample covariance matrix used in CFC by the general linear combination (GLC) covariance matrix estimates. Then we use the modified CFC to estimate the covariance matrix of array observation data in the standard capon beamforming formulation. The merits of our method we term GLC-CFC include applicability to arbitrary number of snapshots, robustness to the correlated sources and without the requirement of specifying any user-parameters. The excellent performance of our method in small snapshots size is demonstrated via numerical examples and compared with other classical adaptive beamforming algorithms.

Recently, robust minimum variance (MV) beamforming which optimizes the worst-case performance has been proposed in S.A. Vorobyov et al. (2003), R.G. Lorenz and S.P. Boyd (2005). The worst-case approach, however, might be overly conservative in practical applications. In this paper, we propose a more flexible approach that formulates the robust adaptive beamforming problem as a probability-constrained optimization problem with homogeneous quadratic cost function. Unlike the general probability-constrained problem which can be nonconvex and NP-hard, our problem can be reformulated as a convex nonlinear programming (NLP) problem, and efficiently solved using interior-point methods. Simulation results show an improved robustness of the proposed beamformer as compared to the existing state-of-the-art robust adaptive beamforming techniques

The performance of adaptive beamforming degrades in presence of signal model mismatches. In particular, when the desired signal is present in training snapshots, the adaptive beamforming is quite sensitive to desired signal steering vector mismatch. Therefore, a robust adaptive beamforming for actual system is proposed based on the reconstruction of interference covariance matrix and mismatched steering vector compensation. In the proposed method, the interference covariance matrix is firstly reconstructed by using Root-MUSIC method to estimate Direction-of-Arrival (DOA) of signals, where the desired signal component is removed from the training snapshots. Subsequently, the mismatched desired signal steering vector is compensated by solving a quadratically constrained quadratic programming problem. Simulation results show that the performance of proposed algorithm outperforms the existing robust adaptive beamforming, and the output signal-to-interference-plus-noise ratio (SINR) is close to optimal values. Therefore, the proposed algorithm could be significantly effective for actual system.

This paper deals with the problem of two-dimensional (2-D) adaptive array beamforming with multiple beam constraints (MBC) using a generalized sidelobe canceller (GSC). We present a method for the construction of signal blocking matrix required by the 2-D GSC. The resulting 2-D adaptive beamformer can provide almost the same performance as conventional 2-D adaptive beamformers based on a linearly constrained minimum variance (LCMV) criterion. The effectiveness of the proposed GSC is that the construction of the required signal blocking matrix requires only the computation of a few entries from analytical formulas. In comparison with conventional methods, the proposed technique gets rid of the computational complexity due to the eigendecomposition required for finding the 2-D signal blocking matrix. For dealing with the performance degradation due to coherent interference, we present a 2-D weighted spatial smoothing scheme to effectively alleviate the coherent jamming effect. Several simulation examples are provided for illustration and comparison.

The adaptive beamforming is one of the key techniques for array signal processing. However, the matrix inversion operation in the existing methods will cost a large amount of computational complexity, which results in poor real-time processing ability. In order to reduce the amount of computational cost, a fast and robust adaptive beamforming method based on complex-valued radial basis function (CRBF) neural network is proposed. In the proposed method, the CRBF neural network is established, thus the direct matrix inversion is avoided by the nonlinear mapping processing from the array covariance matrix to the adaptive weight vector, and therefore the calculation speed of adaptive weight vectors is increased. Based on the simulation results, the proposed method is verified that the speed of adaptive beamforming is increased compared with sample matrix inversion (SMI) algorithm method and an improved performance is achieved compared with that of conventional real-valued RBF neural network beamformer.

Cognitive radio (CR) concepts were introduced by J. Mitola in 1999/2000. It is an approach with high potential to allow most-intensive usage of the precious natural source spectrum. CR is capable of sensing the communication environments and of adapting to its environment by adjusting the radio parameters. With beam-forming techniques, CR can direct its main beam towards CR users while creating nulls to licensed users (LU's) in up-link in order to share the same spectrum with LU's without disturbing them. Adaptive beam-forming (AB) techniques are used for interference reduction by null broadening (NB) of the beam patterns of a CR base station in down-link operations. In this way by steering those NB angular sectors towards selected regions the LU's will experience less interference. Distributed Beam-forming (DB) is a new concept to form beams by distributed wireless sensors in order to transmit signals over a long distance with less transmit power. At IRCTR of Delft University cognitive radio concepts receive broad attention in the Radio Advanced Technology and Systems (RATS) program. Several MSc's and PhD's participate in this program. In this invited paper the latest IRCTR results on AB and DB are overviewed. Furthermore, our Intelligent-WiMAX (I-WiMAX) initiative is summarized with some focus on adaptive OFDM and on applications for green communications and positioning.

In the last few years, the demand of robust beamforming techniques has been increased significantly to serve numerous purposes. However, beamforming under low Signal to Noise Ratio (SNR) condition has always been a challenging task, which becomes more tedious in case of multiple sources. On the other hand, there are numerous factors such as steering vector error or similar estimation error problems that confine the efficiency of major beamforming techniques. Classical methods employ Eigen-Value Decomposition (EVD) and Singular Value Decomposition (SVD) over covariance matrix of the received signal; however their efficiency is limited under low SNR and multi-source condition, and perform inferiorly in case of steering vector errors. Such approaches are limited to achieve optimal Direction-of-Arrival (DOA) estimation that degrades the overall performance of the beamformer. Considering all these limitations, in this research, the focus is made on designing a robust DOA estimation model, followed by a novel beamformer for 8-element Uniform Linear Array (ULA). The simulation work consists two parts DOA estimation and beamforming. Unlike classical MUSIC and ESPRIT algorithms popular for DOA estimation our proposed model exploits the propagation method based subspace method where at first covariance matrix is obtained for the received signal, which is followed by normalization and Cross-Correlation matrix estimation. The obtained correlation matrix is processed for Generalized Eigen-Value Decomposition (GEVD) that efficiently obtained (orthogonal) subspace and SOI separation to yield DOA information. This approach enables more efficient DOA estimation even under low-SNR and steering vector error conditions. After obtaining DOA information, a novel adaptive beamformer is designed by using MVDR and FROST in parallel. DOA information from proposed model is given as input to the adaptive MVDR FROST beamforming model. Exploiting dynamic Signal-to-Interference ratio (SINR) by each beamformer our proposed method introduces an adaptation model that intends to achieve higher SINR value. MATLAB 2018a based simulation confirmed the robustness of the proposed model in terms of DOA estimation and beamforming results.

A beamforming technique is proposed to guarantee a feasible reception performance in mobile communications. The proposed algorithm called CLMS is jointly operating a Capon and a least mean square (LMS) adaptive beamforming techniques. The CLMS algorithm works as the Capon and the LMS beamformers for unknown and known data periods, respectively. The CLMS algorithm is evaluated in a mobile reception channel of the geometrically based single bounce circular model (GBSBCM). Compensation abilities over multipaths and a phase distortion are analyzed and compared for the proposed, Capon, LMS beamforming algorithms. A decision feedback equalizer (DFE) is also considered to mitigate remaining multipaths by concatenating the beamformer.

Adaptive beamforming can be used as a method for estimating an unknown waveform from a source impinging on an array of sensors. When the direction-of-arrival (DOA) of the incoming signal is known, the minimum variance distortionless response (MVDR) beamformer provides a distortionless version of the signal while suppressing noise and interference. However, if there is a mismatch between the look direction of the beamformer and the actual DOA of the signal, there can be significant degradation in performance. We use a Bayesian approach with the MVDR criterion to derive an adaptive beamformer which has nearly optimal performance under good conditions, and is robust to uncertainty in DOA under poor conditions.

Floating high-frequency surface-wave radar provides an effective solution to widening the range of detection by such radar systems. However, for high-frequency radars with long coherence integration times, the yaw angle variations during this period can have a significant impact on the accuracy of direction-of-arrival estimation. Although adaptive beamforming methods are applicable to yaw angle compensation, their effectiveness can be significantly reduced when the measured distortion of antenna patterns is considered. To solve this problem, an iterative adaptive beamforming of focusing concept is proposed in this paper to compensate for yaw rotation. Firstly, an adaptive beamforming technique, called balanced-focusing pseudo-fixed beamforming, is developed to improve the ability of beam shape control by shortening the constraint range of the azimuth. Then, the shortened focusing range is determined by one iterative strategy that iteratively reduces the focusing length and selects the focusing center. The simulation results demonstrate that the proposed algorithm is applicable to significantly improve the precision and stability of direction-of-arrival estimation. This algorithm is also validated against the results obtained from two cooperative signals and ship echoes in a field experiment.

A new adaptive beamforming technique based on neural networks (NNs) is proposed. The NN training is accomplished by applying a novel optimization method called Mutated Boolean PSO (MBPSO). In the beginning of the procedure, the MBPSO is repeatedly applied to a set of random cases to estimate the excitation weights of an antenna array that steer the main lobe towards a desired signal, place nulls towards several interference signals and achieve the lowest possible value of side lobe level. The estimated weights are used to train e-ciently a NN. Finally, the NN is applied to a new set of random cases and the extracted radiation patterns are compared to respective patterns extracted by the MBPSO and a well-known robust adaptive beamforming technique called Minimum Variance Distortionless Response (MVDR). The aforementioned comparison has been performed considering uniform linear antenna arrays receiving several interference signals and a desired one in the presence of additive Gaussian noise. The comparative results show the advantages of the proposed technique.

Adaptive beamforming techniques are widely used in radar, communication, sonar, navigation and other signal processing fields. The conventional experimental systems for adaptive beamforming are often carried out with a large number of Radio Frequency equipment, which leads to high cost and complexity. Therefore, it is necessary to construct an experimental system with low cost and high flexibility to verify the performance of adaptive beamforming algorithms. In this paper, an experimental adaptive beamforming platform by utilizing the microphone array is designed, where the principle of adaptive beamforming, the structure and function of each part of whole experiment system are introduced clearly. Furthermore, the corresponding experiments are deployed to verify the adaptive beamforming algorithms for radar system. The experimental results show that the designed experimental platform can validate the adaptive beamforming algorithms easily and effectively. (5 pages)