Minimum Variance Distortionless Response Method Research Articles

Improved Beamforming in 3D Space Applied to Realistic Planar Antenna Arrays by Using the Embedded Element Patterns

Most of beamforming methods rely on the proper estimation of the steering vectors of the incoming signals in order to calculate appropriate array feeding weights. However, this estimation is often performed on a theoretical basis, since most methods assume that the array elements radiate like isotropic sources and consider only the phase differences between them due to their different spatial positions. This is a rough estimation as it ignores both the non-isotropic radiation pattern of the array elements and the mutual coupling between them. To overcome these limitations, we use a different approach for the construction of steering vectors based on the embedded patterns of the array elements, extracted through full-wave analysis. This approach is used in this paper to modify two well-known beamforming methods, namely the null steering beamforming and the minimum variance distortionless response method. Both modified methods are applied to a realistic model of a microstrip planar antenna array, and thus, both the azimuth and polar angles of the main lobe and nulls directions are controlled (beamforming in 3D space). Extensive statistical analyses are performed by implementing several scenarios of escalating difficulty, in order to examine the performance and temporal response of the modified beamforming methods in comparison to the respective conventional methods and also in comparison to beamforming methods based on evolutionary techniques.

Lamb wave imaging based on multi-frequency sparse decomposition

Based on the assumption of damage sparsity, scattering signals can be directly sparsely decomposed in the time domain to obtain the scattering coefficients to generate images for indicating damage, which has been comprehensively studied in recent years. However, in these previous studies, the dimension of the constructed dictionary matrix is proportional to the product of the number of discrete imaging points and the signal length, which will cause the “dimensional disaster” problem. Considering the energy and useful information of the received Lamb wave signals are limited within a certain frequency bandwidth, a Lamb wave imaging method based on multi-frequency sparse decomposition in the frequency domain is proposed for damage localization in isotropic plate-like structures. A sparse representation model for the scattering signals in the frequency domain is established based on the constructed frequency domain dictionary matrix. Each single frequency component of the scattering signals obtained from the sensor array is sparsely decomposed one by one to obtain the frequency-dependent scattering coefficients. After that, images indicating damage locations can be generated by fusing the multi-frequency scattering coefficients. Both numerical simulations and experiments on aluminum plates are implemented to validate the proposed method, which provides an alternative tool for Lamb wave based damage localization. Results with a higher signal-to-noise ratio, fewer artifacts, and lower background noise are obtained compared with the conventional delay-and-sum and minimum variance distortionless response methods.

Multi-beam symbol-level secure transmission against hybrid eavesdropping

In this paper, we consider a physical layer security (PLS) problem for a hybrid wiretapping wireless system in millimeter-wave transmission, where the active eavesdropper and passive eavesdropper (Eve) may coexist to intercept the confidential messages and emit jamming signals. To achieve secure and reliable transmission, we propose a switched phased-array directional modulation (DM) scheme that employs multi-beam symbol-level precoding with aided artificial noise (AN) technique at the transmitter, and array reception at legitimate users (LU). Here we consider a more practical case that the information of the eavesdropper (Eve) is unknown by the transmitter. Leveraging DM beamforming, we aim to minimize transmit message power by optimizing the beamforming vector, subject to prescribed symbol-level constraints, thus generating exact/relaxed phases at LU. The remaining transmit power can be utilized to generate AN. Additionally, by means of the minimum variance distortionless response method at the LU, the jamming caused by active Eve can be efficiently eliminated. Simulation results demonstrate the superiority of the proposed scheme.

MVDR Beamformer Design by Imposing Unit Circle Roots Constraints for Uniform Linear Arrays

A 2004 paper had offered a theoretical proof that ideally the roots of the minimum variance distortionless response (MVDR) beamformer array polynomial lie on the unit circle (UC). However, existing MVDR methods fail to exploit this fundamental property adequately. This paper proposes a new adaptive beamforming design via UC roots optimization for uniform linear arrays (ULA). The proposed method starts with the sample matrix inversion (SMI) roots and optimizes the MVDR criterion for each root separately by splitting the $N$ -dimensional MVDR problem into multiple 1-D optimization problems. Conjugate symmetry is imposed on individual 1st-order factors of the MVDR polynomial during optimization that guarantees UC roots. The proposed UC Roots Constrained MVDR (UCRC-MVDR) method is non-iterative and has a closed-form solution. It also works well with limited number of snapshots. UCRC-MVDR is computationally efficient and parallelizable as all roots can be optimized concurrently. In extensive simulation studies, UCRC-MVDR exhibits consistently superior performance over existing MVDR approaches, and its performance is closer to the ideal clairvoyant case than existing MVDR methods.

Joint Design of the Transmit and Receive Beamforming in MIMO Radar Systems

In this paper, we investigate the problem of joint design of the transmit and receive beamforming weight vectors for multiple-input multiple-output (MIMO) radar systems in the presence of signal-dependent interference, which is distinct from its existing counterparts focusing on joint design of the temporal codes of transmit waveforms and spatial-temporal receive filter. The design problem is formulated as output signal-to-interference-plus-noise ratio (SINR) maximization subject to a similarity constraint on the transmit beamforming weight, such that a good transmit beampattern can be guaranteed. Due to the existence of signal dependence, the resultant problem is NP-hard, and therefore, an iterative scheme is devised. Specifically, in each iteration, the receive beamforming is optimized with the minimum variance distortionless response method, then the transmit beamforming is obtained via the semidefinite relaxation (SDR) technique. It is proved that the proposed SDR-based algorithm is able to produce a rank-one solution. Numerical simulations are provided to demonstrate the effectiveness of the proposed algorithm.

Damage imaging for composite using Lamb wave based on minimum variance distortion-less response method

It is highly probable for the structures of carbon fiber reinforced plastics (CFRP) to suffer from invisible impact damage, for which the identification of such damage is of great significance. For the purpose of damage localization, this paper proposes a minimum variance distortion-less response (MVDR) algorithm that employs linear array sensor. In addition, a near field signal model based on active Lamb wave is established and the propagation of Lamb wave is investigated in composite laminates through the method of simulation. Moreover, a damage imaging system is also set up for composites to verify the effectiveness of the MVDR algorithm. Besides, in the study, wavelet transform is used as well to extract narrowband signals and promote signal-to-noise. It is shown by the results that the proposed algorithm can accurately identify the location of damage through the method of imaging. It is concluded that the maximum error of damage identification is 1.2 cm and MVDR algorithm has great potential in the field, damage imaging of composite materials. As a result, it provides a novel idea for damage imaging of composite materials.

Resolution improvement of dipole source localization for artificial lateral lines based on multiple signal classification

The lateral line is a critical mechanosensory organ that enables fish to perceive the surroundings accurately and rapidly. Massive efforts have been made to build an artificial lateral line system rivaling that of fish for underwater vehicles. Dipole source localization has become a standard problem for evaluating the sensing capabilities of the developed systems. In this paper we propose, for the first time, the multiple signal classification (MUSIC) method in order to achieve high-resolution dipole source localization based on spatial spectrum estimation. We also present the minimum variance distortionless response (MVDR) by making an improvement to the previous Capon’s method. Experiments are conducted on a linear prototype of lateral line canal and the localization performance of these two methods are compared. The results show that the MUSIC method provides an overall localization resolution improvement of 10.4% and maintains a similar level of localization accuracy compared with the MVDR method. Further studies show that the MUSIC method has the potential of localizing two closer incoherent dipole sources with a minimum lateral separation of 20 mm, versus 70 mm for the MVDR method, at a dipole-array distance of half the array length. Both localization methods have strong robustness to the vibrational state of the dipole source. Our work provides a promising and robust way to meet the high-resolution and multi-source sensing requirements of underwater vehicles.

Spectrally Compatible Waveform Design for MIMO Radar in the Presence of Multiple Targets

This paper investigates the problem of the spectrally compatible waveform design for multiple-input multiple-output (MIMO) radar in the presence of multiple targets and signal-dependent interference. Unlike the existing approaches to designing the waveform for a single target via output signal-to-interference-plus-noise ratio (SINR) maximization, a new method is proposed to deal with a more general problem, i.e., designing a spectrally compatible waveform for multiple targets, by minimizing the waveform energy of the overlayed space-frequency bands under constraints of waveform similarity and individual SINR requirements. Due to the existence of signal dependence, the formulated optimization problem is NP-hard. Toward this end, an iterative algorithm is developed. Concretely, at each iteration, the receive filter is first obtained with the aid of the minimum variance distortionless response method, then the transmit waveform is optimized by employing the dual ascent method. Both the convergence and asymptotic optimality of this algorithm are discussed. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach.

Magnitude Square Coherence (MSC) Estimation via an ARMA Model Based on Analytic DCT and Group Delay

A new method of magnitude square coherence (MSC) estimation by an auto-regressive moving average (ARMA) model based on analytic discrete cosine transform (ADCT) and group delay (GD) property is proposed. The estimation is achieved by modeling the Welch-MSC derived from ADCT and the ARMA model realized by GD. The ADCT provides twice frequency resolution and reduced variance compared to those of conventional DFT. The proposed MSC estimate is superior to that based on MSC estimation using DFT, in terms of normalized sum of the sample mean square error (NSSMSE), maximum sample root-mean-square error and bias. The proposed method for the two examples involving two stationary stochastic processes reduces the NSSMSE by 60 and 30% over those of ARMA-MSC based on DFT. Further, the Welch-MSC based on ADCT itself reduces the performance indices over that based on DFT (significant for example-2). The proposed method is also applied to signals with sinusoids whose frequencies are located at off the DFT grid bin and closely spaced. The minimum variance distortionless response method of MSC estimation known for its frequency resolution fails to detect and resolve closely spaced off bin frequencies, whereas the proposed ADCT-based Welch-MSC and its ARMA detect and resolve those frequencies. The DFT-based Welch-MSC and its ARMA version though detect off the bin sinusoids, but due to their poor frequency resolution cannot resolve the closely spaced sinusoids. The average variance per frequency bin of ADCT-ARMA and DFT-ARMA is 0.0061 and 0.0108 (i.e., 43.52% reduction by ADCT), respectively.

Optimizing passive cavitation mapping by refined minimum variance-based beamforming method: Performance evaluations in macaque models

Microbubble-mediated focused ultrasound (FUS) therapies harness mechanical and/or thermal effects to deliver drugs or ablate tissues. Passive acoustic mapping (PAM) enables the spatio-temporal monitoring of cavitation activity, which is critical for the clinical translation of this technique. Traditional PAM is based on delay-and-sum (DAS) beamforming, a method whose quality tends to deteriorate due to issues including multi-bubble interference, distortion in the wavefront caused by the presence of the skull, unmodeled variability of array elements, etc. To provide for robustness, here we consider the use of minimum variance adaptive beamforming to PAM and demonstrate significant improvement in image quality compared to DAS. The minimum variance distortionless response (MVDR) method was evaluated and further improved by adding diagonal loading and by using subarray covariance estimates. Results demonstrate improvements in both the resolution and image contrast compared to DAS using either traditional or a refined MVDR beamformer. The axial full width at half maximum of the microbubble activity at the focus was reduced to 79.5% and 38.5% of that in DAS image for traditional and refined MVDR beamformers, respectively. Moreover, the refined MVDR method greatly enhanced the robustness while traditional MVDR beamforming induced self-nulling effects. We anticipate that the proposed method will improve our ability to monitor and control FUS-induced cavitation-based therapies.

빔 공간 초점 최소 분산 빔 형성을 이용한 근접장 음원 위치 추정

초점 MVDR(Minimum Variance Distortionless Response) 빔 형성은 근접장에서 표적의 위치를 추정하는데 적용될 수 있다. 하지만 배열을 구성하는 센서의 수가 많아질수록 공분산 행렬의 역행렬을 구하는데 많은 계산량을 필요로 한다. 본 논문에서는 부 배열의 원거리 빔 형성기 출력들로부터 빔 공간을 형성하고 이를 이용하여 초점 MVDR 빔 형성을 수행하는 방식을 제안하였다. 제안된 방법의 성능을 분석하기 위하여 모의실험을 수행하였다. 모의실험 결과, 제안된 방법의 공간 분해능이 기존의 지연 합 빔 형성기를 이용한 경우 보다 높게 나타났다. The focused MVDR (Minimum Variance Distortionless Response) can be applied for source localization in near field. However, if the number of sensors are increased, it requires a large amount of calculation to obtain the inverse of the covariance matrix. In this paper we propose a focused MVDR method using that beam space is formed from output of far field beamformer at the subarray. The performances of the proposed method was evaluated by simulation. As a result of simulation, the proposed method has the higher spatial resolution performance then the conventional delay-and-sum beamformer.

Effect of Errors in Beamforming Analysis Applied for MVDR and CBF Method

Minimum Variance Distortionless Response (MVDR) method can achieve a lower null level of beamforming compared to the Conventional Beamformer (CBF) method. It can not only minimize the array system mean output power but also maintain a distortion less response to desired signal as it adaptively depends on sample data. The effect of errors in beamforming analysis is applied using MVDR and CBF method. The errors include variance of weight and steering vector with different input SIR. These errors can affect the performance of array system’s mean output power and SINR for both CBF and MVDR. However, the MVDR method has more robust characteristics compared to the CBF method in the case of slight errors. The errors analysis also shows that factors of variance can weaken the performance of MVDR beamformer for suppressing clutters.

Real-valued MVDR beamforming using spherical arrays with frequency invariant characteristic

Complex-valued minimum variance distortionless response (MVDR) beamforming for wideband signals has very high computational amount. In this paper, we design a novel real-valued MVDR beamformer for spherical arrays. The dependence of the array steering matrix on source signal directions and frequencies is decoupled using spherical harmonic decomposition. Then a compensation network is designed to solve the frequency dependence of the array response and to get a new array response only determined by the spherical harmonics of the source directions. All frequency bins of wideband signals can be used together instead of being processed independently. By exploiting the property of the conjugate spherical harmonics, a unitary transform can be found to acquire a real-valued frequency invariant steering matrix (FISM). Based on the FISM, real-valued MVDR (RV-MVDR) is developed to obtain good performance with low computational amount. Simulation results demonstrate the performance of our proposed method for beamforming and direction-of-arrival (DOA) estimation by comparing with the complex-valued and real-weighted MVDR methods.

Subspace-based DOA with linear phase approximation and frequency bin selection preprocessing for interactive robots in noisy environments

This work develops a method of estimating subspace-based direction of arrival (DOA) that uses two proposed preprocesses. The method can be used in applications that involve interactive robots to calculate the direction to a noise-contaminated signal in noisy environments. The proposed method can be divided into two parts, which are linear phase approximation and frequency bin selection. Linear phase approximation rectifies the phases of the two-channel signals that are affected by noise, and reconstructs the covariance matrix of the received signals according to the compensative phases using phase line regression. To increase the accuracy of DOA result, a method of frequency bin selection that is based on eigenvalue decomposition (EVD) is utilized to detect and filter out the noisy frequency bins of the microphone signals. The proposed techniques are adopted in a method of subspace-based DOA estimation that is called multiple signal classification (MUSIC). Experimental results reveal that the mean estimation error obtained using proposed method can be reduced by 7.61° from the conventional MUSIC method. The proposed method is compared with the covariance-based DOA method that is called the minimum variance distortionless response (MVDR). The DOA improves the mean estimation accuracy by 4.98° relative to the conventional MVDR method. The experimental results demonstrate that both subspace-based and covariance-based DOA algorithms with the proposed preprocessing method outperform the DOA estimation in detecting the direction of signal in a noisy environment.

Three Decades of Development in DOA Estimation Technology

This paper presents a brief overview of narrowband direction of arrival (DOA) estimation algorithms and techniques. A comprehensive study is carried out in this paper to investigate and evaluate the performance of variety of algorithms for DOA estimation. Two categories of DOA estimation algorithms are considered for discussion which are Classical methods and Subspace based techniques. Classical methods include Sum-and-Delay method and Capon’s Minimum Variance Distortionless Response (MVDR) while Subspace based techniques are multiple signal classification (MUSIC) and The Minimum Norm Technique. Also ESPIRIT technique is evaluated. Inefficiencies are pointed out and solutions are suggested to overcome these shortfalls. Simulation results shows that the MUSIC algorithm is able to better represent the DOAs of signals with more prominent peaks. The Min-Norm algorithm also identifies the DOAs of signals similar to the MUSIC algorithm, but produces spurious peaks at other locations. The MVDR method identifies the DOAs of signals, but the locations are not represented by sharp peaks, due to spectral leakage. The classical beamformer also produces several spurious peaks. MUSIC show higher accuracy and resolution than the other algorithms. It should be noted that MUSIC is more applicable because it can be used for different array geometries.

Minimum variance ultrasonic imaging applied to an in situ sparse guided wave array

Ultrasonic guided wave imaging with a sparse, or spatially distributed, array can detect and localize damage over large areas. Conventional delay-and-sum images from such an array typically have a relatively high noise floor, however, and contain artifacts that often cannot be discriminated from damage. Considered here is minimum variance distortionless response (MVDR) imaging, which is a variation of delay-and-sum imaging whereby weighting coefficients are adaptively computed at each pixel location. Utilization of MVDR significantly improves image quality compared with delay-and-sum imaging, and additional improvements are obtained from incorporation of a priori scattering information in the MVDR method, use of phase information, and instantaneous windowing. Simulated data from a through-hole scatterer are used to illustrate performance improvements, and a performance metric is proposed that allows for quantitative comparisons of images from a known scatterer. Experimental results from a through-hole scatterer are also provided that illustrate imaging efficacy.

Performance Evaluation of an Algorithm for Estimation of DOA Using Model Estimation Technique

This paper proposes a model for estimating the direction of arrival (DOA) of a signal source impinging on a Uniform Linear Array(ULA). An algorithm which uses this model for estimating the delay of the signal received at two separated sensors, in a system identification perspective has been developed and its performance is compared with the results obtained through beam forming using conventional and Minimum Variance Distortionless Response(MVDR) methods. The unknown parameter, which is the phase delay at the sensors, as a result of the target presence at any bearing is estimated using the proposed method. The phase delayed signals at any sensor is generated by interpolating the samples form the previous sensor. The interpolation coefficients are estimated by considering them as part of the state vector of an Extended Kalman Filter (EKF). The EKF is used to recursively estimate the interpolation coefficients and thereby the delay. Simulation results demonstrate the feasibility of the model and the algorithm in estimating DOA both for narrowband and broadband signals. The mean of the estimates shows a reasonable degree of convergence to the true value. The variance of the estimate of the proposed method is less than that of the conventional method and very close to the MVDR method. Further it has been found that the proposed method exhibits a faster convergence.

MVDR-based coherence weighting for high-frame-rate adaptive imaging

Some success has been demonstrated in the extensive studies of adaptive imaging, but these approaches are generally not suitable for high-frame-rate (HFR) imaging where broad transmit beams are required. In this study, we propose an effective adaptive imaging method suitable for HFR imaging based on coherence-factor (CF) weighting and the minimum-variance-distortionless-response (MVDR) method. The CF is an index of focusing quality estimated from receive-channel data in which the amplitude of each image pixel is weighted by the corresponding CF so as to reduce the unwanted sidelobes. Direct implementation of CF weighting in HFR imaging does not provide satisfactory results because the broad transmit beams required for HFR imaging reduce the accuracy of CF calculations. In this study, we alleviated this problem by applying the MVDR method. We test the proposed method with the synthetic transmit aperture method where only 8 firings are required to form an image. Both simulations and clinical breast imaging data were used, and the proposed method enhanced the mean contrast by around 4.6 dB and the mean contrast-to-noise ratio by around 20%. The results demonstrate that the proposed method is effective at improving the image quality.

Kernel Antenna Array Processing

We introduce two support vector machine (SVM)-based approaches for solving antenna problems such as beamforming, sidelobe suppression, and maximization of the signal-to-noise ratio. A basic introduction to SVM optimization is provided and a complex nonlinear SVM formulation developed to handle antenna array processing in space and time. The new optimization formulation is compared with both the minimum mean square error and the minimum variance distortionless response methods. Several examples are included to show the performance of the new approaches

A generalized MVDR spectrum

The minimum variance distortionless response (MVDR) approach is very popular in array processing. It is also employed in spectral estimation where the Fourier matrix is used in the optimization process. First, we give a general form of the MVDR where any unitary matrix can be used to estimate the spectrum. Second and most importantly, we show how the MVDR method can be used to estimate the magnitude squared coherence function, which is very useful in so many applications but so few methods exist to estimate it. Simulations show that our algorithm gives much more reliable results than the one based on the popular Welch's method.