Steering Vector

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Chong Meng Samson See - One of the best experts on this subject based on the ideXlab platform.

  • adaptive uncertainty based iterative robust capon beamformer using Steering Vector mismatch estimation
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Joni Polili Lie, Wee Ser, Chong Meng Samson See
    Abstract:

    To overcome the signal-to-interference-and-noise ratio (SINR) performance degradation in the presence of large Steering Vector mismatches, we propose an iterative robust Capon beamformer (IRCB) with adaptive uncertainty level. The approach iteratively estimates the actual Steering Vector (SV) based on conventional robust Capon beamformer (RCB) formulation that uses an uncertainty sphere to model the mismatch between the actual and presumed SV. At each iteration, the adaptive uncertainty algorithm self-adjusts the uncertainty sphere according to the estimated mismatch SV. This estimation is derived based on the geometrical interpretation of the mismatch and can be expressed as a simple closed-form expression as a function of the presumed SV and the signal-subspace projection. The other variant of the proposed algorithm that uses a flat ellipsoid to model the mismatch is also proposed. Simulation results show that the proposed approaches offer better interference suppression capability and achieve higher output SINR, as compared to other diagonal-loading-based approaches.

  • robust minimum ell_ 1 norm adaptive beamformer against intermittent sensor failure and Steering Vector error
    IEEE Transactions on Antennas and Propagation, 2010
    Co-Authors: Ying Zhang, Joni Polili Lie, Chong Meng Samson See
    Abstract:

    A robust adaptive beamformer is described to mitigate against Steering Vector error and intermittent sensor(s) failure which exists in the form of impulsive noise in the received signal of failed sensor(s). This new beamformer iteratively minimizes the l 1 -norm of the beamformer's output, subject to a prespecified set of quadratic constraints which target on attenuating the influence caused by Steering Vector error. To solve the proposed optimization problem, gradient descent algorithm is adopted. The choice of the Lagrange multiplier ? as well as the adaptive step-size ?(k) are derived in detail. Simulation results verify validity and advantages of the proposed algorithms over some existing methods.

  • robust adaptive beamforming and Steering Vector estimation in partly calibrated sensor arrays a structured uncertainty approach
    International Conference on Acoustics Speech and Signal Processing, 2010
    Co-Authors: Lei Lei, Joni Polili Lie, A B Gershman, Chong Meng Samson See
    Abstract:

    Two new approaches to adaptive beamforming in sparse subarray-based sensor arrays are proposed. Each subarray is assumed to be well calibrated but the intersubarray gain and/or phase mismatches are assumed to remain unknown or imperfectly known. Our first approach is based on a worst-case beamformer design that, unlike the existing worst-case designs, exploits a structured ellipsoidal uncertainty model for the signal Steering Vector. Our second approach exploits the idea of estimating the signal Steering Vector by maximizing the output power of the minimum variance beamformer. Several modifications of our second approach are developed for the cases of gain-and-phase and phase-only intersubarray distortions.

Olivier Besson - One of the best experts on this subject based on the ideXlab platform.

  • Robust adaptive beamforming using a Bayesian Steering Vector error model
    Signal Processing, 2013
    Co-Authors: Olivier Besson, Stephanie Bidon
    Abstract:

    We propose a Bayesian approach to robust adaptive beamforming which entails considering the Steering Vector of interest as a random variable with some prior distribution. The latter can be tuned in a simple way to reflect how far is the actual Steering Vector from its presumed value. Two different priors are proposed, namely a Bingham prior distribution and a distribution that directly reveals and depends upon the angle between the true and presumed Steering Vector. Accordingly, a non-informative prior is assigned to the interference plus noise covariance matrix R, which can be viewed as a means to introduce diagonal loading in a Bayesian framework. The minimum mean square distance estimate of the Steering Vector as well as the minimum mean square error estimate of R are derived and implemented using a Gibbs sampling strategy. Numerical simulations show that the new beamformers possess a very good rate of convergence even in the presence of Steering Vector errors.

  • ICASSP - Bayesian robust adaptive beamforming based on random Steering Vector with bingham prior distribution
    2013 IEEE International Conference on Acoustics Speech and Signal Processing, 2013
    Co-Authors: Olivier Besson, Stephanie Bidon
    Abstract:

    We consider robust adaptive beamforming in the presence of Steering Vector uncertainties. A Bayesian approach is presented where the Steering Vector of interest is treated as a random Vector with a Bingham prior distribution. Moreover, in order to also improve robustness against low sample support, the interference plus noise covariance matrix R is assigned a non informative prior distribution which enforces shrinkage to a scaled identity matrix, similarly to diagonal loading. The minimum mean square distance estimate of the Steering Vector as well as the minimum mean square error estimate of R are derived and implemented using a Gibbs sampling strategy. The new beamformer is shown to converge within a limited number of snapshots, despite the presence of Steering Vector errors.

  • matched direction detectors and estimators for array processing with subspace Steering Vector uncertainties
    IEEE Transactions on Signal Processing, 2005
    Co-Authors: Olivier Besson, L L Scharf, François Vincent
    Abstract:

    In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the Steering Vector but, on the other hand, some knowledge about the Steering Vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Crame/spl acute/r-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations.

  • performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random Steering Vector errors
    IEEE Transactions on Signal Processing, 2005
    Co-Authors: Olivier Besson, François Vincent
    Abstract:

    Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the Steering Vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random Steering Vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR.

  • Steering Vector errors and diagonal loading
    IEE Proceedings - Radar Sonar and Navigation, 2004
    Co-Authors: François Vincent, Olivier Besson
    Abstract:

    Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. The authors consider its application to the case of Steering Vector errors, i.e. when there exists a mismatch between the actual Steering Vector of interest and the presumed one. More precisely, the problem addressed is that of optimally selecting the loading level with a view to maximising the signal-to-interference-plus-noise ratio in the presence of Steering Vector errors. First, an expression is derived for the optimal loading for a given Steering Vector error and it is shown that this loading is negative. Next, random Steering errors are considered and the optimal loading is averaged with respect to the probability density function of the Steering Vector errors, yielding a very simple expression for the average optimal loading. Numerical simulations attest to the validity of the analysis and show that diagonal loading with the derived optimal loading factor provides a performance close to optimum.

Shengqi Zhu - One of the best experts on this subject based on the ideXlab platform.

  • robust adaptive beamforming against large Steering Vector mismatch using multiple uncertainty sets
    Signal Processing, 2018
    Co-Authors: Yang Feng, Guisheng Liao, Shengqi Zhu, Cao Zeng
    Abstract:

    Abstract Many efforts have been recently devoted to adaptive beamformers using one uncertainty set to achieve robustness against Steering Vector mismatch. However, these robust adaptive beamformers based on worst-case performance optimization suffer from difficulty in selecting an appropriate size of the uncertainty set. Besides, their performances degrade dramatically if large Steering Vector mismatch occurs. This motivates us to develop a robust beamforming approach to handle the large uncertainty set problem. In this paper, we utilize multiple small uncertainty sets, instead of using a single large set, to cover the whole large uncertainty region. Two efficient algorithms, iterative semidefinite programming-based robust adaptive beamforming (ISDP-RAB) and iterative linearization-based robust beamforming (IL-RAB), are developed to solve the nonconvex problem. Simulation results indicate that the proposed method offers a significant performance improvement in case of large Steering Vector mismatch.

  • A robust STAP method for airborne radar with array Steering Vector mismatch
    Signal Processing, 2016
    Co-Authors: B. Liao, Lei Huang, Chongtao Guo, Guisheng Liao, Shengqi Zhu
    Abstract:

    In this paper, we consider the problem of space-time adaptive processing (STAP) for airborne radar in the presence of direction-of-arrival (DOA) and Doppler frequency uncertainties, either of which would result in Steering Vector mismatch. A robust STAP method is devised by introducing an accurate Steering Vector estimator. In particular, by considering the mismatched DOA and Doppler frequency, a spatial-temporal integral covariance matrix including the actual Steering Vector component is first constructed. The subspace corresponding to the clutter-plus-noise is then extracted from the so-obtained matrix and used to impose an appropriate constraint to estimate the actual Steering Vector. The resultant problem is a non-convex quadratically constrained quadratic program (QCQP), which is solved using the semidefinite programming (SDP) relaxation technique. Numerical examples are presented to demonstrate the performance of the proposed approach in different hypothetical scenarios. HighlightsA spatial-temporal integral covariance matrix is constructed by considering the mismatched DOA and Doppler frequency.The subspace corresponding to the clutter-plus-noise is extracted from the spatial-temporal integral covariance matrix.Clutter-plus-noise subspace is used for impose an appropriate constraint to estimate the actual Steering Vector.

  • Knowledge-aided adaptive beamforming against signal Steering Vector mismatch with small sample support
    2012 IEEE International Conference on Signal Processing Communication and Computing (ICSPCC 2012), 2012
    Co-Authors: Yongchan Gao, Guisheng Liao, Shengqi Zhu, Xuepan Zhang
    Abstract:

    In this paper, a knowledge-aided adaptive beamforming approach against signal Steering Vector mismatch with small sample support is proposed. First, a combination covariance matrix of the prior covariance matrix, the sample covariance matrix and an identity matrix is obtained by the minimum mean-square error criterion. Then the mismatch between the actual and the presumed signal Steering Vector is modeled as a worst-case performance optimization constraint. Based on the combination covariance matrix and the constraint, the adaptive beamformer is formulated. The validity of the proposed beamformer is evaluated by simulation results, when the sample support is small and the signal steer Vector mismatch exists.

Sergiy A. Vorobyov - One of the best experts on this subject based on the ideXlab platform.

  • New Designs on MVDR Robust Adaptive Beamforming Based on Optimal Steering Vector Estimation
    IEEE Transactions on Signal Processing, 2019
    Co-Authors: Yongwei Huang, Mingkang Zhou, Sergiy A. Vorobyov
    Abstract:

    The robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) Steering Vector is considered in the paper. The common criteria to find the best estimate of the Steering Vector are the beamformer output signal-to-noise-plus-interference ratio (SINR) and output power, while the constraints assume as little as possible prior inaccurate knowledge about the SOI, the propagation media, and the antenna array. Herein, in order to find the optimal Steering Vector, a 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 SOI is away from the DOA region of all linear combinations of the interference Steering Vectors. The prior knowledge required is some allowable error norm bounds and approximate knowledge of the antenna array geometry and angular sector of the SOI. It turns out that the array output power maximization problem is a non-convex quadratically constrained quadratic programming problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the SOI Steering Vector. The results are generalized to the case when an ellipsoidal constraint is considered instead of the similarity constraint, 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.

  • robust adaptive beamforming based on Steering Vector estimation with as little as possible prior information
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Arash Khabbazibasmenj, Sergiy A. Vorobyov, Aboulnasr Hassanien
    Abstract:

    A general notion of robustness for robust adaptive beamforming (RAB) problem and a unified principle for minimum variance distortionless response (MVDR) RAB techniques design are formulated. This principle is to use standard MVDR beamformer in tandem with an estimate of the desired signal Steering Vector found based on some imprecise prior information. Differences between various MVDR RAB techniques occur only because of the differences in the assumed prior information and the corresponding signal Steering Vector estimation techniques. A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed. The objective for estimating the Steering Vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference Steering Vectors and their linear combinations. The prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual Steering Vector lies. Mathematically, the proposed MVDR RAB is expressed as the well known non-convex quadratically constrained quadratic programming problem with two constraints, which can be efficiently and exactly solved. Some new results for the corresponding optimization problem such as a new algebraic way of finding the rank-one solution from the general-rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank-one are derived. Our simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.

  • Robust Adaptive Beamforming Based on Steering Vector Estimation via Semidefinite Programming Relaxation
    arXiv: Information Theory, 2010
    Co-Authors: Arash Khabbazibasmenj, Sergiy A. Vorobyov, Aboulnasr Hassanien
    Abstract:

    We develop a new approach to robust adaptive beamforming in the presence of signal Steering Vector errors. Since the signal Steering Vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the actual Steering Vector, which then is used for obtaining the optimal beamforming weight Vector. The objective for finding such an estimate of the actual signal Steering Vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate of the Steering Vector does not converge to an interference Steering Vector. Our objective and constraints are free of any design parameters of non-unique choice. The resulting optimization problem is a non-convex quadratically constrained quadratic program, which is NP hard in general. However, for our problem we show that an efficient solution can be found using the semi-definite relaxation technique. Moreover, the strong duality holds for the proposed problem and can also be used for finding the optimal solution efficiently and at low complexity. In some special cases, the solution can be even found in closed-form. Our simulation results demonstrate the superiority of the proposed method over other previously developed robust adaptive beamforming methods for several frequently encountered types of signal Steering Vector errors.

  • Robust adaptive beamforming via estimating Steering Vector based on semidefinite relaxation
    2010 Conference Record of the Forty Fourth Asilomar Conference on Signals Systems and Computers, 2010
    Co-Authors: Arash Khabbazibasmenj, Sergiy A. Vorobyov, Aboulnasr Hassanien
    Abstract:

    Most of the known robust adaptive beamforming techniques can be unified under one framework. This is to use minimum variance distortionless response principle for beamforming Vector computation in tandem with sample covariance matrix estimation and Steering Vector estimation based on some information about Steering Vector prior. Motivated by such unified framework, we develop a new robust adaptive beamforming method based on finding a more accurate estimate of the actual Steering Vector than the available prior. The objective for finding such Steering Vector estimate is the maximization of the beamformer output power under the constraints that the estimate does not converge to an interference Steering Vector and does not change the norm of the prior. The resulting optimization problem is a non-convex quadratically constrained quadratic programming problem, which is NP hard in general, but can be efficiently and exactly solved in our specific case. Our simulation results demonstrate the superiority of the proposed method over other robust adaptive beamforming methods.

  • adaptive beamforming with joint robustness against mismatched signal Steering Vector and interference nonstationarity
    IEEE Signal Processing Letters, 2004
    Co-Authors: Sergiy A. Vorobyov, A B Gershman, Zhiquan Luo
    Abstract:

    Adaptive beamforming methods degrade in the presence of both signal Steering Vector errors and interference nonstationarity. We develop a new approach to adaptive beamforming that is jointly robust against these two phenomena. Our beamformer is based on the optimization of the worst case performance. A computationally efficient convex optimization-based algorithm is proposed to compute the beamformer weights. Computer simulations demonstrate that our beamformer has an improved robustness as compared to other popular robust beamforming algorithms.

Amir Leshem - One of the best experts on this subject based on the ideXlab platform.

  • robust adaptive beamforming based on interference covariance matrix reconstruction and Steering Vector estimation
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Yujie Gu, Amir Leshem
    Abstract:

    Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the Steering Vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected Steering Vector from getting close to the interference Steering Vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the Steering Vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.

  • robust adaptive beamforming based on jointly estimating covariance matrix and Steering Vector
    International Conference on Acoustics Speech and Signal Processing, 2011
    Co-Authors: Amir Leshem
    Abstract:

    In this paper, a new adaptive beamforming algorithm with joint robustness against covariance matrix uncertainty as well as Steering Vector mismatch is proposed. First, the theoretical covariance matrix is estimated based on the shrinkage method. Subsequently, the difference between the actual and the presumed Steering Vector is estimated by solving a quadratic convex optimization problem, which enables correction of the presumed Steering Vector. Unlike other robust beamforming techniques, neither the norm of the Steering Vector nor the upper bound of the norm of the mismatch Vector is assumed in our approach. Simulation results show the effectiveness of the proposed algorithm both in terms of output performance and computational complexity.

  • ICASSP - Robust adaptive beamforming based on jointly estimating covariance matrix and Steering Vector
    2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011
    Co-Authors: Amir Leshem
    Abstract:

    In this paper, a new adaptive beamforming algorithm with joint robustness against covariance matrix uncertainty as well as Steering Vector mismatch is proposed. First, the theoretical covariance matrix is estimated based on the shrinkage method. Subsequently, the difference between the actual and the presumed Steering Vector is estimated by solving a quadratic convex optimization problem, which enables correction of the presumed Steering Vector. Unlike other robust beamforming techniques, neither the norm of the Steering Vector nor the upper bound of the norm of the mismatch Vector is assumed in our approach. Simulation results show the effectiveness of the proposed algorithm both in terms of output performance and computational complexity.

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