Signal Steering Vector Research Articles

Fast and robust adaptive beamforming algorithms for large-scale arrays with small samples

The adaptive beamformer of large-scale sensor array mainly suffers from two limits. One limit is an insufficient number of training snapshots, which usually results in an ill-posed sample covariance matrix in many real applications. The other limit is the high computation complexity of the beamformer that severely restricts its online processing. To overcome these two limits, two fast and robust adaptive beamforming algorithms are proposed in this paper, which refers to the linear kernel approaches and formulates the weight vector as a linear combination of the training samples and the signal steering vector. The proposed algorithms only need to calculate a low-dimensional combination vector instead of the high-dimensional adaptive weight vector, which remarkably reduces the computation complexity. Moreover, regularization techniques are utilized to suppress the excessive variation of the combination vector caused by an underdetermined estimation of the Gram matrix. Experimental results show that the proposed algorithms achieve better performance and lower computation complexity than algorithms in the literature. Especially, like the kernel approaches, the proposed algorithms achieve good performance under the small sample case.

Single-Point Array Response Control: An Efficient Beampattern Synthesis Approach Based on the Maximum Magnitude Response Principle

This article considers the beampattern synthesis problem, and a single-point array response control (SPARC) algorithm is presented to adjust the array response at an arbitrary direction. Based on the theoretical analysis, it is found that the adaptive array theory-based optimal weight vector is a linear combination of the signal steering vector and the interference steering vector multiplied by a complex factor, and that the complex factor determines the array response at the interference direction. Inspired by this observation, the SPARC algorithm is presented to achieve quiescent pattern control. In contrast to other array response control-based pattern synthesis techniques, the SPARC algorithm obtains a deterministic expression of the complex factor after maximizing the magnitude response at the main-beam direction, and the closed-form expression of the designed weight vector is devised. Because of different pattern constraints in focused and shaped beampatterns, two low-complexity pattern synthesis schemes are presented employing the SPARC algorithm in an iterative manner. Moreover, the parameter selection principle of the SPARC and its comparison with other pattern synthesis methods are discussed. Simulation results show the effectiveness of the SPARC algorithm and the efficiency of the beampattern synthesis schemes.

Robust widely linear beamforming using estimation of extended covariance matrix and steering vector

The distribution of the received signals in many array processing applications is noncircular. Although optimal widely linear beamformer (WLB) can provide the best performance for noncircular received signals, its performance degrades severely under model mismatches in practical applications. As a remedy, we propose a robust WLB by using precise reconstruction of extended interference-plus-noise covariance matrix (EINCM) and low-complexity estimation of extended desired signal steering vector (EDSSV). We propose to first determine the steering vectors, powers, and noncircularity coefficients of all signals and the noise power. In contrast to the previous reconstruction methods using the integration over a wide angular sector, we reconstruct the interference-plus-noise covariance matrix (INCM) and the pseudo INCM accurately according to their definitions. By using INCM and pseudo INCM, we can precisely reconstruct the EINCM. We propose to estimate the EDSSV by intersecting two extended subspaces, which are respectively formed by eigendecomposing the extended sample covariance matrix and the extended desired signal covariance matrix. Unlike the convex optimization methods, the proposed EDSSV estimation does not require any optimization programming and yields a solution with closed expression in low computational complexity. Simulation results show that the proposed robust WLB provides near optimal performance under several model mismatch cases.

Robust Wideband Adaptive Beamforming Based on Focusing Transformation and Steering Vector Compensation

The wideband adaptive beamforming method would deteriorate severely when the desired signal is contained in the training snapshots, especially the mismatched signal steering vector existed simultaneously. Therefore, a robust wideband adaptive beamforming method is proposed based on focusing transformation and steering vector compensation. In proposed method, the received wideband signals are first decomposed into narrow sub-bands. Then, based on the direction of arrivals of signals, the interference plus noise covariance matrix of each sub-band is reconstructed to remove the desired signal and transformed into the reference frequency by the focusing transformation. Subsequently, the mismatched signal steering vector is compensated based on the error vector decomposition and the optimization of output power of adaptive beamformer. Finally, the adaptive weight vector of robust wideband beamforming is calculated based on the minimum variance distortionless response criterion. The effectiveness of proposed method is verified by numerical simulations.

Robust adaptive beamforming for coprime array with steering vector estimation and covariance matrix reconstruction

Coprime array exhibits many advantages over the uniform linear array (ULA) with the same number of physical sensors in resolution performance and interference suppression capability. In this study, the authors take the advantages of coprime array to improve the robustness of adaptive beamformer. In the coprime virtual ULA (CV-ULA), they prove that a constructed Toeplitz matrix can be taken as the sample covariance matrix from the perspective of virtual signal characteristics. The CV-ULA Capon spectrum estimator is modified to obtain the directions and powers of all impinging signals. Since the real directions of all impinging signals are located at different angular sectors, they form independent signal subspace for each impinging signal. They also assign independent steering vector mismatches for different impinging signals to obtain their real steering vectors. The steering vector mismatch of each impinging signal is independently obtained by solving its own convex optimisation problem. They reconstruct the interference-plus-noise covariance matrix (INCM) with precise steering vectors and powers of interference signals. The proposed weight vector is computed by combining the desired signal steering vector and the reconstructed INCM. Extensive simulations show that the proposed algorithm provides robustness against many types of model mismatches.

Distributed Target Detection Using Samples Filtered with Normalized Conjugate Signal Steering Vector

This paper studied the problem of adaptive detection of distributed targets in colored noise with unknown covariance matrix (CM), for the case where limited noise-only (training) data are available to estimate this CM. We first filter the test and training data with the normalized conjugate signal steering vector which is matched to the target signal, to preserve the signal power while suppressing the noise power; second, we derive the generalized likelihood ratio test. The new detector has the desired constant false alarm rate feature against the noise CM; it needs less training data, has a lower computational complexity and performs better (more robust) for matched (mismatched) signals, when compared with its natural counterparts.

Jointly Optimal Denoising, Dereverberation, and Source Separation

This paper proposes methods that can optimize a Convolutional BeamFormer (CBF) for jointly performing denoising, dereverberation, and source separation (DN+DR+SS) in a computationally efficient way. Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response beamformer has been usedas the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed. In the blind signal processing area, an approach for jointly optimizing dereverberation and source separation (DR+SS) has been proposed, however, this approach requires huge computing cost, and has not been extended for application to DN+DR+SS. To overcome the above limitations, this paper develops new approaches for jointly optimizing DN+DR+SS in a computationally much more efficient way. To this end, we first present an objective function to optimize a CBF for performing DN+DR+SS based on the maximum likelihood estimation, on an assumption that the steering vectors of the target signals are given or can be estimated, e.g., using a neural network. This paper refers to a CBF optimized by this objective function as a weighted Minimum-Power Distortionless Response (wMPDR) CBF. Then, we derive two algorithms for optimizing a wMPDR CBF based on two different ways of factorizing a CBF into WPE filters and beamformers. Experiments using noisy reverberant sound mixtures show that the proposed optimization approaches greatly improve the performance of the speech enhancement in comparison with the conventional cascade configuration in terms of the signal distortion measures and ASR performance. It is also shown that the proposed approaches can greatly reduce the computing cost with improved estimation accuracy in comparison with the conventional joint optimization approach.

Robust adaptive beamforming for MIMO radar in the presence of covariance matrix estimation error and desired signal steering vector mismatch

Owing to covariance matrix estimation error, desired signal steering vector mismatch, and the existence of target signal in training samples, most of adaptive beamforming algorithms suffer from a great performance degradation. Aim at this, this study proposes a robust adaptive beamforming algorithm for multiple-input-multiple-output radar. To be specific, the sample covariance matrix is replaced by the reconstructed covariance matrix, to narrow the difference between the maximum and minimum noise eigenvalues. In addition, the diagonal loading technique is applied to correct the mismatched desired signal steering vector by maximising the output signal-to-interference-plus-noise ratio of adaptive beamformer, and a simple closed-form solution to loading factor can be further obtained. Computer simulation results demonstrate that the proposed algorithm can efficiently improve the robustness of adaptive beamformer against both covariance matrix estimation error and desired signal steering vector mismatch.

A Tunable Detector for Distributed Target Detection in the Situation of Signal Mismatch

This letter investigates the problem of distributed target detection with signal mismatch in homogeneous environment. Precisely, the actual signal steering vector is not aligned with the nominal one which is assumed by radar system. Within this framework, we propose a tunable detector which can adjust its directivity (robustness or selectivity) flexibly and effectively by changing a tunable parameter. Moreover, this tunable detector encompasses the generalized Kelly's generalized likelihood ratio test (GKGLRT) and the generalized adaptive matched filter (GAMF) as its two special cases. Finally, to test the effectiveness of this detector, the real data received by the IPIX radar are used for experiments. The results illustrate the superiority of the proposed detector both in simulation environment and realistic environment.

DOA Estimation of Coherent Signals Based on the Sparse Representation for Acoustic Vector-Sensor Arrays

This paper focuses on the problem of the DOA estimation of coherent signals for the acoustic vector-sensor arrays (AVSAs) in the presence of the isotropic ambient noise. We propose a high-resolution DOA estimation method based on the acoustic intensity principle and the sparse representation technique. First, two cross-covariance matrices are constructed by employing the acoustic pressure and particle velocity components of the AVSA, which eliminates the isotropic noise. Then, in order to fully explore the DOA information of the particle velocity components, an augmented matrix is formed based on the two cross-covariance matrices. We observe an interesting fact that the left singular vector corresponding to the maximum singular value of the augmented cross-covariance matrix is the linear combination of all the signal steering vectors. Based on this fact, a high-resolution DOA estimation algorithm is developed via sparsely representing the left singular vector. This method does not require the prior knowledge of the noise variance or the number of signals to construct the sparse representation model. Simulation and experimental results demonstrate the proposed method outperforms the MUSIC method based on the forward/backward spatial smoothing and some existing sparse representation methods in estimation accuracy and angular resolution, especially in the cases of a low signal-to-noise ratio and/or coherent signals with small angular separations.

Improved OP approach utilising correlated projection and eigenspace processing for robust adaptive beamforming

The capability of orthogonal projection (OP) approach degrades severely in the presence of array model mismatch, especially when the training samples are mixed with the strong desired signal. Therefore, an improved OP robust adaptive beamforming is proposed based on correlated projection and eigenspace processing in wide input signal-to-noise ratio to remove the desired signal self-null effect and improve robustness. In the proposed approach, the interference subspace is constructed combining the correlated projection and eigenspace processing first. Then, the interference-plus-noise covariance matrix is accurately reconstructed via super-resolution spatial spectrum estimator to eliminate desired signal from sample covariance matrix. Subsequently, the desired signal steering vector is corrected applying correlated projection and then the adaptive weighted vector is modified by OP approach. Simulation results demonstrate that the capability of the proposed approach is almost consistently same as the optimal beamformer in many scenarios.

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.

Adaptive detectors with enhanced selectivity capabilities in partially homogeneous environments

This study deals with the problem of adaptive detection in the presence of mismatch signals in partially homogeneous environment. To enhance the selectivity of the detector, the authors add a fictitious signal under the null hypothesis. The fictitious signal is orthogonal to the nominal signal steering vector in the quasi-whitened observation space. Two generalised likelihood ratio test-based mismatch selective detectors are derived. Simulation results show that the one-step mismatch selective detector coincides with the adaptive coherence estimator and the two-step mismatch selective detector has a better mismatch rejection capability than the generalised adaptive matched filter.

Recursive Updating Algorithm for Robust Adaptive Beamforming in a Uniform Circular Array

When the phase-mode transformation technique is used in a uniform circular array, its output performance is known to degrade owing to the approximations applied to the formulation. In this paper, we develop a robust recursive updating algorithm based on the worst-case performance optimization and phase-mode transformation in the uniform circular array, which provides efficient robustness not only against the signal steering vector mismatches, but also against the transformation errors. The proposed algorithm belongs to the class of the diagonal loading technique and the transformation matrix belongs to a certain ellipsoid set. The weight vector is updated by the Lagrange multiplier method, in which the parameters are derived simply. The proposed algorithm has a closed-form solution, in which we analyse the reasonable ranges of two key parameters. The convergence performance and the output SINR performance are also analysed. In additional, the implementation complexity costs of the proposed algorithm and MVDR algorithm are presented in this paper. Our robust algorithm has a low implementation complexity cost and achieves the mean output array SINR consistently close to the optimal one. Simulation results are presented to compare the performances of our algorithm with the conventional algorithms.

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.

Middle Subarray Interference Covariance Matrix Reconstruction Approach for Robust Adaptive Beamforming With Mutual Coupling

In this letter, a middle subarray interference-plus-noise covariance matrix (INCM) reconstruction approach is proposed to mitigate the mutual coupling problem in robust adaptive beamforming. In the proposed approach, the banded symmetric Toeplitz structure of mutual coupling matrix in the uniform linear array is employed. The INCM of middle subarray is first reconstructed by using the Capon spectrum of middle subarray to integrate over the possible interference region. Similarly, the desired signal covariance matrix of middle array is calculated over the desired signal region, and the desired signal steering vector of middle array is estimated. Finally, the proposed middle subarray beamformer weight vector is obtained. Simulation results validate the superiority and effectiveness of the proposed method.

Robust Astronomical Imaging in the Presence of Radio Frequency Interference

Radio astronomical observations are increasingly contaminated by radio frequency interference (RFI), rendering the development of effective RFI suppression techniques a pressing task. In practice, the existence of model mismatch makes the observing environment more challenging. In this paper, we develop a robust astronomical imaging method in the presence of RFI and model mismatch. The key contribution of the proposed method is the accurate estimation of the actual signal steering vector by maximizing the beamformer output power subject to a constraint that prevents the estimated steering vector from converging to the interference steering vectors. The proposed method is formulated as a quadratically constrained quadratic programming problem that can be solved using efficient numerical approaches. Simulation results demonstrate the effectiveness of the proposed method.

Analysis of Necessity of FDA Selecting Optimal Frequency Interval

The relationship between the output signal to jamming and noise ratio (SJNR) of frequency diverse array (FDA) and the correlation coefficient between the jamming and signal steering vector are deduced. The influence of the change of signal and jamming position on the output SINR is obtained. When jamming is located in mainlobe, the improper frequency interval will sharply reduce the output SINR and form a null. The detection ability of the FDA radar will also drop sharply and the null will change periodically with the selection of frequency interval. Both the theories and simulations verified this periodic null and demonstrated the necessity for selecting FDA’s optimal frequency interval.

Robust adaptive beamforming using iterative adaptive approach

ABSTRACTThe performance of traditional reconstruction-based robust adaptive beamformers may degrade when the array is not well calibrated. This performance degradation is mainly caused by the Capon spectrum estimator which can not estimate the spatial power spectrum accurately. In contrast to existing approaches, we propose two new reconstruction-based robust adaptive beamformers by using the accurate iterative adaptive approach (IAA) spectrum to combat the covariance matrix uncertainties and the steering vector mismatches. The first one employs the low-complexity IAA (IAA-LC) algorithm to obtain the interference power estimates and reconstruct the interference-plus-noise covariance matrix (INCM) with the computational complexity further reduced. The second one reconstructs the INCM by updating the power estimates corresponding to each interference steering vector with the use of knowledge-aided IAA (IAA-KA) algorithm. The desired signal steering vector is corrected by searching for the direction corresponding to the maximum power, which circumvents the use of optimization program. Simulation results show that our proposed beamformers outperform the others and can achieve the robust performance in the cases of array model mismatches.

New Designs on MVDR Robust Adaptive Beamforming Based on Optimal Steering Vector Estimation

The robust adaptive beamforming design problem based on estimation of the signal of interest steering vector is considered in the paper. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the signal of interest steering vector. The common criteria to find the best estimate of the steering vector are the beamformer output SINR and output power, while the constraints assume as little as possible prior inaccurate knowledge about the signal of interest, the propagation media, and the antenna array. Herein, a new beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the signal of interest is away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, the prior information required consists of some allowable error norm bounds, the approximate knowledge of the antenna array geometry, and the angular sector of the signal of interest. It turns out that the array output power maximization problem is a non-convex QCQP problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the signal of interest steering vector. The results are generalized to the case where an ellipsoidal constraint is considered, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.