Adaptive Beamforming Method Research Articles

Multi-Constraint Adaptive Beamforming in the Presence of the Desired Signal

Compared with single-constraint adaptive beamforming, multi-constraint adaptive beamforming is more adaptable to different environments. However, as an effective multi-constraint adaptive beamforming method, the multi-point optimal and precise array response control (MOPARC) method is sensitive to the presence of the desired signal. To improve the robustness of multi-constraint adaptive beamforming, we propose a novel algorithm by incorporating the MOPARC method with the interference-plus-noise covariance matrix (INCM) reconstruction. First, we analyze and determine that the problem is due to the initial weight calculation process of the MOPARC method. Then, we reconstruct the INCM to modify the initial weight. Based on the modified initial weight, a modified MOPARC algorithm is proposed. The proposed algorithm is more robust to the presence of the desired signal than the MOPARC method. Simulations demonstrate the effectiveness and superiority of the proposed algorithm.

Ship Echo Identification Based on Norm-Constrained Adaptive Beamforming for an Arrayed High-Frequency Coastal Radar

A frequency-modulated continuous-wave (FMCW) radar, operated at the central frequency of 27.75 MHz and the bandwidth of 300 kHz has been established on the seashore near the Taichung harbor (24°18.591' N, 120°31.389 E), Taiwan. Sixteen vertical dipole antennas were located linearly and attached with 16 receiving channels. One purpose of the radar is to monitor the ships that navigate toward, away, and around the harbor. In this article, we applied the radar beamforming methods that transform the temporal radar signals as brightness on the 2-D range-azimuthal domain, making the ship echoes visible directly on the spatial domain. Three beamformers, linear Fourier, directionally constrained minimum power (DCMP), and norm-constrained DCMP (NC-DCMP) algorithms, were employed to produce range-angle (RA) brightness distribution that is different from the conventionally used range-Doppler (RD) spectra in ship detection. Both DCMP and NC-DCMP are adaptive beamforming methods. With the auxiliary of a bandstop filter to suppress the sea echoes, the NC-DCMP beamformer was demonstrated to surpass the other two beamformers and could provide more visible ship echoes in the RA brightness distribution. Automatic Identification System (AIS) information was also used to validate the radar-determined ship locations from the RA brightness distribution. Although some ships having the AIS information were not observed clearly by the radar, the radar detected some targets without AIS information.

Single-Channel LCMV-Based Adaptive Beamforming With Time-Modulated Array

A novel single-channel linearly constrained minimum variance (LCMV)-based adaptive beamforming method with time-modulated array is proposed and verified. Time-modulated technique is utilized to generate a modulated single-channel signal. Furthermore, in digital domain, with $l_2$ norm optimization, covariance matrix of original signal is recovered from the sideband signals, which are extracted from the single-channel signal. Finally, the optimal weighting vectors can be determined by LCMV. The proposed method has lower channel mismatches, hardware complexity, and cost compared to the traditional multichannel structure. And in the procedure, only fixed time sequences are needed to calculate the weights and obtain the output signal. Simulation results are provided to show the procedure and verify its effectiveness.

Adaptive Ultrasound Beamforming Using Deep Learning.

Biomedical imaging is unequivocally dependent on the ability to reconstruct interpretable and high-quality images from acquired sensor data. This reconstruction process is pivotal across many applications, spanning from magnetic resonance imaging to ultrasound imaging. While advanced data-adaptive reconstruction methods can recover much higher image quality than traditional approaches, their implementation often poses a high computational burden. In ultrasound imaging, this burden is significant, especially when striving for low-cost systems, and has motivated the development of high-resolution and high-contrast adaptive beamforming methods. Here we show that deep neural networks, that adopt the algorithmic structure and constraints of adaptive signal processing techniques, can efficiently learn to perform fast high-quality ultrasound beamforming using very little training data. We apply our technique to two distinct ultrasound acquisition strategies (plane wave, and synthetic aperture), and demonstrate that high image quality can be maintained when measuring at low data-rates, using undersampled array designs. Beyond biomedical imaging, we expect that the proposed deep learning based adaptive processing framework can benefit a variety of array and signal processing applications, in particular when data-efficiency and robustness are of importance.

Lamb Waves and Adaptive Beamforming for Aberration Correction in Medical Ultrasound Imaging.

Phase aberration in transcranial ultrasound imaging (TUI) caused by the human skull leads to an inaccurate image reconstruction. In this article, we present a novel method for estimating the speed of sound and an adaptive beamforming technique for phase aberration correction in a flat polyvinylchloride (PVC) slab as a model for the human skull. First, the speed of sound of the PVC slab is found by extracting the overlapping quasi-longitudinal wave velocities of symmetrical Lamb waves in the frequency-wavenumber domain. Then, the thickness of the plate is determined by the echoes from its front and back side. Next, an adaptive beamforming method is developed, utilizing the measured sound speed map of the imaging medium. Finally, to minimize reverberation artifacts caused by strong scatterers (i.e., needles), a dual probe setup is proposed. In this setup, we image the medium from two opposite directions, and the final image can be the minimum intensity projection of the inherently co-registered images of the opposed probes. Our results confirm that the Lamb wave method estimates the longitudinal speed of the slab with an error of 3.5% and is independent of its shear wave speed. Benefiting from the acquired sound speed map, our adaptive beamformer reduces (in real time) a mislocation error of 3.1, caused by an 8 mm slab, to 0.1 mm. Finally, the dual probe configuration shows 7 dB improvement in removing reverberation artifacts of the needle, at the cost of only 2.4-dB contrast loss. The proposed image formation method can be used, e.g., to monitor deep brain stimulation procedures and localization of the electrode(s) deep inside the brain from two temporal bones on the sides of the human skull.

Direction of Arrival Estimation and Robust Adaptive Beamforming With Unfolded Augmented Coprime Array

An augmented coprime array systematically employs two sparse subarrays to produce a large-scale difference co-array with attractive merits, such as enhanced degrees of freedom (DOFs) and enlarged array aperture, whereas the interleaved subarrays are susceptible to mutual coupling. In this paper, we propose an unfolded augmented coprime array (UACA) obtained by careful crafting of small sparse subarrays to fill the holes in the difference co-array generated by unfolding operation. Specifically, UACA can significantly reduce the number of sensor pairs with small spacing and hence inherently weaken the mutual coupling effect. Meanwhile, an increase of the DOFs and improved direction of arrival (DOA) estimation accuracy can be achieved in the presence of mutual coupling. As an application of UACA, we propose a decoupled interference-plus-noise covariance matrix (INCM) reconstruction method for robust adaptive beamforming (RAB) with UACA. Therein, mutual coupling coefficients are estimated based on the remodeled contaminated steering vector and the noise subspace. The estimated mutual coupling matrix is utilized to reconstruct the decoupled covariance matrix which in turn is used to obtain refined DOA estimates, interferer power estimates, and the desired INCM. Extensive simulation results are provided to verify the effectiveness of UACA and the decoupled INCM reconstruction method for RAB.

Sparse Array Design for Adaptive Beamforming via Semidefinite Relaxation

In this letter, we propose a sparse array design method for adaptive beamforming in the presence of interferences. Our solution is based on finding the beamformer weight vector such that maximum output signal-to-interference-plus-noise ratio is attained. To control the sidelobes of the beampattern, quadratic fractional constraints are also introduced to optimize the beamformer weights. We formulate the array design problem as real-valued quadratically constrained quadratic program (QCQP) with reweighted l1-norm to promote sparsity. Moreover, we adopt semidefinite relaxation (SDR) and linear fractional SDR together to solve the QCQP problem. The resulting array yields excellent beamforming performance and a beampattern with low sidelobes. Numerical results demonstrate the effectiveness of the proposed sparse array design.

Robust Adaptive Beamforming Based on Linearly Modified Atomic-Norm Minimization With Target Contaminated Data

In practice, adaptive beamforming usually faces non-ideal situations where a limited number of snapshots are available, the training data are corrupted by desired target signals, and the array mismatches exist. Traditional methods often degrade significantly under the above situation. In order to solve this problem, a new adaptive beamforming method based on atomic-norm optimization technique is proposed in this paper. In the proposed method, the interference subspace is estimated by minimizing the rank of interference data matrix while making the signals bounded within a ball of Frobenius norm around the observed data. This non-convex problem is solved using alternative optimization which decomposes it into two iterative steps. Each step can be formulated as semi-definite programming, and solved efficiently. Unlike traditional methods, the proposed method can estimate the target signals, target directions, and interference subspace simultaneously. This property guarantees that the proposed beamformer is free from the influence of target signals, and able to adjust pointing direction adaptively. Then it is derived theoretically that the estimation of interference subspace in the proposed method is consistent, and bounded. A fast implementation algorithm based on alternating direction method of multipliers is also derived. Compared with traditional methods, the proposed method not only performs better with target-contaminated training data, and erroneous prior of target direction, but also requires much less snapshots to work. The effectiveness of the proposed method, and its advantages over traditional methods are verified based on simulated, and actual measured radar data.

A novel transcranial ultrasound imaging method with diverging wave transmission and deep learning approach

Real time brain transcranial ultrasound imaging is extremely intriguing because of its numerous applications. However, the skull causes phase distortion and amplitude attenuation of ultrasound signals due to its density: the speed of sound is significantly different in bone tissue than in soft tissue. In this study, we propose an ultrafast transcranial ultrasound imaging technique with diverging wave (DW) transmission and a deep learning approach to achieve large field-of-view with high resolution and real time brain ultrasound imaging. DW transmission provides a frame rate of several kiloHz and a large field of view that is suitable for human brain imaging via a small acoustic window. However, it suffers from poor image quality because the diverging waves are all unfocused. Here, we adopted adaptive beamforming algorithms to improve both the image contrast and the lateral resolution. Both simulated and in situ experiments with a human skull resulted in significant image improvements. However, the skull still introduces a wavefront offset and distortion, which degrades the image quality even when adaptive beamforming methods are used. Thus, we also employed a U-Net neural network to detect the contour and position of the skull directly from the acquired RF signal matrix. This approach avoids the need for beamforming, image reconstruction, and image segmentation, making it more suitable for clinical use.

A Low Complexity Robust Adaptive Beamforming Method with Orthogonality Constraint

Performance of many adaptive beamforming methods degrades when antenna array steering vector mismatch exists and popular optimization-based methods suffer from heavy computation complexity. In this paper, we investigate robust adaptive beamforming technique with low complexity. An optimization problem is constructed based on orthogonality constraint instead of conventional norm constraint; therefore, semidefinite programming (SDP) relaxation is avoided. We present the approach to obtain closed-form solution by imposing Lagrange multiplier methodology. Numerical experiments demonstrate that proposed low complexity method outperforms other previously developed beamforming methods and reduces computation time significantly.

New BSS‐based ABF for heterogeneous ionospheric clutter mitigation in HFSWR

Ionospheric clutter is detrimental to target detection in high-frequency surface-wave radar (HFSWR). Adaptive beamforming (ABF) has been adopted to suppress the ionospheric clutter in recent years. Unfortunately, the performance of ABF degrades due to the heterogeneity of the ionospheric clutter. In this study, a new approach is proposed to suppress the ionospheric clutter. A novel heterogeneous ionospheric clutter model based on the mixture of mutually independent ionospheric clutter sources is established. The blind source separation (BSS) approach is used to separate the clutter sources first. Then the separated components are exploited to estimate the spatial covariance matrix (SCM) of the cell under test. The SCM estimation based on BSS is more accurate than the classical sample matrix inversion method under the heterogeneous ionospheric clutter. Therefore, the ABF performance improves due to the better SCM estimation. The simulation and real data results demonstrated the effectiveness of the new BSS-based ABF method in HFSWR. The signal-to-clutter-plus-noise ratio of the new method improved compared with the traditional ABF based on the SMI method. The new method can help to detect targets under the heterogeneous ionospheric clutter. It may also be a promising methodology in other ABF applications.

Research on Frequency Domain Filtering Method Based on Frequency Response Zero Control Technology

Airspace adaptive beamforming has been widely used in radar anti-jamming. In this paper, by applying the appropriate model, the spatial adaptive beamforming method is applied to the time domain filtering to form an adaptive filter. For the filter, only the single frequency can form a null trap. This paper proposes a frequency response zero control technology. The broadband signal is filtered and achieved good results.

Robust adaptive beamforming method based on desired signal steering vector estimation and interference‐Plus‐noise covariance matrix reconstruction

Here, the authors propose a robust adaptive beamforming method based on desired signal steering vector estimation and interference-plus-noise covariance matrix reconstruction, so as to attenuate the influences of the desired signal steering vector mismatch and the limited training snapshots on the performance of adaptive beamformer. More precisely, the desired signal steering vector is estimated by minimising the sine value of the angle between the presumed desired signal steering vector and the eigenvectors of sample covariance matrix. Besides, the sample covariance matrix is reconstructed by reducing the dispersion extent of the noise eigenvalues and eliminating the desired signal component from the sample covariance matrix. The proposed method can not only accelerate the convergence speed of adaptive beamforming algorithm, but also avoid the desired signal cancellation phenomenon when the desired signal is present in the training snapshots. Simulation results demonstrate the superiority of the proposed method.

Robust adaptive beamforming method for large‐scale array with automatic diagonal loading and steering vector estimation

Here, the authors propose a novel robust adaptive beamforming method, which is robust to both of the covariance matrix mismatch and the steering vector estimation mismatch. Their method was based on a recently proposed adaptive beamforming technique for large-scale arrays. In this beamforming technique, a sparse sub-array having much smaller number of antenna elements is first selected from the original physical array to perform digital sampling, and then the beamforming coefficients for the original full array are calculated by using only the digital samples from the selected sub-array. In their robust method, they calculate the diagonal loading level automatically by using the spatial-matched method. Then, the steering vector of the desired signal is estimated by maximising the beamformer output power under a constraint that the estimated steering vector does not converge to any of the interference steering vectorsor their linear combinations. Numerical examples are provided to demonstrate the effectiveness of the proposed method against covariance matrix mismatch and steering vector error.

Robust adaptive beamforming using a novel signal power estimation algorithm

Recently, many robust adaptive beamforming (RAB) methods based on covariance matrix reconstruction have been proposed. Motivated by the idea, in this paper, a novel and efficient signal power estimator is devised to reconstruct the interference-plus-noise covariance (INC) matrix, with the corresponding RAB algorithm proposed. Firstly, the steering vectors of the incoming sources are derived using the Capon spatial spectrum and known array geometry. Secondly, a set of linear equations is established based on the signal subspace projection, from which the powers of the incoming sources are estimated. Based on the presumed angular sector of the signal-of-interest (SOI), the steering vectors and powers of the SOI and interferences are distinguished, and the INC matrix is then reconstructed. Finally, the beamformer is determined by the estimated INC matrix and SOI steering vector. The proposed algorithm is computationally more efficient than other reconstruction-based methods because there are closed-form solutions for the signal powers. Simulation results indicate that our proposed algorithm performs better than the existing methods at high signal-to-noise ratios (SNRs), and achieves nearly optimal performance across a wide range of SNR.

Robust Wideband Adaptive Beamforming With Null Broadening and Constant Beamwidth

In the cases of rapidly moving interference and look-direction error, robustness and output signal to interference and noise ratio (SINR) of conventional wideband adaptive beamforming methods are degraded severely. In order to solve these problems, a robust wideband adaptive beamforming with null broadening and constant beamwidth is proposed. We first propose a taper matrix constructed by adding virtual interferences for null broadening, where the reference frequency and number of virtual interferences of taper matrix are determined based on numerical methods. This is followed by reconstructing the array covariance matrix based on taper matrix. Spatial response variation (SRV) constraint is then applied for a constant beamwidth over the entire frequency band. Finally, the adaptive weight vector for null broadening and constant beamwidth is obtained by using Lagrange multiplier method. The effectiveness of proposed method is verified by numerical simulations.

Fast and robust adaptive beamforming method based on complex‐valued RBF neural network

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.

Singular value decomposition filter for speckle reduction in adaptive ultrasound imaging

Various adaptive beamforming methods have been developed recently for improvement of image quality in medical ultrasonic imaging. Such adaptive beamformers improve the spatial resolution and contrast, but often degrade the contrast-to-noise ratio (CNR) because speckles are well-resolved owing to improvement in the spatial resolution. For improvement of CNR, speckle reduction techniques are required. However, a typical smoothing filter, such as a Gaussian filter, blurs the boundary between different structures in an ultrasonic image. In the present study, a filter based on singular value decomposition was developed for improvement in CNR, while the sharpness of the boundary between different stucutures is preserved. The proposed method was evaluated by a basic experiment using a phantom with an anechoic cyst region. The CNR was improved from 2.93 to 11.06 dB by the proposed method.

Robust adaptive beamforming for fast moving interference based on the covariance matrix reconstruction

Adaptive beamforming methods are sensitive to underlying assumptions on the environment, sources, or sensor array violation, especially when interferences are moving fast. In this study, the non-stationary interference source is estimated during the period in which snapshots are taken. Then, a new interference-plus-noise covariance matrix reconstruction is introduced which is derived from a simplified power spectral density function that can be used to shape the directional response of the beamformer. Finally, the beamformer is designed to impose nulls towards the regions of the moving interference based on the reconstructed covariance matrix. The essence of the proposed method is to express the inverse of the reconstructed covariance matrix which needs less computational complexity calculation. The effectiveness of the proposed method is demonstrated by numerical results.

Low‐complexity robust adaptive beamforming method for MIMO radar based on covariance matrix estimation and steering vector mismatch correction

In this study, the authors consider a low-complexity robust adaptive beamforming problem in a collocated multiple-input multiple-output (MIMO) radar. This study is motivated by the fact that in practical applications, the conventional adaptive beamforming algorithm for MIMO radar requires a large computational complexity and suffers from a great performance degradation because of the finite number of training snapshots, the desired signal steering vector mismatch and the corruption of training data by the desired signal. Since the dimension of the virtual steering vector of the MIMO radar is relatively large, the proposed method can estimate the covariance matrix by using a low-complexity method to effectively improve the computational efficiency of the adaptive beamforming algorithm and the robustness of the beamformer against the covariance matrix uncertainty. Besides, based on the estimated covariance matrix, the proposed method can also correct the desired signal steering vector mismatch to efficiently prevent the desired signal cancellation phenomenon. Simulation results demonstrate that the performance of the proposed method is always close to that of the optimal processing in a wide range of signal-to-noise ratio or of the number of training snapshots.