Robust STAP Against Unknown Mutual Coupling Based on Middle Subarray Clutter Covariance Matrix Reconstruction

A robust STAP method for airborne radar based on clutter covariance matrix reconstruction and steering vector estimation

To obtain an antenna array with isotropic radiation, spherical antenna array (SAA) is the right array configuration. The challenges of locating signals transmitted within the proximity of antenna array have been investigated considerably in the literature. However, near‐field (NF) source localization of signals has hitherto not been investigated effectively using SAA in the presence of mutual coupling (MC). MC is another critical problem in antenna arrays. This paper presents an NF range and direction‐of‐arrival (DoA) estimation technique via the direction‐independent and signal invariant spherical harmonics (SH) characteristics in the presence of mutual coupling. The energy of electromagnetic (EM) signal on the surface of SAA is captured successfully using a proposed pressure interpolation approach. The DoA estimation within the NF region is then calculated via the distribution of pressure. The direction‐independent and signal invariant characteristics, which are SH features, are obtained using the DoA estimates in the NF region. We equally proposed a learning scheme that uses the source activity detection and convolutional neural network (CNN) to estimate the range of the NF source via the direction‐independent and signal invariant features. Considering the MC problem and using the DoA estimates, an accurate spectrum peak in the multipath situation in conjunction with MC and a sharper spectrum peak from a unique MC structure and smoothing algorithms are obtained. For ground truth performance evaluation of the SH features within the context of NF localization, a numerical experiment is conducted and measured data were used for analysis to incorporate the MC and consequently computed the root mean square error (RMSE) of the source range and NF DoA estimate. The results obtained from numerical experiments and measured data indicate the validity and effectiveness of the proposed approach. In addition, these results are motivating enough for the deployment of the proposed method in practical applications.

Space-time adaptive monopulse processing for airborne radar in non-homogeneous environments

As training samples are not always target-free in space-time processing for airborne radar, the traditional methods usually use the sample covariance matrix (SCM) as the test covariance matrix (TCM) to censor contaminated training samples. However, the SCM cannot represent the property of the cell under test (CUT) accurately, resulting in low selection efficiency. To deal with this problem, this letter proposes a novel training sample selection method based on covariance matrix whitening. Specifically, we utilize the reconstructed subaperture's clutter covariance matrix (RSCCM) of the CUT as the TCM. The RSCCM is only determined by the CUT and can characterize the CUT directly. Then, we use the RSCCM to whiten the subaperture's covariance matrix of the training sample. A criterion for selecting the training samples is derived based on the maximum eigenvalue of the whitened subaperture's covariance matrix, which is related to the energy of the outliers and more stable than the statistic of the generalized inner product method. Simulations are conducted to evaluate the performance of the proposed method.

An eigenstructure-based method for direction finding in the presence of sensor mutual coupling, gain, and phase uncertainties is presented. The method provides estimates of the directions-of-arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor and the mutual coupling in the receiving array. The proposed algorithm is able to calibrate the array parameters without prior knowledge of the array manifold, using only signals of opportunity and avoiding the need for deploying auxiliary sources at known locations. The algorithm is described in detail, and its behavior is illustrated by numerical examples. >

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.

Estimating the directions-of-arrival (DOA) of plane waves that impinge on an antenna array is an important issue in mobile communication systems. Because of their symmetry uniform circular arrays are attractive array configurations in the context of DOA estimation. In realistic antenna arrays mutual coupling between the antenna elements influences the electromagnetic characteristics of the antenna elements and affects the reliability and accuracy of the developed algorithms. We propose a 2-D DOA estimation algorithm that incorporates mutual coupling in full detail. Although mutual coupling complicates the receiving characteristics of an antenna array, the circular symmetry is still obtained in the presence of mutual coupling and a phase mode expansion of the array manifold is still possible. This enables us to apply UCA-RARE to estimate the azimuth angles independent from the elevation angles. Next, for each azimuth angle we perform a new search-free rooting algorithm, which provides the elevation estimate, based on the expansion of the array manifold into a double Fourier series.

This paper reports investigations into mutual coupling effects on performance of a beamforming transmission scheme of a multiple-input multiple-output (MIMO) system operating under Rician channel conditions. It is shown that the presence of mutual coupling in a transmitting array antenna degrades the radiation pattern. However, it does not adversely affect the system capacity. If the correlated Rayleigh component (NLOS) dominates the channel, the mutual coupling leads to lower capacity. The presence of mutual coupling results in a higher capacity when the LOS component prevails. For some specific ranges of array inter-element spacing, mutual coupling can be seen as beneficial in terms of increasing the capacity when a signal beamforming strategy is applied.

The disturbance covariance matrix in radar space time adaptive processing (STAP) must be estimated from training sample observations. Traditional maximum likelihood (ML) estimators are effective when training is generous but lead to degraded false alarm rates and detection performance in the realistic regime of limited training. We exploit physically motivated constraints such as 1.) rank of the clutter subspace which can be inferred using existing physics based models such as the Brennan rule, and 2.) the Toeplitz constraint that applies to covariance matrices obtained from stationary random processes. We first provide a closed form solution of the rank constrained maximum likelihood (RCML) estimator and then subsequently develop an efficient approximation under joint Toeplitz and rank constraints (EASTR). Experimental results confirm that the proposed EASTR estimators outperform state-of-the-art alternatives in the sense of widely used measures such as the signal to interference and noise ratio (SINR) and probability of detection - particularly when training support is limited.

The problem of Angle-of-Arrival estimation of multiple sources in the presence of mutual coupling is addressed. In this paper, we derive a Mean-Squared-Error (MSE) expression of a recently proposed algorithm that could estimate the Angles-of-Arrival of multiple sources in the presence of more mutual coupling parameters, compared to traditional methods. The MSE expression is compared with the MSE of MUSIC with known mutual coupling parameters and to the Cramer-Rao bound (CRB) of any unbiased estimator that estimates the Angles-of-Arrival in the presence of mutual coupling. It is shown that the proposed method is asymptotically unbiased. In addition, it is also shown that the method attains CRB for large number of antennas with fixed coupling parameters and uncorrelated sources. For high SNR, the CRB is not necessarily attained, however, we study the gap between the derived MSE and the CRB.

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positive semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. The low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.

This paper proposes a new method for cross array to estimate two-dimensional direction of arrival (2-D DOA) in the presence of mutual coupling. In this method, the array elements which are affected by the same mutual coupling are chosen onx-axis andz-axis, respectively. Then a new matrix is constructed with the proper entries of cross covariance matrix of the chosen elements outputs onx-axis andz-axis. Propagation method (PM) and rotational invariance techniques for uniform linear array (ULA) are utilized in the constructed matrix to obtain two parameters correlated with elevations and azimuths. While calculating and pairing the two parameters, only once eigendecomposing and several division operations are required with the relationship among the matrix, its eigenvalues, and corresponding eigenvectors. Simulations are presented to validate the performance of the proposed method.

Traditional space-time (ST) adaptive processing (STAP) theory is based on the assumption of narrowband or “zero-bandwidth,” where the decorrelation within the ST snapshot is ignored. However, with radar bandwidths increasing, this assumption becomes invalid due to the deteriorated decorrelation of the received signals within the ST snapshot. The decorrelation directly causes the dispersion of the received signals in both spatial and temporal domains, leading to the spreading of the clutter spectrum in the 2-D frequency (Doppler-spatial frequency) domain. With the spreading of the clutter spectrum, the clutter suppression notch in the traditional STAP filters is widened, resulting in a relative poor ability to detect slow-moving targets. In this article, we focus on the clutter suppression for wideband radar STAP. A generalized signal model of the ground clutter is first established for the wideband array radar. Using this outcome, we analyze the influence of bandwidth on the characteristics of the ground clutter and quantitatively describe the 2-D spreading of the ground clutter on the Doppler-spatial frequency plane. Moreover, the model of clutter covariance matrix for wideband STAP (W-STAP) is established. Finally, a 2-D keystone transform (KT) algorithm, referred to as ST KT (ST-KT), is proposed to eliminate the spreading of the ground clutter in the 2-D frequency domain caused by increasing bandwidths. Simulation results are employed to validate the theoretical analysis and verify the overperformance of the ST-KT based W-STAP method in terms of the output signal-to-clutter-plus-noise ratio (SCNR) of moving targets.

In this paper, the effects of mutual coupling on the performance of GPS anti-jam antennas are discussed. For space-only processing (SOP) based adaptive antennas operating in the presence of CW interfering signals, it is shown that the performance with mutual coupling is similar to the performance in the absence of mutual coupling. The performance of the adaptive antenna degrades when wide-band interfering signals are introduced. The degradation with mutual coupling is larger than when mutual coupling is excluded in the performance evaluation. Furthermore, it is demonstrated that the improper design of individual elements can be the cause of this performance degradation. Space-time adaptive processing (STAP) is shown to recover the lost performance that SOP based adaptive antennas incur in the presence of wide-band interference. Finally, it is demonstrated that improper element design can be a cause of performance degradation even when STAP is used.

Many applications require precise estimates of high-dimensional covariance matrices. The standard estimator is the sample covariance matrix, which is conceptually simple, fast to compute and has favorable properties in the limit of infinitely many observations. The picture changes when the dimensionality is of the same order as the number of observations. In such cases, the eigenvalues of the sample covariance matrix are highly biased, the condition number becomes large and the inversion of the matrix gets numerically unstable.
\nA number of alternative estimators are superior in the high-dimensional setting, which include as subcategories structured estimators, regularized estimators and spectrum correction methods. In this thesis I contribute to all three areas. 
\nIn the area of structured estimation, I focus on models with low intrinsic dimensionality. I analyze the bias in Factor Analysis, the state-of-the-art factor model and propose Directional Variance Adjustment (DVA) Factor Analysis, which reduces bias and yields improved estimates of the covariance matrix.
\nAnalytical shrinkage of Ledoit and Wolf (LW-Shrinkage) is the most popular regularized estimator. I contribute in three aspects: first, I provide a theoretical analysis of the behavior of LW-Shrinkage in the presence of pronounced eigendirections, a case of great practical relevance. I show that LW-Shrinkage does not perform well in this setting and propose aoc-Shrinkage which yields significant improvements. Second, I discuss the effect of autocorrelation on LW-Shrinkage and review the Sancetta-Estimator, an extension of LW-Shrinkage to autocorrelated data. I show that the Sancetta-Estimator is biased and propose a theoretically and empirically superior estimator with reduced bias. Third, I propose an extension of shrinkage to multiple shrinkage targets. Multi-Target Shrinkage is not restricted to covariance estimation and allows for many interesting applications which go beyond regularization, including transfer learning. I provide a detailed theoretical and empirical analysis.
\nSpectrum correction approaches the problem of covariance estimation by improving the estimates of the eigenvalues of the sample covariance matrix. I discuss the state-of-the-art approach, Nonlinear Shrinkage, and propose a cross-validation based covariance (CVC) estimator which yields competitive performance at increased numerical stability and greatly reduced complexity and computational cost. On all data sets considered, CVC is on par or superior in comparison to the regularized and structured estimators.
\nIn the last chapter, I conclude with a discussion of the advantages and disadvantages of all covariance estimators presented in this thesis and give situation-specific recommendations. In addition, the appendix contains a systematic analysis of Linear Discriminant Analysis as a model application, which sheds light on the interdependency between the generative model of the data and various covariance estimators.