Spatial Steering Vectors Research Articles

Phase response similarity based waveform design for FDA-MIMO radar

The transmit degrees-of-freedom (DOFs) of multiple-input multiple-output (MIMO) radar depend on the orthogonality of transmit waveforms. However, ideal orthogonal waveforms are unrealistic because existing waveforms cannot avoid influence of cross-correlation sidelobes. In this paper, a waveform design algorithm is proposed by introducing the phase response similarity (PRS) concept. The PRS enables consistency of spatial steering vectors for different time instance. In this case, the spatial power spectrum of signal in the transmit spatial domain will be well-focused, which is the desired property for the jammer suppression application. Moreover, we further explore the combination of correlation amplitude and phase response as the objective function, which improves the anti-jammer performance. Simulation examples are conducted to verify the effectiveness and performance gains of the proposed method.

Space-Time Adaptive Processing Based on Modified Sparse Learning via Iterative Minimization for Conformal Array Radar.

Space-time adaptive processing (STAP) is a well-known technique for slow-moving target detection in the clutter spreading environment. For an airborne conformal array radar, conventional STAP methods are unable to provide good performance in suppressing clutter because of the geometry-induced range-dependent clutter, non-uniform spatial steering vector, and polarization sensitivity. In this paper, a knowledge aided STAP method based on sparse learning via iterative minimization (SLIM) combined with Laplace distribution is proposed to improve the STAP performance for a conformal array. The proposed method can avoid selecting the user parameter. the proposed method constructs a dictionary matrix that is composed of the space-time steering vector by using the prior knowledge of the range cell under test (CUT) distributed in clutter ridge. Then, the estimated sparse parameters and noise power can be used to calculate a relatively accurate clutter plus noise covariance matrix (CNCM). This method could achieve superior performance of clutter suppression for a conformal array. Simulation results demonstrate the effectiveness of this method.

Adaptive Mutual Coupling Compensation Method for Airborne STAP Radar With End-Fire Array

Because the maximum radiation direction of the end-fire array antenna points to the axis of the array and the small element spacing required to suppress the grating lobes, the mutual coupling effect between the arrays is more serious than that of the broadside array. The article first established the end-fire array antenna pattern model and clutter signal model with the effect of mutual coupling. The clutter signal model includes two cases, ideal mutual coupling effect and mutual coupling error. On this basis, we take a ten-element uniform linear array using CST Microwave Studio to validate our model. Then we analyze the clutter distribution characteristics of the end-fire array airborne radar and the effect of mismatch on the spatial steering vector. Finally, an adaptive mutual coupling compensation method based on covariance matrix reconstruction is proposed. In general, clutter suppression methods with end-fire array take no account of the mutual coupling error changing over time, but the proposed method first adaptively estimates the mutual coupling error based on the airborne radar echo data and uses the estimated normalized impedance matrix to compensate the spatial steering vector, then combines the system parameters to construct the clutter covariance matrix. The simulations indicate that this method accurately estimate the impedance matrix, and it eliminates the clutter power reduction and spatial steering vector mismatch caused by mutual coupling error. Moreover, it also solves the serious non-stationary clutter problem of the end-fire array airborne radar.

A Two-Stage STAP Method Based on Fine Doppler Localization and Sparse Bayesian Learning in the Presence of Arbitrary Array Errors.

In the presence of unknown array errors, sparse recovery based space-time adaptive processing (SR-STAP) methods usually directly use the ideal spatial steering vectors without array errors to construct the space-time dictionary; thus, the steering vector mismatch between the dictionary and clutter data will cause a severe performance degradation of SR-STAP methods. To solve this problem, in this paper, we propose a two-stage SR-STAP method for suppressing nonhomogeneous clutter in the presence of arbitrary array errors. In the first stage, utilizing the spatial-temporal coupling property of the ground clutter, a set of spatial steering vectors with array errors are well estimated by fine Doppler localization. In the second stage, firstly, in order to solve the model mismatch problem caused by array errors, we directly use these spatial steering vectors obtained in the first stage to construct the space-time dictionary, and then, the constructed dictionary and multiple measurement vectors sparse Bayesian learning (MSBL) algorithm are combined for space-time adaptive processing (STAP). The proposed SR-STAP method can exhibit superior clutter suppression performance and target detection performance in the presence of arbitrary array errors. Simulation results validate the effectiveness of the proposed method.

Wideband Channel Estimation for IRS-Aided Systems in the Face of Beam Squint

Intelligent reflecting surfaces (IRSs) improve both the bandwidth and energy efficiency of wideband communication systems by using low-cost passive elements for reflecting the impinging signals with adjustable phase shifts. To realize the full potential of IRS-aided systems, having accurate channel state information (CSI) is indispensable, but it is challenging to acquire, since these passive devices cannot carry out transmit/receive signal processing. The existing channel estimation methods conceived for wideband IRS-aided communication systems only consider the channel's frequency selectivity, but ignore the effect of beam squint, despite its severe performance degradation. Hence we fill this gap and conceive wideband channel estimation for IRS-aided communication systems by explicitly taking the effect of beam squint into consideration. We demonstrate that the mutual correlation function between the spatial steering vectors and the cascaded two-hop channel reflected by the IRS has two peaks, which leads to a pair of estimated angles for a single propagation path, due to the effect of beam squint. One of these two estimated angles is the frequency-independent `actual angle', while the other one is the frequency-dependent `false angle'. To reduce the influence of false angles on channel estimation, we propose a twin-stage orthogonal matching pursuit (TS-OMP) algorithm.

Passive Radar STAP Detection and DoA Estimation Under Antenna Calibration Errors

This article addresses the problem of clutter cancelation for slowly moving target detection and localization in multichannel passive radar onboard mobile platforms. A post-Doppler space-time adaptive processing (STAP) approach is exploited in the case of an angle-dependent imbalance affecting the receiving channels. While the clutter suppression capability is ensured by the adaptivity of space-time filtering, different solutions are compared, aimed at recovering the detection performance losses associated with channel calibration errors. A space-time generalized-likelihood ratio test (GLRT) scheme is considered, where the steering vector is not specified in the spatial domain, resulting in a noncoherent integration of target echoes across the receiving channels. This is compared with a fully coherent GLRT scheme where echoes from the stationary scene are exploited for the proper calibration of spatial steering vector mismatch. The first scheme proves to be a simple solution for target detection in the passive radar case, offering comparable clutter cancelation capability. The second scheme, at the expense of an additional stage, offers slightly better detection performance and preserves target direction-of-arrival (DoA) estimation capability. Finally, the STAP scheme is employed for the maximum-likelihood estimation of target DoA, evaluating the role of the steering vector calibration against the negative impact of channel imbalance. The effectiveness of the proposed approaches is tested against both simulated and experimental data from a DVB-T-based mobile passive radar.

Moving Target Detection and Parameter Estimation via a Modified Imaging STAP with a Large Baseline in Multistatic GEO SAR

With the development trends of multistatic spaceborne synthetic aperture radar (SAR), geosynchronous SAR (GEO SAR) employing several formation-flying small satellites also has great potential for remote sensing. The small satellites can cooperate to acquire multi-channel data for moving target detection and parameter estimation in strong clutters. However, multistatic GEO SAR has large satellite spacing and a curved trajectory, which induce the near-field effects and channels out of alignment, respectively, bringing about challenges for the spatial adaptive processing. These problems produce a high-order term in the multi-channel slant range model, making the traditional model and adaptive processing method invalid. In this paper, to meet the requirement of SAR focusing, we firstly derive a fourth-order slant range model and a third-order path difference model for multistatic GEO SAR. Secondly, based on the derived model, the principle of stationary phase and series reversion method are utilized to derive the spatial steering vector for a moving target, which is a basis of spatial adaptive processing in the range-Doppler domain. Thirdly, the time-domain match filtering is constructed based on the fourth-order slant range model to image the moving target. Additionally, the moving targets are detected in the image domain. The motion parameter is estimated by iteratively maximizing the output signal to clutter and noise ratio (SCNR) through the range of possible target velocities. Finally, considering that the GEO SAR is still in development, the computer simulations are carried out to verify the effectiveness and evaluate the performance.

Semi-blind joint symbols and multipath parameters estimation of MIMO systems using KRST/MKRSM coding

In this paper, we propose a new MIMO communication system in a time-varying multipath environment, using a Khatri-Rao space-time (KRST) coding combined with a multiple Khatri-Rao product of symbol matrices (MKRSM). It is shown the signals received at the receiver form a tensor which satisfies a (M+2)-order nested PARAFAC model, where (M−1) denotes the number of symbol matrices considered for MKRSM coding. Such a generalization of the nested PARAFAC model to (M+N)-order tensors is first studied from a general point of view, with the discussion of some parameter estimation methods depending on the a priori knowledge on the model. Then, a semi-blind receiver composed of three stages, is developed for jointly estimating the transmitted symbols and the multipath parameters.In the first stage, the transmitted symbols and a matrix unfolding of the effective channel including the fading coefficients and the steering matrices, are estimated using closed-form algorithms based on Khatri-Rao factorizations. In the second one, the channel estimation is refined by means of a simplified least-squares algorithm which takes the column orthonormality assumption on the coding matrix into account. In the third one, an alternating least-squares algorithm, combined with a rectification for the Vandermonde factors containing the spatial steering vectors at the transmitter and receiver sides, is applied to estimate the multipath parameters from the estimated channel. A complexity analysis is made for the receivers, and an expected Cramer-Rao bound related to channel estimation is established. Extensive Monte Carlo simulation results show that the semi-blind receiver which combines the channel estimation refinement with the rectification technique exhibit very interesting performance.

Moving target modelling and indication in MIMO GEO SAR

Multiple-input multiple-output geosynchronous synthetic aperture radar (MIMO GEO SAR), composed by several mini-satellites in GEO orbits, has more spatial degrees of freedom, which helps to suppress clutter and improves the performance of ground moving target indication (GMTI). However, in order to ensure the satellite safety, the satellite spacing in MIMO GEO SAR is very large. It results in the failure of far-field assumption and causes the moving target defocusing because of the mismatch between the steering vector in far-field sources and the moving target echo. Here, a new signal model based on the near-field sources is first given according to the GEO SAR satellite-ground geometry relationship. Then, considering the phase difference between the different channels, the spatial steering vector is derived and the weight vector for adaptive processing is proposed to suppress clutter and indicate the moving target. Finally, computer simulations are carried out for the validation of the proposed method.

A knowledge aided SPICE space time adaptive processing method for airborne radar with conformal array

Abstract For airborne conformal array radar, it is difficult to suppress clutter using conventional space-time adaptive processing (STAP) methods because the geometry results in range-dependent clutter and nonuniform spatial steering vector. In order to improve the performance of conformal array clutter suppression, a knowledge aided method based on semiparametric/sparse iterative covariance-based estimation STAP, named with KASPICE-STAP, is proposed here. The KASPICE-STAP method requires the knowledge of the clutter ridge spread of the testing range cell. Based on this knowledge, we can construct a dictionary matrix which consists of the clutter space-time steering vectors. Subsequently, by using the dictionary matrix, a relatively accurate covariance matrix of clutter plus noise can be calculated with the KASPICE-STAP method. The proposed approach can work efficiently in complex environments only with the data of cell under test. Compared with other existing sparse recovery STAP methods, the proposed method has global convergence properties and it does not require making any difficult selection of hyperparameters. The improvement factor (IF) curves and range-Doppler images demonstrate the effectiveness of the proposed method.

Design of generalised sidelobe canceller‐based adaptive wideband beamformer without pre‐steering delays

Implementation errors of pre-steering (PS) delays lead to severe performance degradation in the generalised sidelobe canceller-based adaptive wideband beamformer (G-AWBF). Therefore, a G-AWBF without PS delays is proposed. To eliminate PS delays, the G-AWBF is designed in the linear space spanned by the generalised steering vector (GSV) which is defined as the Kronecker product of spatial and temporal steering vectors. Based on GSVs, the quiescent weight and blocking matrix are constructed to substitute PS delays. Compared with the conventional G-AWBF, due to the removal of PS delays, an improved signal to interference and noise ratio can be achieved with reduced system complexity. With less adaptive weights and various versions of unconstrained adaptive algorithms being applicable, the proposed G-AWBF outperforms the existing Frost-based AWBF without PS delays in terms of computational load and robustness. Numerical experiments illustrate the effectiveness and superiority of the proposed G-AWBF.

Practical signal processing algorithm for wide‐area surveillance‐GMTI mode

On the basis of the real data acquired with an X-band airborne wide-area surveillance (WAS)-GMTI radar, a practical signal processing algorithm for WAS-GMTI mode is proposed, and it is simple and effective for real-time processing. The key feature of the new algorithm is that the spatial steering vector and fixed channel error are estimated according to the result of the Doppler centroid estimation. This is due to the fact that the angle corresponding to the Doppler centroid is just the antenna look direction. In this study, the detailed description of the algorithm is presented with four steps: pre-processing, clutter suppression, constant false alarm rate detection and parameter estimation. Besides, to observe the effect of the proposed algorithm, the real data processing results are shown after each step. Finally, moving target positioning results of five successive scan periods is presented to demonstrate the effectiveness of the new algorithm.

DOA and Polarization Estimation Based on Sparse COLD Array

Direction of arrival (DOA) ambiguity influences the performance of array signal processing. To address this problem, a DOA and polarization estimation method is proposed in this paper. Based on sparse uniform concentric semi-circular array consisting of concentred orthogonal loop and dipole pairs, the actual array steering vector can be transformed into a virtual one without additional computation. By applying dot division and dot product operation to outer and inner circular ring array spatial steering vectors, two new spatial steering vectors of arrays whose inter-element spacing are less and much larger than half wavelength are obtained respectively, the cyclic phase ambiguity is disambiguated effectively. In the proposed algorithm, all the array elements (actual and virtual) contribute toward the derivation of both the coarse estimations and the fine estimations, thereby achieving full exploitation of the entire physical aperture, the estimation precision is herein improved.

Estimating DOA and polarization with spatially spread loop and dipole pair array

The nonuniform L-shaped spatially spread loop and dipole (SSLD) array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival (DOA), frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops, the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array, then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.

Direction Finding and Information Detection Algorithm with an L-Shaped CCD Array

ABSTRACTThis paper proposes a quaternion-ESPRIT (estimate signal parameters via rotation invariance) algorithm for estimating frequency, direction of arrival (DOA) and polarization, using a collocated crossed dipole (CCD) L-shaped array configuration. First, two sets of synchronous sampling data are used to construct the data covariance matrix, the array steering vector of the whole array is estimated using a quaternion eigenvalue decomposition of the data covariance matrix. Second, the direction cosine of the x-axis and y-axis are acquired by applying block operation to the spatial steering vectors, hence the estimates of two-dimensional DOA are obtained. Finally, the polarization parameters are estimated using the relationship between the dipole sub-array steering vectors of the x-axis and y-axis. The closed-form solutions for each parameter are obtained and parameters can automatically match. The simulation results verify that the performance of quaternion method is obviously better than that of the long-vector method.

선형-원형배열 안테나에 따른 MIMO의 DOA 추정과 적응 빔성형 분석

Abstract In this paper, DOA(direction of arrival) of multiple incident signals received from linear array antenna and circular array antenna, which is based on nonparametric estimation algorithm, and adaptive beam-forming algorithm are studied and analyzed. In nonparametric estimation algorithm, we minimize a regularized objective function for finding a estimate of the signal energy as a function of angle, using nonquadratic norm which leads to supper resolution and noise suppression. And then, DOA is estimated by the signal and noise spatial steering vector, and adaptive beam-forming pattern is improved by weight vectors obtained from the spatial vector. Especially, the discrimination ability of DOA and the adaptive beam-forming ability according to antenna array methods and the number of array elements are compared and considered. Key Words : linear array, Circular array, DOA, Nonparametric Estimation algorithm, Adaptive Beam-forming pattern, Weight vector, Super resolution 본 논문은 2011년도 대진대학교 학술연구지원비로 수행되었음.

이동통신 환경에서 다중신호의 DOA 추정과 적응 빔성형

The DOA(direction of arrival), which is based on parametric and nonparametric estimation algorithm, and adaptive beamforming algorithm for mobile communication environments are researched and analyzed. In parametric estimation algorithm, eigenvalues of the signal component and the noise component are obtained from correlation matrix of received signal by array antenna and power spectrum of the received signal is discriminated from them. Otherwise, in nonparametric estimation algorithm, we minimize a regularized objective function for finding a estimate of the signal energy as a function of angle, using nonquadratic norm which leads to supper resolution and noise suppression. And then, DOA is estimated by the signal and noise spatial steering vector, and adaptive beam-forming pattern is improved by weight vectors obtained from the spatial vector. Therefore, the improved directional estimation algorithm with regularizing sparsity constraints offers super-resolution and noise suppression compared to other algorithms.

On robust beamforming for InSAR phase estimation

In InSAR signal processing, the performance of the interferometric phase estimation degrades in the case of image coregistration errors and spatial steering vector errors. In this letter, a method of interferometric phase estimation based on robust beamforming is introduced. The proposed method can take advantage of the optimal weighted joint data (OWJD) vector and of the robust adaptive beamformer to auto-coregister the SAR images and mitigate the effect of the spatial steering error on the interferometric phase estimation. Theoretical analysis and experimental results show that the method can provide accurate estimation of the interferometric phase in the presence of the coregistration error and spatial steering vector error. Numerical results on the simulated and real data demonstrate the effectiveness and robustness of the proposed method.

Handling partially calibrated conformal antenna arrays in range–dependence compensation for airborne bistatic space–time adaptive processing radar

The authors consider space-time adaptive processing (STAP) when the radar returns are recorded by a conformal antenna array (CAA). The statistics of the secondary data snapshots used to estimate the optimum weight vector are not identically distributed with respect to range, thus preventing the customary STAP processor from achieving its optimum performance. The compensation of the range dependence of the secondary data requires precise knowledge of the array response for any direction of arrival (DOA), and, thus, of the spatial steering vectors (SVs). The authors propose a novel registration-based range-dependence compensation algorithm that gives an accurate estimate of the interference-plus-noise covariance matrix under the hypotheses that calibrated spatial SVs are available only for a small set of DOAs, and that the errors in the model giving the true spatial SV for each DOA are DOA dependent. The performance in terms of signal-to-interference-plus-noise ratio loss is promising.

Joint Domain Localized Adaptive Processing Using Nonorthogonal Steering Vectors

The joint domain localized (JDL) processing adaptive algorithm significantly speeds up space-time adaptive processing by working within a localized processing region in the angle–Doppler domain. The two-dimensional data collected in space and time domains are transformed to the angle–Doppler domain using the spatial and temporal steering vectors. However, the algorithm depends on the assumption that the steering vectors form an orthogonal set. In practice, due to the mutual coupling between antenna elements, the spatial steering vectors are nonorthogonal. This paper presents a modification of the JDL algorithm to account for the nonorthogonality of the spatial steering vectors. The modification is extended to allow for the use of windows in transforming from the space-time to the angle–Doppler domain. Improvements in detection capability are demonstrated using examples from the MCARM database.