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Obtaining the signal steering vector (SV) in array perturbation scenarios is vital for an adaptive beamformer. Recently, a robust Capon beamformer (RCB)-like SV estimation (RCB-SVE) method has been given to optimize the SV by maximizing the signal of interest spectrum with an uncertainty set constraint. However, the SV solution to this method cannot be acquired in a closed form and therefore, leading to difficult applications. To address this issue, in this paper, we propose a closed-form expression of the RCB-SVE, which is based upon the Lagrange multiplier method. In particular, to accurately calculate the Lagrange multiplier, we take advantage of a high-order polynomial rooting scheme to get the unique Lagrange multiplier by using its positive feature. The aforesaid steps are free of any approximation or iteration processing. Typical experiments have verified that the proposed beamformer is more effectively implemented than the RCB-SVE and enjoys satisfactory SV estimation results in general array perturbation scenarios. [ABSTRACT FROM AUTHOR]

In order to compensate for high path loss, massive multiple-input multiple-output (MIMO) has been adopted in wireless communication systems operating at millimeter-wave (mmWave) bands. In particular, analog beamformer has been employed in hybrid massive MIMO systems to reduce the cost caused by radio frequency (RF) chains. However, due to hardware limitation, only conventional beamformer can be used at base station (BS) in existing hybrid massive MIMO systems, and as a consequence, inter-user-interference (IUI) cannot be removed completely in the presence of multiple users because of the sidelobe of conventional beamformer. In this letter, we will show that by utilizing the reconstructed spatial covariance matrix (SCM), adaptive beamformer can be also used at the BS in hybrid massive MIMO systems. Thanks to the reconstructed SCM, nulling directions of the adaptive beamformer can be adjusted adaptively to the directions of non-desired users, and therefore the residual IUI can be effectively removed. Simulation results show that the adaptive beamformer can outperform the conventional beamformer significantly in hybrid massive MIMO systems. [ABSTRACT FROM AUTHOR]

In a dynamic environment, close-range and fast-moving interferers transit the resolution cells rapidly, challenging the minimum variance distortionless response (MVDR) beamformer’s ability to place accurate notches in each interferer’s direction. One common approach to overcome this problem is to apply a broader or wider notch at the interferer location. The hybrid double zero (HDZ) MVDR beamformer is a simple and robust method to form a wider notch by implicitly generating second-order notches in the beampattern. The HDZ beampattern is a product of adaptive and fixed factors. The adaptive component has wide second-order notches to suppress moving interferers, while the fixed component improves the white noise gain (WNG) and ensures the array weight vector length matches the array size. However, the challenge for the HDZ beamformer is choosing the ideal number of second-order notches to suppress the moving interferers in a dynamic environment. In practice, the number of moving interferers is unknown and may also change over time. Therefore, an HDZ beamformer with a fixed number of second-order notches may not effectively suppress all the moving interferers if the number of interferers surpasses the number of second-order notches. The need for a time-varying number of second-order notches leads us to design a universal HDZ (UHDZ) beamformer that is universal over this parameter. The UHDZ beamformer rivals the best beamformer in a set of HDZ beamformers with a fixed number of second-order notches without needing prior knowledge of the number of moving interferers or the environment. This paper evaluates the performance of the UHDZ beamformer in simulations and microphone array experiments that include multiple moving interferers.

Although the use of coherent plane wave compounding is a promising technique for enabling the attainment of very high frame rate imaging, it achieves relatively low image quality because of data-independent reconstruction. Adaptive beamformers rather than delay-and-sum (DAS) conventional techniques have been proposed to improve the imaging quality. The minimum variance (MV) and delay-multiply-and-sum (DMAS) beamformers have been validated as effective in improving image quality. The MV improves mainly the resolution of the image, while being computationally expensive and having little impact on contrast. The DMAS increases the contrast while over-suppressing the speckle region in the case of 2-D summation for multi-transmission applications. In a new approach, a beamformer based on MV and DMAS is proposed to enhance both spatial resolution and contrast in plane wave imaging. Prior to estimating the weight vector of MV, the backscattered echoes are decorrelated without any spatial smoothing. This enhances the robustness of MV without compromising the improvement in resolution. With a shift from element space to beamspace, MV weights are calculated using the spatial statistics of a set of orthogonal beams, which allows the high-complexity algorithm to be run faster. After that, the MV weights are applied to the DMAS output vector beamformed over different transmissions. The proposed method can result in better contrast resolution, thereby avoiding over-suppression. The complexity of the applied DMAS version is also similar to that of DAS. Imaging results reveal that the proposed method offers improvements over the traditional compounding method in terms of spatial and contrast resolution. It also can achieve a higher image quality compared with some existing adaptive methods applied in the literature. [ABSTRACT FROM AUTHOR]

Abstract Background The minimum variance (MV) beamformer can significantly improve the image resolution in ultrasound imaging, but it has limited performance in noise reduction. We recently proposed the covariance matrix-based statistical beamforming (CMSB) for medical ultrasound imaging to reduce sidelobes and incoherent clutter. Methods In this paper, we aim to improve the imaging performance of the MV beamformer by introducing a new pixel-based adaptive weighting approach based on CMSB, which is named as covariance matrix-based adaptive weighting (CMSAW). The proposed CMSAW estimates the mean-to-standard-deviation ratio (MSR) of a modified covariance matrix reconstructed by adaptive spatial smoothing, rotary averaging, and diagonal reducing. Moreover, adaptive diagonal reducing based on the aperture coherence is introduced in CMSAW to enhance the performance in speckle preservation. Results The proposed CMSAW-weighted MV (CMSAW-MV) was validated through simulation, phantom experiments, and in vivo studies. The phantom experimental results show that CMSAW-MV obtains resolution improvement of 21.3% and simultaneously achieves average improvements of 96.4% and 71.8% in average contrast and generalized contrast-to-noise ratio (gCNR) for anechoic cyst, respectively, compared with MV. in vivo studies indicate that CMSAW-MV improves the noise reduction performance of MV beamformer. Conclusion Simulation, experimental, and in vivo results all show that CMSAW-MV can improve resolution and suppress sidelobes and incoherent clutter and noise. These results demonstrate the effectiveness of CMSAW in improving the imaging performance of MV beamformer. Moreover, the proposed CMSAW with a computational complexity of $$O(N^2)$$ O ( N 2 ) has the potential to be implemented in real time using the graphics processing unit.

Adaptive antenna array employing phase shifters only can reduce the hardware cost and power consumption, but the related optimization is well understood to be difficult to solve. In this paper, we examine the use of both continuous phase shifters (CPS) and discrete phase shifters (DPS) in antenna array for adaptive interference suppression. First, we formulate the phase-only tuning problem with CPS via quadratically constrained quadratic program (QCQP), which can be approximated through semidefinite relaxation (SDR) and solved by convex-optimization solvers efficiently. We also demonstrate that quantizing such results directly may not necessarily give acceptable performance. Then, we propose to use binary quadratic program (BQP) for the optimization of the adaptive beamformer utilizing DPS with an arbitrary number of control bits to specify the phase-shift levels. The resultant BQP can be relaxed and solved efficiently too. Moreover, due to the similarity between the CPS and DPS formulation, we can mix them in a single beamforming scheme to provide additional compromises between the output signal-to-interference and noise ratio (SINR) performance and implementation cost. Simulations show that in the considered interference-limited environment, our proposed beamformers with CPS, DPS, and hybrid phase shifters (HPS) give desirable results as expected.

Background: The minimum variance (MV) beamformer can significantly improve the image resolution in ultrasound imaging, but it has limited performance in noise reduction. We recently proposed the covariance matrix-based statistical beamforming (CMSB) for medical ultrasound imaging to reduce sidelobes and incoherent clutter.Methods: In this paper, we aim to improve the imaging performance of the MV beamformer by introducing a new pixel-based adaptive weighting approach based on CMSB, which is named as covariance matrix-based adaptive weighting (CMSAW). The proposed CMSAW estimates the mean-to-standard-deviation ratio (MSR) of a modified covariance matrix reconstructed by adaptive spatial smoothing, rotary averaging, and diagonal reducing. Moreover, adaptive diagonal reducing based on the aperture coherence is introduced in CMSAW to enhance the performance in speckle preservation.Results: The proposed CMSAW-weighted MV (CMSAW-MV) was validated through simulation, phantom experiments, and in vivo studies. The phantom experimental results show that CMSAW-MV obtains resolution improvement of 21.3% and simultaneously achieves average improvements of 96.4% and 71.8% in average contrast and generalized contrast-to-noise ratio (gCNR) for anechoic cyst, respectively, compared with MV. in vivo studies indicate that CMSAW-MV improves the noise reduction performance of MV beamformer.Conclusion: Simulation, experimental, and in vivo results all show that CMSAW-MV can improve resolution and suppress sidelobes and incoherent clutter and noise. These results demonstrate the effectiveness of CMSAW in improving the imaging performance of MV beamformer. Moreover, the proposed CMSAW with a computational complexity of [Formula: see text] has the potential to be implemented in real time using the graphics processing unit. [ABSTRACT FROM AUTHOR]

In the field of adaptive array signal processing, MVB is a classic and effective interference cancellation technology. Under the ideal assumption, the anti-jamming performance of minimum variance beamformer (MVB) increases with the increase in the number of antenna elements. However, due to the limited sample effect of the sample covariance matrix, there is a certain upper limit of MVB performance in practical application, which means that the signal-to-interference-and-noise ratio (SINR) will not be further improved by increasing the number of antenna elements. This paper analyzes the reasons for the upper bound of MVB performance and proposes a feasible enhanced cascaded beamformer scheme. By combining adaptive beamformer with fixed beamformer, the near-optimal SINR is achieved. Finally, the effectiveness of the proposed algorithm is verified by computer simulation. [ABSTRACT FROM AUTHOR]

Recent proposals of deep learning-based beamformers for ultrasound imaging (US) have attracted significant attention as computational efficient alternatives to adaptive and compressive beamformers. Moreover, deep beamformers are versatile in that image post-processing algorithms can be readily combined. Unfortunately, with the existing technology, a large number of beamformers need to be trained and stored for different probes, organs, depth ranges, operating frequency, and desired target ‘styles’, demanding significant resources such as training data, etc. To address this problem, here we propose a switchable and tunable deep beamformer that can switch between various types of outputs such as DAS, MVBF, DMAS, GCF, etc., and also adjust noise removal levels at the inference phase, by using a simple switch or tunable nozzle. This novel mechanism is implemented through Adaptive Instance Normalization (AdaIN) layers, so that distinct outputs can be generated using a single generator by merely changing the AdaIN codes. Experimental results using B-mode focused ultrasound confirm the flexibility and efficacy of the proposed method for various applications. [ABSTRACT FROM AUTHOR]

Plane-wave compounding is an active topic of research in ultrasound imaging because it is a promising technique for ultrafast ultrasound imaging. Unfortunately, due to the data-independent nature of the traditional compounding method, it imposes a fundamental limit on image quality. To address this issue, adaptive beamformers have been implemented in the compounding procedure. In this article, a new adaptive beamformer for the 2-D data set obtained from multiple plane-wave transmissions is investigated. In the proposed scheme, the minimum variance (MV) weights are applied to the backscattered echoes. Then, the final image is obtained by employing a modified version of the delay multiply-and-sum (DMAS) beamformer in the coherent compounding. The results demonstrate that the presented MV-DMAS scheme outperforms the conventional coherent compounding in both terms of resolution and contrast. It also offers improvements over the 2-D-DMAS and some MV-based methods presented in the literature, such that it achieves at least 20.9% enhancement in sidelobe reduction compared with the best result of MV-based methods. Also, by the proposed method, the in vivo study shows an improved generalized contrast-to-noise ratio (GCNR) that implies a higher probability of lesion detection. [ABSTRACT FROM AUTHOR]

The present work introduced an adaptive beamformer based on a Fibonacci branch search (FBS) based heuristic algorithm is proposed for uniform linear arrays. The proposed optimization technique inspired by the Fibonacci sequence principle, designated Fibonacci branch search (FBS), used the new tree's fundamental branch structure and interactive searching rules to obtain the global optimal solution in the search space. The branch structure of FBS is selected by two types of multidimensional points on the basis of the shortening fraction formed by the Fibonacci sequence; in this mode, interactive global and local searching rules are implemented alternately to reach optimal solutions, avoiding stagnating in local optima. The proposed FBS is also used to construct an adaptive beamforming technique as a real-time implementation to achieve near-optimal performance due to its simplicity and high convergence; the performance of FBS is compared with that of five typical heuristic optimization algorithms. Simulation results demonstrate the superiority of the proposed FBS approach in locating the optimal solution with higher precision and further improvement in the adaptive beamforming performance.

Hearing loss is one of the most common chronic diseases. For people with hearing loss, communicating with other people, particularly in an environment with considerable background noise, is difficult. Recently, several hearing aids have been developed to improve speech comprehension in a noisy environment. The use of an adaptive beamformer is one of the alternative methods for improving speech intelligibility. However, the adaptive beamformer requires the location of the desired speaker to estimate the time differences of arrival (TDOAs) of speech sources to numerous spatially separated sensors in acoustics. In general, the technique of steered response power source localization was used to estimate the TDOA; however, this technique was easily affected by environmental reverberation. To overcome the aforementioned concern, a novel hearing aid is proposed in this paper. By using an image processing technology, the location of the desired speaker could be manually selected to provide precise information on the TDOA. Moreover, adaptive signal enhancements were implemented in a field-programmable gate array to enhance the speech of interest in real time. The experimental results indicate that the proposed system could improve speech intelligibility in various noisy environments. Therefore, the proposed system may be employed to improve the daily lives of people with hearing the loss in the future.

To develop an adaptive beamformer against the signal of interest (SOI) steering vector mismatch, a robust Capon beamformer (RCB) like steering vector estimation method based on the interference matrix reduction is proposed. Different from the RCB and its modified versions that optimize the SOI steering vector with the Capon power estimator, this article designs an SOI power estimator to formulate the steering vector optimization problem with an uncertainty set constraint. In terms of that, the unknown SOI covariance matrix is needed to realize the SOI power estimator, an efficient interference matrix reconstruction way via SOI blocking and matrix eigen-transition is exploited to reduce the interference component from the sample covariance matrix. Herein, after solving the given steering vector optimization problem and adding the noise component to the aforesaid interference matrix, the weight vector of the derived algorithm is, thereby, computed using the estimated SOI steering vector and interference covariance matrix. The proposed method only requires the source number and prior direction of the SOI. The numerical simulations show that the proposed approach can outperform the compared ones with reduced complexity in the situation of various steering vector mismatches. [ABSTRACT FROM AUTHOR]

In ultrasound (US) imaging, various types of adaptive beamforming techniques have been investigated to improve the resolution and the contrast-to-noise ratio of the delay and sum (DAS) beamformers. Unfortunately, the performance of these adaptive beamforming approaches degrades when the underlying model is not sufficiently accurate and the number of channels decreases. To address this problem, here, we propose a deep-learning-based beamformer to generate significantly improved images over widely varying measurement conditions and channel subsampling patterns. In particular, our deep neural network is designed to directly process full or subsampled radio frequency (RF) data acquired at various subsampling rates and detector configurations so that it can generate high-quality US images using a single beamformer. The origin of such input-dependent adaptivity is also theoretically analyzed. Experimental results using the B-mode focused US confirm the efficacy of the proposed methods. [ABSTRACT FROM AUTHOR]

• The ULA can be represented in terms to two smaller virtual ULAs (VULAs) using the Kronecker product. • MVDR adaptive beamformers are obtained separately for the VULAs, and combined using the Kronecker product to obtain the full-length KP-MVDR beamformer. • Implementing the fixed DS beamformer on one VULA and the MVDR adaptive beamformer on the other results in the KP-DS-MVDR and KP-MVDR-DS hybrid beamformers. • The Kronecker product beamformers are more robust to errors in the statistical estimates of the data, and provide superior performances to the conventional DS and MVDR beamformers. • The Kronecker product beamformers require less data (faster convergence) to achieve their steady state performances compared to the conventional MVDR beamformer. This work presents a Kronecker product based methodology of frequency-domain beamforming of large sensor arrays for far-field broadband speech signals. The principal idea involves splitting up a given uniform linear array (ULA) into two smaller virtual ULAs (VULAs), using the Kronecker product. The linear system of the original ULA is bifurcated into two smaller linear systems of the VULAs. Henceforth, traditional adaptive beamformers such as the minimum-variance-distortionless-response (MVDR) beamformer may be obtained for each of the VULAs, using lesser data to estimate the statistics. The short-length beamformers, obtained from the VULAs, are finally combined by the Kronecker product to derive the full-length Kronecker product beamformer. Additionally, the VULAs allow fixed and adaptive beamforming to be implemented separately on each of them. As fixed beamformers do not employ statistical information, the Kronecker product hybrid beamformers reduce the original linear system to just a small linear system involving one VULA. Accordingly, hybrid beamformers may be implemented using traditional fixed beamformers, such as the delay-and-sum (DS) beamformer, on one VULA, and traditional adaptive beamformers, such as the MVDR, on the other. The proposed Kronecker product beamformers are observed to provide faster convergence and superior robustness with respect to the traditional beamformers. [ABSTRACT FROM AUTHOR]

This paper proposes a new division-free generalized sidelobe canceller-based adaptive beamformer and its efficient hardware realization. A discrete cosine transform-based blocking matrix is proposed for uniform linear array to decorrelate the input so as to achieve a faster convergence speed. A new variable step-size least mean squares algorithm for complex input is proposed to further improve the convergence and the steady-state performance of the adaptive beamformer. Moreover, a variable regularization scheme is incorporated to mitigate possible signal cancellation due to possible mismatches in steering vector. Furthermore, a statistical analysis on the mean and mean squares convergence of the algorithm is performed and validated using Monte Carlo simulations. An efficient architecture of the proposed adaptive beamformer is also proposed for its real-time implementation. It employs a novel division-free approach by quantizing the normalization factor into a limited number of levels so that the division can be implemented using canonical signed digits, resulting in multiplier-less realization. The performance of the resultant division-free implementation can achieve similar convergence and steady-state performance as a conventional divider approach while achieving at least 21% less hardware resources and 26.85% higher operating speed in Xilinx Virtex7 (XC7VX330T) field programming gate array for an eight-sensor uniform linear array. Finally, the beam can be stabilized remarkably in only 1 μs at a system clock frequency of 124 MHz.

Although the minimum variance beamformer (MVB) shows a significant improvement in resolution and contrast in medical ultrasound imaging, its high computational complexity is a major problem in a real-time imaging system. Therefore, it seems necessary to propose a new method with a lower computational complexity that preserves the advantages of the MVB. In this paper, the MVB was implemented with a partial generalized sidelobe canceler (GSC) with a blocking matrix based on our previous study, which projected the incoming signals to a lower dimensional space. The partial GSC separated the weight vector into one fixed and one adaptive weight, whereby the optimization could be performed with lower complexity on the adaptive part. In addition, this dimension reduction allowed us to increase the length of the subarray when using a spatial smoothing method, which was used to decorrelate the incoming signals. The subarray length was limited to half the length of the full array size in the ordinary MVB, while the proposed beamformer could cross over this limitation. The results demonstrated that the point spread function of the proposed beamformer was about 6.3 times narrower than the classic MVB, while the contrast was almost saved. These results were achieved with linear computational complexity by the proposed method, while it was cubic for the MVB. For a sample scenario, the proposed method needed only 1.8% of the required ops of the MVB. [ABSTRACT FROM AUTHOR]

A key requirement of an adaptive sensor array involves the ability to deterministically adjust the directional response of the array to reduce noise and reverberations, null interferences, and enhance the gain and recognition of the desired signal. This paper presents a low-carbon adaptive broadband beamforming algorithm called the regulated-element Frost beamformer. It enhances the desired signal based on the noise conditions of the individual omnidirectional sensors deployed in a complex dynamic environment that is prone to steering errors. The investigation of this algorithm was carried out in an interference-dominant, noisy automobile environment characterized by diffuse noise conditions. An embedded system measurement of real-time signals was carried out using omnidirectional acoustic sensors mounted in a model convertible F-Type car driven at speed limits of 20 to 50 mph. The simulation results indicate an array gain enhancement of 2 dB higher than the conventional Frost beamformer and it requires less sensors and filter taps for real-time reconfigurable implementations. The experimental results reveal that the average array gain of the regulated-element beamformer is 2.9 dB higher than the conventional Frost beamformer response. The minimum floor array gain of the regulated-element beamformer is 5 dB, representing 70% noise reduction than the conventional adaptive beamformers.

Objective: Adaptive beamformer methods that have been extensively used for functional brain imaging using EEG/MEG (magnetoencephalography) signals are sensitive to model mismatches. We propose a robust minimum variance beamformer (RMVB) technique, which explicitly incorporates the uncertainty of the lead field matrix into the estimation of spatial-filter weights that are subsequently used to perform the imaging. Methods: The uncertainty of the lead field is modeled by ellipsoids in the RMVB method; these hyperellipsoids (ellipsoids in higher dimensions) define regions of uncertainty for a given nominal lead field vector. These ellipsoids are estimated empirically by sampling lead field vectors surrounding each point of the source space, or more generally by building several forward models for the source space. Once these uncertainty regions (ellipsoids) are estimated, they are used to perform the source-imaging task. Computer simulations are conducted to evaluate the performance of the proposed RMVB technique. Results: Our results show that robust beamformers can outperform conventional beamformers in terms of localization error, recovering source dynamics, and estimation of the underlying source extents when uncertainty in the lead field matrix is properly determined and modeled. Conclusion: The RMVB can be substituted for conventional beamformers, especially in applications where source imaging is performed off-line, and computational speed and complexity are not of major concern. Significance: A high-quality source imaging can be utilized in various applications, such as determining the epileptogenic zone in medically intractable epilepsy patients or estimating the time course of activity, which is a required step for computing the functional connectivity of brain networks. [ABSTRACT FROM AUTHOR]

A novel feedback beamformer is proposed for receiving multipath coherent signals. First, a subtraction-based minimum variance distortionless response beamformer is utilized to obtain an estimation of the desired signal. Then its output is fed back to the original full aperture array where a minimum mean square error (MMSE) beamformer is applied. Due to multipath-matched feature of the MMSE beamformer, the novel feedback beamformer can combine multipath signals without aperture loss. Two feedback schemes are proposed and their effectiveness is verified via simulation. [ABSTRACT FROM AUTHOR]

Minimum variance beamformer (MVB) improves the resolution and contrast of medical ultrasound images compared with delay and sum (DAS) beamformer. The weight vector of this beamformer should be calculated for each imaging point independently, with a cost of increasing computational complexity. The large number of necessary calculations limits this beamformer to application in real-time systems. A beamformer is proposed based on the MVB with lower computational complexity while preserving its advantages. This beamformer avoids matrix inversion, which is the most complex part of the MVB, by solving the optimization problem iteratively. The received signals from two imaging points close together do not vary much in medical ultrasound imaging. Therefore, using the previously optimized weight vector for one point as initial weight vector for the new neighboring point can improve the convergence speed and decrease the computational complexity. The proposed method was applied on several data sets, and it has been shown that the method can regenerate the results obtained by the MVB while the order of complexity is decreased from O(L3) to O(L2). [ABSTRACT FROM AUTHOR]