Sub-Nyquist radars require fewer measurements, facilitating low-cost design, flexible resource allocation, etc. By applying compressed sensing (CS) method, such radars achieve close performance to traditional Nyquist radars. However in low signal-to-noise ratio (SNR) scenarios, detecting weak targets is challenging: low probability of detection and many spurious targets could occur in the recovery results of traditional CS method. To overcome this issue, we propose a weighted sparse recovery based track-before-detect (TBD) method for weak targets detection by accumulating multi-frame information. Particularly, tracking results of targets are utilized as prior knowledge to enhance the recovery accuracy, thus improving the detection performance. Numerical results show that our method improves the detection performance particularly and reduces the occurrence of spurious targets in low SNR situations compared with traditional CS method.

We propose tensor-based four-dimensional sub-Nyquist radar that samples in spectral, spatial, Doppler, and temporal domains at sub-Nyquist rates while simultaneously recovering the target's direction, Doppler velocity, and range without loss of native resolutions. We formulate the radar signal model wherein the received echo samples are represented by a partial third-order tensor. We then apply compressed sensing in the tensor domain and use our tensor-orthogonal matching pursuit (OMP) and tensor completion algorithms for signal recovery. Our numerical experiments demonstrate joint estimation of all three target parameters at the same native resolutions as a conventional radar but with reduced measurements. Furthermore, tensor completion methods show enhanced performance in off-grid target recovery with respect to tensor-OMP.

Partitioning the antenna array into different subarrays is a flexible scheme in the joint radar and communication system. However, the traditional fixed partition of the antenna array cannot make full use of the complete aperture. In this paper, we propose a novel antenna partition scheme. In this scheme, the antenna is randomly and dynamically chosen as radar or communication unit. The dynamic randomness introduces extra channel capacity of the communication system, and enables the radar system approximately obtain the resolution and sidelobe level of a full antenna array simultaneously. The channel capacity, Cramér Rao Bound and the ambiguity function are theoretically analyzed. Pareto Front is used to demonstrate the performance improvement of the proposed system over the traditional fixed partition system.

This letter addresses the detection of a subspace distributed target signal obscured by disturbance. The disturbance consists of a clutter component with an unknown subspace structure and a white noise component with unknown noise power. A detection strategy is proposed based on the volume cross-correlation function, which provides a metric that measures the linear (in) dependency between two subspaces. Simulation results indicate that the proposed detector can achieve better performance than several peer methods, without resorting to secondary data and a priori knowledge about the clutter subspace including its rank.

In this paper, a new perturbation analysis algorithm for the MUltiple SIgnal Classification (MUSIC) estimator applied to a Hermitian Toeplitz covariance matrix is presented. Inspired by the perspective that the MUSIC algorithm can be recognized as a structured matrix approximation, the perturbation of parameter estimates can be predicted more accurately by seeking the minimum of a Frobenius norm. The prediction results are analytically expressed through a weighted least squares method. The performance of the MUSIC estimators can also be predicted using our algorithm.

This paper concerns sparse Bayesian learning (SBL) problem for group sparse signals. Group sparsity means that the signal components can be divided into groups, and the entries in one group are simultaneously zero or nonzero. In SBL, each group is controlled by a hyper-parameter. The marginal likelihood maximization (MLM) problem is to maximize the marginal likelihood of a given hyper-parameter by fixing all others. The main contribution of this paper is to solve the MLM problem by finding roots of a polynomial. Hence the global minimum of the marginal likelihood can be found efficiently. Furthermore, most large matrix inverses involved in MLM are replaced with the singular value decompositions of much smaller matrices, which substantially reduces the computational complexity. The proposed method is significantly different from the popular expectation maximization techniques in the literature where multiple iterations are required for MLM and the convergence to global optimum of marginal likelihood is not guaranteed.

It has been widely recognized that structure information helps in sparse signal recovery. In this paper, a general form of block structure is considered, which is often referred to hierarchically sparse model. It is assumed that the unknown sparse signal can be divided into blocks, and a block contains either all zero components or a fraction of nonzero components. This model sits between the standard sparse model (without block structure) and the strict block sparse model (all entries in nonzero blocks are nonzero). The focus of this paper is to analyze the convex optimization approach to recover hierarchically sparse signals. The technique we employed is based on the approximated message passing framework and the associated state evolution. The minimum number of measurements required for exact recovery, also known as phase transition (PT), has been quantified in an asymptotic region. We show that the PT depends on two parameters: the fraction of nonzero components in nonzero blocks, and the uniformity of the magnitudes of nonzero components. Based on the PT analysis, we characterize the regions at which the convex optimization methods designed for the standard, hierarchically, and block sparse models are optimal respectively.

Detecting the presence of target subspace signals with unknown clutters is a well-known hard problem encountered in various signal processing applications. Traditional methods fails to solve this problem because prior knowledge of clutter subspace is required, which can not be obtained when target and clutter are intimately mixed. In this paper, we propose a novel subspace detector that can detect target signal buried in clutter without knowledge of clutter subspace. This detector makes use of the geometrical relation between target and clutter subspaces and is derived based upon the calculation of volume of high dimensional geometrical objects. Moreover, the proposed detector can accomplish the detection simultaneously with the learning processes of clutter, a property called “detecting while learning”. The performance of detector was showed by theoretical analysis and numerical simulation.

In this paper, we propose a novel model to study the efficiency of detecting latent connection relationships, represented by a given set of graphs, among N users. A subset of active nodes transmit following a common codebook over a multiple access Boolean channel. To maximize the error exponent of the structure detection, we formulate an optimization problem whose objective is to max-minimize the pairwise Chernoff information, and the constraint is a probability simplex due to the users' multiple dependency relationships, which are further shown to have close relationship to the internal connectivity of graphs. Case studies are provided to show certain inherent properties of the optimal solution. In addition, we present a particular case with two equally weighted complementary Paley graphs of prime square order, whose optimal solution for the codebook is proved and the resulting exponent is shown to be O(1/N). The case study demonstrates how the fundamental graph discrepancy property affects the solution to the problem.

Compressive sensing (CS) provides a new perspective for data reduction without compromising performance when the signal of interest is sparse or has intrinsically low-dimensional structure. The theoretical foundation for most of the existing studies on CS is based on the stable embedding (i.e., a distance-preserving property) of vectors that are sparse or in a union of subspaces via random measurement matrices. To the best of our knowledge, few existing literatures of CS have clearly discussed the stable embedding of linear subspaces via compressive measurement systems. In this paper, we explore a volume-based stable embedding of multidimensional signals based on Grassmann manifold, via Gaussian random measurement matrices. The Grassmann manifold is a topological space, in which each point is a linear vector subspace, and is widely regarded as an ideal model for multidimensional signals generated from linear subspaces. In this paper, we formulate the linear subspace spanned by multidimensional signal vectors as points on the Grassmann manifold, and use the volume and the product of sines of principal angles (also known as the product of principal sines) as the generalized norm and distance measure for the space of Grassmann manifold. We prove a volume-preserving embedding property for points on the Grassmann manifold via Gaussian random measurement matrices, i.e., the volumes of all parallelotopes from a finite set in Grassmann manifold are preserved upon compression. This volume-preserving embedding property is a multidimensional generalization of the conventional stable embedding properties, which only concern the approximate preservation of lengths of vectors in certain unions of subspaces. In addition, we use the volume-preserving embedding property to explore the stable embedding effect on a generalized distance measure of Grassmann manifold induced from volume. It is proved that the generalized distance measure, i.e., the product of principal sines between different points on the Grassmann manifold, is well preserved in the compressed domain via Gaussian random measurement matrices. Numerical simulations are also provided for validation.

Compressive Sensing (CS) provides a new perspective for dimensionnality reduction without compromising performance. The theoretical foundation for most of existing studies of CS is a stable embedding (i.e., a distance-preserving property) of certain low-dimensional signal models such as sparse signals or signals in a union of linear subspaces. However, few existing literatures clearly discussed the embedding effect of points on the Grassmann manifold in under-sampled linear measurement systems. In this paper, we explore the stable embedding property of multi-dimensional signals based on Grassmann manifold, which is a topological space with each point being a linear subspace of ℝN(or ℂN), via the Gaussian random matrices. It should be noted that the stability mentioned here is about the volume-preserving instead of distance-preserving, because volume is the key characteristic for linear subspace spanned by multiple vectors. The theorem of the volume-preserving stable embedding property is proposed, and sketched proofs as well as discussions about our theorem is also given.

Feature selection in Fingerprint-based localization systems is of great importance, because of its capability to reduce the overhead in handling high- dimensional data while ensuring positioning accuracy. Several methods for such a task have been proposed, but they either do not consider the correlation between features, or propose an inefficient method to deal with the correlation. The study in this paper proposes a novel feature selection scheme based on the Sparse multi-class SVM (MSVM) technique which can address the feature selection problem via efficiently handling the correlation among them. The scheme first rules out several "unimportant" features via a simple criterion for scalability, and then selects a portion of the remaining features by controlling the sparsity of the optimization results of the Sparse MSVM. The method is applied to a realistic GSM-based fingerprinting localization system and the experimental results show that it outperforms several previous ones via reducing the mean localization error by about 20%.

This letter considers the problem of observation strategy design for compressed sensing. An adaptive method, based on Cramer-Rao bound minimization, is proposed to design the sensing matrix. Simulation results demonstrate that the adaptively constructed sensing matrix can lead to much lower recovery errors than those of traditional Gaussian matrices and some existing adaptive approaches.

Based on the covariance-like fitting criterion we propose a direction of arrival (DOA) estimation algorithm that embeds a weighting scheme in the objective function without selection of any hyperparameters. With an assumption of uncorrelated sources, we formulate the problem of DOA estimation as a linearly constrained quadratic optimization under power constraints. Numerical results show that the proposed method not only is robust to this assumption but also has the superior performance in comparison with some other sparsity-driven methods.

A method of Micro-Doppler component separation based on parametric sparse time-frequency representation is proposed in this paper. The received signal is decomposed into a family of parametric basis signals that are dependent of the target angular velocity, and the significant coefficients of the sparse solution indicate the initial phases and the Doppler amplitudes of Micro-Doppler components. The performance of the proposed method in terms of Micro-Doppler component separation is evaluated by simulations.

A novel high resolution ISAR imaging method based on adaptive sparse recovery is proposed in his paper. The ISAR signal in each range bin is sparsely represented by an over-complete chirplet basis matrix, which can be determined by an unknown parameter set. An adaptive parametric sparse recovery method is proposed to retrieve both the parameter set and the ISAR image. This goal is achieved by sequentially minimizing the L1norm of the sparse signal and the energy of the recovery error in an iterative manner.

Using multiple measurement vectors (MMV), we propose an algorithm based on weighted ℓ1minimization for direction- of-arrival (DOA) estimation, in which the weights are obtained by exploiting the orthogonality between the noise subspace and the array manifold matrix. The proposed algorithm penalizes the nonzero entries whose indices correspond to the row support of the jointly sparse signals by smaller weights and the other entries whose indices are more likely to be outside of the row support of the jointly sparse signals by larger weights, and therefore it can encourage sparsity at the true source locations. Numerical examples prove that the proposed algorithm has better performance than existing algorithms based on regular ℓ1minimization.

Inverse synthetic aperture radar (ISAR) imaging of maneuvering targets via matching pursuit (MP) can produce high resolution and remove sidelobe effect, providing that the target rotation rate is already known. For non-cooperative uniformly rotating targets, the rotation rate is unknown and should be retrieved together with the ISAR image. In this paper, a computational efficient parametric MP is proposed to simultaneously retrieve the rotation rate and the high-resolution ISAR image. The joint estimation of ISAR image and rotation rate is converted into alternate independent estimations, i.e. alternately estimating the ISAR image and rotation rate in an iterative manner. With the iterations, the rotation rate estimate converges to the true value and meanwhile the clear ISAR image with high resolution and low sidelobes may be obtained. Numerical examples show that the approach is efficient in estimating the real target rotation rate and recovering the high resolution ISAR image.

Artificial transportation systems (ATS) are an extension of traffic simulations that deal with transportation issues from the complex systems perspective in a systematic and synthetic way. A rule-based iterative ATS design process is presented in this paper, together with a prototype based on the multiagent platform-Swarm and the methods and results of computational experiments conducted on it. Both emergence-based observation and statistical analysis are used to evaluate those results. This paper demonstrates the ability of ATS to generate traffic phenomena from simple consensus rules and the possibility of designing a growing ATS with readily available multiagent tools.

An algorithm based on matching pursuit (MP) technique is proposed for inverse synthetic aperture radar (ISAR) imaging of maneuvering targets. The received ISAR echo is decomposed into many basis sub-signals that are generated by discretizing the target spatial domain and synthesizing the ISAR data for every discretized spatial position, and then the ISAR imaging problem is converted into the sub-signal selection problem. The basis sub-signals that indeed contribute to the ISAR echo are selected by using the MP technique, and the projection coefficients of the ISAR echo on the selected basis sub-signals represent the ISAR image. In the case of unknown rotation rate of the target, the true rotation rate is obtained by combining the MP technique with the maximum contrast search. Numerical examples show that the proposed algorithm can produce high resolution and remove sidelobe artifacts.

In this letter, a novel radial velocity estimation and range shift compensation algorithm is proposed for high-range resolution profiling of moving targets in stepped-frequency (SF) radar. Compared to traditional methods, this algorithm is based on a more precise signal model, and can therefore achieve much higher estimation accuracy. Furthermore, the range shift problem caused by target motion can be resolved without alterations to the radar waveform. The performance of this algorithm is demonstrated using simulated and experimental results.

This letter presents a theoretical comparative study of the performance bounds for point and extended target tracking. As a result of the additional information provided by the high-resolution sensors, the posterior Cramer-Rao lower bound (PCRLB) of the kinematic target states is proven to be always smaller under the extended target tracking framework than the point target model. Three assumptions about the two kinds of target models, which are satisfied in most target tracking problems, are presented as a sufficient condition of the inequality. This comparison result suggests the use of the extended target model to potentially achieve better performance in tracking applications. The superior performance bound is also illustrated with an elliptically modeled extended target tracking example.

A novel STAP algorithm based on sparse recovery technique, called CS-STAP, were presented. Instead of using conventional maximum likelihood estimation of covariance matrix, our method utilizes the echo statistics on spatial-temporal plane, which is extracted from sample data of only ONE training range cell with Compressed Sensing techniques, to construct a new estimator of covariance matrix, and build the optimal detector based on it. Full description of CS-STAP is given. Numerical result on real data has provided the evidence for great potential of CS-STAP as a effective approach when clutter is non-stationary because it need much less training data compared with common STAP methods.

A method for evaluating both the robustness and detection performance of constant false alarm rate (CFAR) detectors is presented in this paper, which is based on the powerful methodology of influence function (IF) developed in the literature on robust statistics. The robustness of different kinds of CFAR detector can be evaluated and compared by calculating the first derivative of the false alarm probability (FAP) at an underlying distribution, which is named IF-FAP. From the analysis of IF-FAP, several conclusions are given here: the robustness of the detector can be asymptotically represented by the IF of the clutter power estimator, while the detection performance can be approximately evaluated by the asymptotic variance of the clutter power estimator which is an explicit functional of the corresponding IF.

In order to improve the clearness of images captured at night, a new enhancement algorithm is proposed in this paper. Its characters are: (1) enhancing the dark image with contrast enhancement and histogram equalization in series, so both the local and global information can be used; (2) a contrast transforming function which is suited to deal with dark image is proposed; (3) it can be realized in real time. The new method shows good performance in dealing with night vision images.