Array Steering Vector Research Articles

Wideband Robust Capon Beamforming for Passive Sonar

In passive sonar, narrowband adaptive beamforming techniques can be exploited to increase the signal-to-interference-plus-noise ratio (SINR), providing that array steering vector (ASV) errors and cross-spectral density matrix (CSDM) estimation errors can be controlled. When beamforming large aperture, many-element arrays in dynamic scenarios, the number of stationary snapshots available for CSDM estimation can be small compared to the number of array elements, leading to the problem of snapshot deficiency. Furthermore, common narrowband approaches become computationally prohibitive for large bandwidths. Here, we exploit the wideband nature of passive sonar signals to alleviate snapshot deficiency and reduce computational complexity. Narrowband robust Capon beamformers (RCBs), which exploit ellipsoidal ASV uncertainty sets to maintain high SINR, are extended to the wideband problem via the steered covariance matrix (STCM) method, yielding wideband RCBs (WBRCBs). To further reduce computational complexity and speed up algorithm convergence, subarray techniques are also incorporated, yielding wideband subarray RCBs (WBSARCBs). These algorithms, which are applicable to arbitrary array geometries, are evaluated using simulated and experimental passive sonar data.

Robust adaptive beamforming based on semi-definite programming and rank-one decomposition

The performance of Capon beamformer degrades sharply in the presence of array steering vector mismatch. To solve this problem, a robust beamforming algorithm based on semi-definite programming and rank-one decomposition is proposed, which improves the robustness of the adaptive beamforming by estimating an actual steering vector. The constraints for estimating the steering vector are deduced under the requirement that the estimate does not weaken the ability to suppress interference and noise, and the analysis shows that the approach to formulating constraint using matrix pre-filter is reasonable. The optimization problem is constructed and converted into a semi-definite relaxation problem, and rank-one decomposition technique is adopted in order to obtain the optimal solution. The simulation results demonstrate that compared with the existing algorithms, the proposed algorithm offers high SINR (signal to interference plus noise power ratio) and accuracy of power estimation, with the sole prior information about the angular vector in which the actual signal lies.

Minimum Redundancy MIMO Array Synthesis by means of Cyclic Difference Sets

Antenna array synthesis is an important issue in MIMO radars. By judiciously designing antenna positions, one can create a very long virtual array steering vector with a small number of antennas and therefore achieve very high spatial resolution at a small cost. This paper presents a combinatorial methodology based on cyclic difference sets (CDSs) for minimum redundancy (MR) MIMO array synthesis which seeks to maximize the virtual array aperture for a given number of antennas. First, the key features of CDSs and the CDS-based MR-MIMO layouts are described. Then, the analytical expression of the maximum contiguous virtual array aperture is derived. Further, based on this expression, an enumerative shifting procedure is developed for identifying the optimal CDS-based MR-MIMO layout. Selected examples are analyzed to point out the computational effectiveness of the CDS-based MR-MIMO array synthesis.

Linearly Constrained Robust Capon Beamforming

In this paper, a novel linearly constrained robust Capon beamformer (LCRCB) framework is proposed. In the LCRCB, linear constraints can be used, e.g., for beampattern control and ellipsoidal array steering vector sets can be exploited, using robust Capon beamforming techniques, e.g., to allow for arbitrary array steering vector errors, such as those arising from calibration errors. The LCRCB is applicable to arbitrary array geometries and can be computed efficiently. For the limiting case that the ellipsoid is a point, we show that the LCRCB coincides with a linearly constrained minimum variance beamformer. To show the utility of the LCRCB, mainbeam and null-pattern control examples are included.

DoA and Polarization Estimation for Arbitrary Array Configurations

In this paper, algorithms for joint high-resolution direction-of-arrival (DoA) and polarization estimation using real-world arrays with imperfections are proposed. Both azimuth and elevation angles are considered. Partially correlated and coherent signals may be handled as well. Unlike most of the work available in the open literature, we consider the case when polarization sensitive antenna arrays, which may be disposed on a conformal surface, may have unknown (but fixed) geometries, be composed of elements with individual beampatterns and be subject to cross-polarization as well as mounting platform effects. Herein, recent results on steering vector modeling from noise-corrupted array calibration measurements are employed. This allows for incorporating all nonidealities of an antenna array into the estimation algorithms in a general and convenient manner. The proposed estimators can be implemented using the fast Fourier transform or polynomial rooting techniques regardless of the array configuration. The stochastic Cramér-Rao lower bound for the estimation problem at hand is established using the results from array steering vector modeling as well. The proposed expression takes into account array nonidealities, making such a bound tight even for real-world arrays. Extensive simulation results are provided using several real-world antenna arrays. The proposed algorithms outperform conventional algorithms available in the literature and have a performance close to the stochastic Cramér-Rao lower bound.

COMPRESSIVE SENSING BASED PARAMETER ESTIMATION FOR MONOSTATIC MIMO NOISE RADAR

The novelty of this letter is that it capitalizes on noise waveform to construct measurement operator at the transmitter and presents a new method of how the analogue to digital converter (ADC) sampling rate in the monostatic multiple-input multiple-output (MIMO) noise radar can be reduced | without reduction in waveform bandwidth | through the use of compressive sensing (CS). The proposed method equivalently converts the measurement operator problems into radar waveform design problems. The architecture is particularly apropos for signals that are sparse in the target scene. In this letter, Estimates of both target directions and target amplitudes using CS for monostatic MIMO noise radar are presented. Sparse bases are constructed using array steering vectors. Orthogonal least squares (OLS) algorithm for reconstruction of both target directions and target amplitudes is implemented. Finally, the conclusions are all demonstrated by simulation experiments.

Robust Capon beamformer based on direction search

In the presence of pointing errors, a direction search based robust Capon beamformer is proposed. The direction of the desired signal is first estimated by searching for the local maximum of the array output power using the first-order Taylor series expansion of the array steering vector, and then the robust Capon beamformer is developed with the estimated direction as the presumed one.

Evaluation of Robust Capon Beamforming for Passive Sonar

Adaptive beamforming is often used in passive sonar, e.g., to improve the detectability of weak sources. The recently proposed robust Capon beamformer (RCB) exploits array steering vector uncertainty sets, eliminating the need for the ad hoc parameter choices often required when implementing robust adaptive beamforming algorithms. Here, we evaluate the performance of the RCB using experimental and simulated underwater acoustics data.

Iterative Robust Minimum Variance Beamforming

Based on worst-case performance optimization, the recently developed adaptive beamformers utilize the uncertainty set of the desired array steering vector to achieve robustness against steering vector mismatches. In the presence of large steering vector mismatches, the uncertainty set has to expand to accommodate the increased error. This degrades the output signal-to-interference-plus-noise ratios (SINRs) of these beamformers since their interference-plus-noise suppression abilities are weakened. In this paper, an iterative robust minimum variance beamformer (IRMVB) is proposed which uses a small uncertainty sphere (and a small flat ellipsoid) to search for the desired array steering vector iteratively. This preserves the interference-plus-noise suppression ability of the proposed beamformer and results in a higher output SINR. Theoretical analysis and simulation results are presented to show the effectiveness of the proposed beamformer.

Reduced dimension robust Capon beamforming for large aperture passive sonar arrays

In passive sonar, adaptive beamforming can be used to increase the array output signal-to-interference-plus-noise ratio (SINR) over delay-and-sum techniques, provided that array steering vector (ASV) and covariance matrix errors are accounted for. By exploiting ellipsoidal sets of the ASV, robust Capon beamformers (RCBs) systematically allow for ASV errors. For large aperture, many-element passive sonar arrays, the computational and sample support requirements often make element-space beamforming unfeasible and one is forced to consider reduced-dimension techniques. Here, a framework is proposed for combining reduced-dimension and RCB methods, producing rapidly converging, low complexity reduced-dimension RCBs (RDRCBs) allowing for ASV errors. The key contribution is the derivation of reduced-dimension ellipsoids, used by the RDRCBs, from typically available element-space sets and the dimension-reducing transformation(s) via propagation. The method allows for any ellipsoidal element-space ASV set and any full (column) rank dimension-reducing transformation. Here, for the application, the author considers the use of beamspace techniques within the RDRCB framework. The SINR of the RDRCBs are analysed, showing where they can outperform their element-space counter-parts. The benefits of using the RDRCBs are illustrated on experimental passive sonar data.

ROBUST ADAPTIVE BEAMFORMING BASED ON COVARIANCE MATRIX RECONSTRUCTION FOR LOOK DIRECTION MISMATCH

The performance degradation in traditional adaptive beamformers can be attributed to the imprecise knowledge of the array steering vector and inaccurate estimation of the covariance matrix. The inaccurate estimation of the covariance matrix is due to the limited data samples and presence of desired signal components in the training data. The mismatch between the actual and presumed steering vectors can be mainly due to the error in the look direction estimate. In this paper, we propose a novel algorithm to estimate the look direction and to reconstruct the covariance matrix so that near optimal performance without the efiect of saturation can be achieved as the input SNR increases. Numerical results also show that all existing beamforming algorithms sufier from saturation efiect as the input SNR increases.

A DIFFERENTIAL EVOLUTION APPROACH FOR ROBUST ADAPTIVE BEAMFORMING BASED ON JOINT ESTIMATION OF LOOK DIRECTION AND ARRAY GEOMETRY

The performance of traditional beamformers tends to degrade due to inaccurate estimation of covariance matrix and imprecise knowledge of array steering vector. The inaccurate estimation of covariance matrix can be attributed to limited data samples and the presence of desired signal in the training data. The mismatch between the actual and presumed steering vectors can be due to the error in the position (geometry) and/or in the look direction estimate. In this paper, we propose a difierential evolution (DE) based robust adaptive beamforming that is able to achieve near optimal performance even in the presence of geometry error. Initially, we estimate an optimal steering vector by maximizing and minimizing the signal power in and out of the desired signal's angular range, respectively. Then, we estimate the look direction and reconstruct the covariance matrix. Based on the obtained steering vector, estimate for look direction and reconstructed covariance matrix, near optimal output SINR, can be obtained with the increase in the input SNR without observing any saturation even in the presence of geometry error. Numerical simulations are presented to demonstrate the e-cacy of the proposed algorithm.

EFFECT OF STEERING ERROR VECTOR AND ANGULAR POWER DISTRIBUTIONS ON BEAMFORMING AND TRANSMIT DIVERSITY SYSTEMS IN CORRELATED FADING CHANNEL

A comparative analysis of transmit diversity and beam- forming for linear and circular antenna arrays in a wireless commu- nications system is presented. The objective is to examine the efiect of random perturbations, angular power distributions on transmit di- versity and beamforming system. The perturbations are modeled as additive random errors, following complex Gaussian multivariate dis- tribution, to the antenna array steering vectors. Using outage prob- ability, probability of error, and dynamic range of transmitter power as performance measures, we have shown signiflcant efiects of array perturbations on the two systems under spatially correlated Rayleigh fading channel. We also examine the efiect of angular power distribu- tions (uniform, truncated Gaussian, and truncated Laplacian), which corresponds to difierent propagation scenario, on the performance of the two systems. Results show that the central angle-of-arrival can

Robust Capon beamformer under norm constraint

In order to improve the robustness against the array steering vector mismatch, the norm constraint on the weight vector is used. By the complete investigation on the Capon beamformer under norm inequality constraint (NICCB), the existence of its solution is analyzed in detail, the choice of the norm inequality constraint parameter for NICCB is analyzed and the selecting range is given. In this paper, the Capon beamformer under norm equality constraint (NECCB) is also proposed and is solved effectively. At the end, numerical examples attest the correctness of the theory, and show that when the norm constraint parameter is selected in the allowable range, the performances of the optimal NICCB and NECCB vary unobvious, but for the same given norm constraint parameter, NECCB has the better performance than NICCB, namely the optimal negative loading that has the preferable robustness.

Robust Adaptive Microphone Array with Mainlobe and Response Ripple Control

Many existing adaptive beamformers possess robustness against arbitrary array steering vector (ASV) mismatches within presumed uncertainty set. However, when the array facing a large steering direction error, their performance degrade significantly since the uncertainty in steering direction generally gives rise to an outstanding mismatch in ASV. In the applications of microphone array, large steering direction error is often unavoidable because of the motion of target speaker. Meanwhile, in addition to conventional adaptive beamformers, microphone array also requests a controlled frequency response to target signal. In this paper, we propose a new adaptive microphone array implemented in frequency domain with controlled mainlobe and frequency response. A compact ASV uncertainty set explicitly modelling steering direction error and the other arbitrary ASV errors is exploited to derive beamformer with robust constraints on array magnitude response. Numerical results show that the proposed microphone array not only produces large controlled robust response region and robust frequency response, but also achieves high performance in SINR enhancement.

Automatic Generalized Loading for Robust Adaptive Beamforming

The goal of this letter is to derive robust adaptive beamformers via generalized loading. In the proposed methods, Hermitian matrices are loaded on sample covariance matrix, and this is different from those methods based on the well-known diagonal loading approach. Furthermore, the computation of the loaded matrix is fully automatic, which is scarce in the literature. Numerical examples show that our methods are more robust to errors on array steering vector and sample covariance matrix than other tested parameter-free methods.

DIRECTION OF ARRIVAL ESTIMATION BASED ON FOURTH-ORDER CUMULANT USING PROPAGATOR METHOD

In this paper direction-of-arrival estimation (DOA) of multiple narrow-band sources, based on higher-order statistics using propagator, is presented. This technique uses fourth-order cumulants of the received array data instead of second-order statistics (auto- covariance) and then the so-called propagator approach is used to estimate the DOA of the sources. The propagator is a linear operator which only depends on the array steering vectors and which can be easily extracted from the received array data. But it does not require any eigendecomposition of the cumulant matrix of the received data like MUSIC algorithm. Computer simulations are carried out to compare the performance of the proposed method to those of methods based on auto-covariance using MUSIC and propagator algorithms.

Wideband DOA estimation algorithms for multiple moving sources using unattended acoustic sensors

The problem of direction of arrival (DOA) estimation for multiple wideband sources using unattended passive acoustic sensors is considered. Several existing methods for narrowband DOA estimation are extended to resolve multiple closely spaced sources in presence of interference and wind noise. New wideband Capon beamforming methods are developed that use various algorithms for combining the power spectra at different frequency bins. A robust wideband Capon method is also studied to account for the inherent uncertainties in the array steering vector. Finally, to improve the resolution within an angular sector of interest and to provide robustness to sensor data loss, the beamspace method is extended and applied to the wideband problems. These methods are then tested and benchmarked on two real acoustic signature data sets that contain multiple ground vehicles moving in various formations.

Image-based refocusing of ultrasound arrays in the presence of strongly scattering objects.

Ultrasound phased arrays are currently being investigated for a dual-mode (imaging/therapy) operation in targeting deep-seated abdominal tumors for selective destruction noninvasively. In some cases, e.g., liver tumors, the target is partially obstructed by the ribcage, which limits the array gain at the target. In addition, the intensity at the ribs may be high enough to cause treatment-limiting pain and/or collateral damage to the tissues surrounding the ribs in the path of the therapeutic beam. Using the imaging capabilities of these dual-mode arrays, we have formulated and experimentally verified a robust minimum variance beamforming algorithm for adaptive refocusing in the presence of the ribs. The algorithm utilizes image data of the treatment region formed using conventional beamforming in estimating the array steering vector at the target and the weighting matrix that maximizes the array gain at the target. In this paper, we will describe the mathematical formulation and present experimental data to demonstrate its robustness. We will also discuss the implications of the method, the use of ultrasound phased arrays for imaging, and therapy of trans-thoracic targets such as the liver and the heart.

Target detection and parameter estimation for MIMO radar systems

We investigate several target detection and parameter estimation techniques for a multiple-input multiple-output (MIMO) radar system. By transmitting independent waveforms via different antennas, the echoes due to targets at different locations are linearly independent of each other, which allows the direct application of many data-dependent beamforming techniques to achieve high resolution and excellent interference rejection capability. In the absence of array steering vector errors, we discuss the application of several existing data-dependent beamforming algorithms including Capon, APES (amplitude and phase estimation) and CAPES (combined Capon and APES), and then propose an alternative estimation procedure, referred to as the combined Capon and approximate maximum likelihood (CAML) method. Via several numerical examples, we show that the proposed CAML method can provide excellent estimation accuracy of both target locations and target amplitudes. In the presence of array steering vector errors, we apply the robust Capon beamformer (RCB) and doubly constrained robust Capon beamformer (DCRCB) approaches to the MIMO radar system to achieve accurate parameter estimation and superior interference and jamming suppression performance.