The estimation problem of structured clutter covariance matrix (CCM) in space-time adaptive processing (STAP) for airborne radar systems is studied in this letter. By employing the prior knowledge and the persymmetric covariance structure, a new estimation algorithm is proposed based on the whitening ability of the covariance matrix. The proposed algorithm is robust to prior knowledge of different accuracy, and can whiten the observed interference data to obtain the optimal solution. In addition, the extended factored approach (EFA) is used in the optimization for dimensionality reduction, which reduces the computational burden. Simulation results show that the proposed algorithm can effectively improve STAP performance even under the condition of some errors in prior knowledge.

Adaptive multilooking is a critical processing step in multi-temporal interferometric synthetic aperture radar (InSAR) measurement, especially in small temporal baseline subsets. Various amplitude-based adaptive multilook approaches have been proposed for the improvement of interferometric processing. However, the phase signal, which is fundamental in interferometric systems, is typically ignored in these methods. To fully exploit the information in complex SAR images, a nonlocal adaptive multilooking is proposed based on complex covariance matrix in this work. The complex signal is here exploited for the similiarity measurement between two pixels. Given the complexity of objects in SAR images, structure feature detection is introduced to adaptively estimate covariance matrix. The effectiveness and reliability of the proposed approach are demonstrated with experiments both on simulated and real data.

A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.

In this paper, we propose an online antenna-pulse selection method in space time adaptive processing, while maintaining considerable performance and low computational complexity. The proposed method considers the antenna-pulse selection and covariance matrix estimation at the same time by exploiting the structured clutter covariance matrix. Such prior knowledge can enhance the covariance matrix estimation accuracy and thus can provide a better objective function for antenna-pulse selection. Simulations also validate the effectiveness of the proposed method.

Spectrum sensing is the first task performed by cognitive radio (CR) networks. In this paper we propose a spectrum sensing algorithm for orthogonal frequency division multiplex (OFDM) signal based on deep learning and covariance matrix graph. The advantage of deep learning in image processing is applied to the spectrum sensing of OFDM signals. We start by building the spectrum sensing model of OFDM signal, and then analyze structural characteristics of covariance matrix (CM). Once CM has been normalized and transformed into a gray level representation, the gray scale map of covariance matrix (GSM-CM) is established. Then, the convolutional neural network (CNN) is designed based on the LeNet-5 network, which is used to learn the training data to obtain more abstract features hierarchically. Finally, the test data is input into the trained spectrum sensing network model, based on which spectrum sensing of OFDM signals is completed. Simulation results show that this method can complete the spectrum sensing task by taking advantage of the GSM-CM model, which has better spectrum sensing performance for OFDM signals under low SNR than existing methods.

Using local time frames to treat non-stationary real world signals as stationary yields Quasi-Stationary Signals (QSS). In this paper, direction of arrival (DOA) estimation of uncorrelated non-circular QSS is analyzed by applying a novel technique to achieve larger consecutive lags using coprime array. A scheme of virtual extension of coprime array is proposed that exploits the difference and sum co-array which can increase consecutive co-array lags in remarkable number by using less number of sensors. In the proposed method, cross lags as well as self lags are exploited for virtual extension of co-arrays both for differences and sums. The method offers higher degrees of freedom (DOF) with a larger number of non-negative consecutive lags equal to MN+2M+1 by using only M+N-1 number of sensors where M and N are coprime with congenial interelement spacings. A larger covariance matrix can be achieved by performing covariance like computations with the Khatri-Rao (KR) subspace based approach which can operate in undetermined cases and even can deal with unknown noise covariances. This paper concentrates on only non-negative consecutive lags and subspace based method like Multiple Signal Classification (MUSIC) based approach has been executed for DOA estimation. Hence, the proposed method, named Virtual Extension of Coprime Array imbibing Difference and Sum (VECADS), in this work is promising to create larger covariance matrix with higher DOF for high resolution DOA estimation. The coprime distribution yielded by the proposed approach can yield higher resolution DOA estimation while avoiding the mutual coupling effect. Simulation results demonstrate its effectiveness in terms of the accuracy of DOA estimation even with tightly aligned sources using fewer sensors compared with other techniques like prototype coprime, conventional coprime, Coprime Array with Displaced Subarrays (CADiS), CADiS after Coprime Array with Compressed Inter-element Spacing (CACIS) and nested array seizing only difference co-array.

An improved beamformer, which uses joint estimation of the reconstructed interference-plus-noise (IPN) covariance matrix and array steering vector (ASV), is proposed. It can mitigate the problem of performance degradation in situations where the desired signal exists in the sample covariance matrix and the steering vector pointing has large errors. In the proposed method, the covariance matrix is reconstructed by weighted sum of the exterior products of the interferences' ASV and their individual power to reject the desired signal component, the coefficients of which can be accurately estimated by the compressed sensing (CS) and total least squares (TLS) techniques. Moreover, according to the theorem of sequential vector space projection, the actual ASV is estimated from an intersection of two subspaces by applying the alternating projection algorithm. Simulation results are provided to demonstrate the performance of the proposed beamformer, which is clearly better than the existing robust adaptive beamformers.

Based on the reconstruction of the augmented interference-plus-noise (IPN) covariance matrix (CM) and the estimation of the desired signal's extended steering vector (SV), we propose a novel robust widely linear (WL) beamforming algorithm. Firstly, an extension of the iterative adaptive approach (IAA) algorithm is employed to acquire the spatial spectrum. Secondly, the IAA spatial spectrum is adopted to reconstruct the augmented signal-plus-noise (SPN) CM and the augmented IPNCM. Thirdly, the extended SV of the desired signal is estimated by using the iterative robust Capon beamformer with adaptive uncertainty level (AU-IRCB). Compared with several representative robust WL beamforming algorithms, simulation results are provided to confirm that the proposed method can achieve a better performance and has a much lower complexity.

In this letter, a novel mainlobe anti-jamming method via eigen-projection processing and covariance matrix reconstruction is proposed. The present work mainly focuses on two aspects: the first aspect is to obtain the eigenvector of the mainlobe interference accurately in order to form the eigen-projection matrix to suppress the mainlobe interference. The second aspect is to reconstruct the covariance matrix which is uesd to calculate the adaptive weight vector for forming an ideal beam pattern. Additionally, the self-null effect caused by the signal of interest and the sidelobe interferences elimination are also considered in the proposed method. Theoretical analysis and simulation results demonstrate that the proposed method can suppress the mainlobe interference effectively and achieve a superior performance.

In this letter, a novel robust adaptive beamforming algorithm is addressed to improve the robustness against steering vector random errors (SVREs), which eliminates the signal of interest (SOI) component from the sample covariance matrix (SCM), based on interference-plus-noise covariance matrix (IPNCM) reconstruction over annulus uncertainty sets. Firstly, several annulus uncertainty sets are used to constrain the steering vectors (SVs) of both interferences and the SOI. Additionally the IPNCM is reconstructed according to its definition by estimating each interference SV over its own annulus uncertainty set via the subspace projection algorithm. Meanwhile, the SOI SV is estimated as the prime eigenvector of the SOI covariance matrix term calculated over its own annulus uncertainty set. Finally, a novel robust beamformer is formulated based on the new IPNCM and the SOI SV, and it outperforms other existing reconstruction-based beamformers when the SVREs exist, especially in low input signal-to-noise ratio (SNR) cases, which is proved through the simulation results.

We address a robust algorithm for the interference-plus-noise covariance matrix reconstruction (RA-INCMR) against random arbitrary steering vector mismatches (RASVMs) of the interferences, which lead to substantial degradation of the original INCMR beamformer performance. Firstly, using the worst-case performance optimization (WCPO) criteria, we model these RASVMs as uncertainty sets and then propose the RA-INCMR to obtain the robust INCM (RINCM) based on the Robust Capon Beamforming (RCB) algorithm. Finally, we substitute the RINCM back into the original WCPO beamformer problem for the sample covariance matrix to formulate the new RA-INCM-WCPO beamformer problem. Simulation results demonstrate that the performance of the proposed beamformer is much better than the original INCMR beamformer when there exist RASVMs, especially at low signal-to-noise ratio (SNR).

Co-channel interference (CCI) is becoming a challenging factor that causes performance degradation in modern communication systems. The receiver equipped with multiple antennas can suppress such interference by exploiting spatial correlation. However, it is difficult to estimate the spatial covariance matrix (SCM) of CCI accurately with limited number of known symbols. To address this problem, this paper first proposes an improved SCM estimation method by shrinking the variance of eigenvalues. In addition, based on breadth-first tree search schemes and improved channel updating, a low complexity iterative detector is presented with channel preprocessing, which not only considers the existence of CCI but also reduces the computational complexity in terms of visited nodes in a search tree. Furthermore, by scaling the extrinsic soft information which is fed back to the input of detector, the detection performance loss due to max-log approximation is compensated. Simulation results show that the proposed iterative receiver provides improved signal to interference ratio (SIR) gain with low complexity, which demonstrate the proposed scheme is attractive in practical implementation.

Polarimetric coherence strongly relates to the types and orientations of local scatterers. An optimization scheme is proposed to optimize the coherence between two polarimetric channels for polarimetric SAR (PolSAR) data. The coherence magnitude (correlation coefficient) is maximized by rotating a polarimetric coherence matrix in the rotation domain around the radar line of sight. L-band E-SAR and X-band Pi-SAR PolSAR data sets are used for demonstration and validation. The coherence of oriented manmade targets is significantly enhanced while that of forests remains relatively low. Therefore, the proposed technique can effectively discriminate these two land covers which are easily misinterpreted by the conventional model-based decomposition. Moreover, based on an optimized polarimetric coherence parameter and the total backscattered power, a simple manmade target extraction scheme is developed for application demonstration. This approach is applied with the Pi-SAR data. The experimental results validate the effectiveness of the proposed method.

This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

A hot clutter mitigation algorithm based on Subbanding and Space Fast-time Adaptive Processing (Fast-time STAP) for Multi-channel Synthetic Aperture Radar (MSAR) is analyzed, and is compared with the method based on just fast-time STAP. Simulation results demonstrate that the method based on subbanding and fast-time STAP performs better than the method based on just fast-time STAP in hot clutter mitigation for MSAR.

In this paper, we present a revision of using eigenvalues of covariance matrices proposed by Tsai et al. as a measure of significance (i.e., curvature) for boundary-based corner detection. We first show the pitfall of Tsai et al.'s approach. We then further investigate the properties of eigenvalues of covariance matrices of three different types of curves and point out a mistake made by Tsai et al.'s method. Finally, we propose a modification of using eigenvalues as a measure of significance for corner detection to remedy their defect. The experiment results show that under the same conditions of the test patterns, in addition to correctly detecting all true corners, the spurious corners detected by Tsai et al.'s method disappear in our modified measure of significance.

We propose an appearance manifold with view-dependent covariance matrix for face recognition from video sequences in two learning frameworks: the supervised-learning and the incremental unsupervised-learning. The advantages of this method are, first, the appearance manifold with view-dependent covariance matrix model is robust to pose changes and is also noise invariant, since the embedded covariance matrices are calculated based on their poses in order to learn the samples' distributions along the manifold. Moreover, the proposed incremental unsupervised-learning framework is more realistic for real-world face recognition applications. It is obvious that it is difficult to collect large amounts of face sequences under complete poses (from left sideview to right sideview) for training. Here, an incremental unsupervised-learning framework allows us to train the system with the available initial sequences, and later update the system's knowledge incrementally every time an unlabelled sequence is input. In addition, we also integrate the appearance manifold with view-dependent covariance matrix model with a pose estimation system for improving the classification accuracy and easily detecting sequences with overlapped poses for merging process in the incremental unsupervised-learning framework. The experimental results showed that, in both frameworks, the proposed appearance manifold with view-dependent covariance matrix method could recognize faces from video sequences accurately.

We propose the construction of an appearance manifold with embedded view-dependent covariance matrix to recognize 3D objects which are influenced by geometric distortions and quality degradation effects. The appearance manifold is used to capture the pose variability, while the covariance matrix is used to learn the distribution of samples for gaining noise-invariance. However, since the appearance of an object in the captured image is different for every different pose, the covariance matrix value is also different for every pose position. Therefore, it is important to embed view-dependent covariance matrices in the manifold of an object. We propose two models of constructing an appearance manifold with view-dependent covariance matrix, called the View-dependent Covariance matrix by training-Point Interpolation (VCPI) and View-dependent Covariance matrix by Eigenvector Interpolation (VCEI) methods. Here, the embedded view-dependent covariance matrix of the VCPI method is obtained by interpolating every training-points from one pose to other training-points in a consecutive pose. Meanwhile, in the VCEI method, the embedded view-dependent covariance matrix is obtained by interpolating only the eigenvectors and eigenvalues without considering the correspondences of each training image. As it embeds the covariance matrix in manifold, our view-dependent covariance matrix methods are robust to any pose changes and are also noise invariant. Our main goal is to construct a robust and efficient manifold with embedded view-dependent covariance matrix for recognizing objects from images which are influenced with various degradation effects.

In the usual optical flow detection, the gradient constraint, which expresses the relationship between the gradient of the image intensity and its motion, is combined with the least-squares criterion. This criterion means assuming that only the time derivative of the image intensity contains noise. In this paper, we assume that all image derivatives contain noise and derive a new optical flow detection technique. Since this method requires the knowledge about the covariance matrix of the noise, we also discuss a method for its estimation. Our experiments show that the proposed method can compute optical flow more accurately than the conventional method.

We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.