Persymmetric Structure Research Articles

Subspace‐based distributed target detection method with small training data samples

AbstractDetecting distributed targets precisely in homogeneous environments has been a hot topic in radar signal processing. Generally, distributed targets are often modelled with subspace models of unknown coordinates, and clutter is modelled as the complex Gaussian distribution with zero mean and unknown covariance matrix, while covariance matrix is estimated with a set of training data without the target signal. However, in practice, the complexity of the external environment makes the training data that satisfy the condition of independent homogeneous distribution less available. Therefore, it is assumed that the covariance matrix of the clutter is persymmetric structure and the approach of dimensionality reduction using subspace transformations is introduced, two detectors based upon generalised likelihood ratio test criterion and Wald test criterion in homogeneous environments are proposed. Theoretical analyses indicate the constant false alarm rate characteristics of the two proposed detectors for unknown clutter covariance matrices. Simulation analyses indicate that the proposed detector works well even with fewer training data samples, and its detection performance outperforms that of existing contrast detectors.

Persymmetric design of jointly detection and bearing estimation for a 2D array radar in training demanding scenarios

The problem of joint detection and bearing estimation for a two-dimensional (2D) array radar in training demanding scenarios is addressed. Regardless of the cause of the angle deviation, we model the 2D steering vector as a fully incremental form. Thus, the 2D array requires the optimization of two target cosine offsets. To relax the requirement of sufficient training data, we incorporate persymmetric structure in the design of the receiver. Unlike traditional joint optimization, the persymmetric structure brings a more complex multidimensional matrix form, making detection optimization more difficult. Then, we transform the optimization problem into a fractional-order programming problem and solve it by Dinkelbach algorithm. Finally, numerical results verify the superiority of the proposed method over conventional methods in insufficient training scenarios. Also, the proposed method is more robust.

Persymmetric detection based on asymptotically optimal convex linear combination

Persymmetric structure has been utilized in space-time adaptive processing for heterogeneous environment, which leads to some detection methods based on persymmetric structure, such as persymmetric adaptive matched filter (PS-AMF). However, when the sample support is extremely limited, these methods still suffer the serious degradation in detection performance due to the large error in estimating covariance matrix. In this paper, an asymptotically optimal convex linear combination between transformed sample covariance matrix and identity matrix is considered herein to improve PS-AMF. The asymptotically optimal convex linear combination is conducive to diminishing the estimate error in estimating the transformed covariance matrix by weighting the transformed sample covariance matrix and identity matrix. Furthermore, the asymptotically optimal convex linear combination is improved by the reutilization of the convex linear combination, and the corresponding coefficients are derived. Then, the detection performance of the proposed method is approximately analyzed. At last, numerical simulations show that the proposed method performs well, compared with its counterparts, when the sample support is extremely limited.

Mixed far-field and near-field source separation and localization based on FOC matrix differencing

This paper investigates the classification and localization of the mixed far-field sources (FFSs) and near-field sources (NFSs) on a symmetrical uniform linear array and proposes a new mixed source localization algorithm. Firstly, we analyze the persymmetric structure property of the far-field (FF) steering vector in matrix differencing. Based on that, we implement the matrix auto-differencing operation on the fourth-order cumulant (FOC) matrix, which eliminates the contribution of the FF signals from the mixed signals. Based on the reserved near-field (NF) parts, an effective subspace-based is performed to estimate NF parameters. Secondly, to reconstruct the NF FOC matrix, we propose a new method to estimate the NF kurtosis from the non-Hermitian statistics matrix. Then, the related NF components can be removed from the mixed signals to avoid interfering with FF direction-of-arrival (DOA) estimations. Based on the subspace technique, the FF DOAs can be determined by the one-dimensional spectrum search. The proposed algorithm does not require additional classification operations, even when NFSs have the same DOAs as FFSs. Finally, several simulations demonstrate the better estimation performance of the proposed algorithm than existing localization algorithms.

Adaptive Subspace Signal Detection in Structured Interference Plus Compound Gaussian Sea Clutter

This paper discusses the problem of detecting subspace signals in structured interference plus compound Gaussian sea clutter with persymmetric structure. The sea clutter is represented by a compound Gaussian process wherein the texture obeys the inverse Gaussian distribution. The structured interference lies in a known subspace, which is independent with the target signal subspace. By resorting to the two-step generalized likelihood ratio test, two-step Rao, and two-step Wald design criteria, three adaptive subspace signal detectors are proposed. Moreover, the constant false-alarm rate property of the proposed detectors is proved. The experimental results based on IPIX real sea clutter data and simulated data illustrate that the proposed detectors outperform their counterparts.

Persymmetric Adaptive Union Subspace Detection

This paper addresses the detection of a signal belonging to several possible subspace models, namely, a union of subspaces (UoS), where the active subspace that generated the observed signal is unknown. By incorporating the persymmetric structure of received data, we propose three UoS detectors based on GLRT, Rao, and Wald criteria to alleviate the requirement of training data. In addition, the detection statistic and classification bound for the proposed detectors are derived. Monte-Carlo simulations demonstrate the detection and classification performance of the proposed detectors over the conventional detector in training-limited scenarios.

Persymmetric Adaptive Array Detection of Spread Spectrum Signals

The spread spectrum signal detection problem is examined in colored noise with an unknown covariance matrix. When the receiver is equipped with a symmetrically spaced linear array, persymmetry exists in the received data. We exploit the persymmetric structures to design adaptive detectors according to the principles of generalized likelihood ratio test (GLRT), Wald test, and Rao test. It turns out that the proposed GLRT has the same form as the proposed Wald test, and the Rao test does not exist. We prove that the proposed detector exhibits a constant false alarm rate against the unknown noise covariance matrix. Numerical examples demonstrate that the proposed detector has better performance than its non-persymmetric counterpart.

Persymmetric Subspace Detectors With Multiple Observations in Homogeneous Environments

In this article, a target detection problem in homogeneous Gaussian noise with unknown covariance matrix is examined using multiple observations, which may be collected from multiple range cells, bands, and/or coherent processing intervals. In order to take into consideration mismatches of the target steering vector, we adopt a subspace model where the target steering vector is assumed to lie in a subspace spanned by the column vectors of a known matrix with unknown target coordinates. By exploiting persymmetric structures, we propose several adaptive detectors according to ad hoc modifications of generalized likelihood ratio test (GLRT), Rao test, and Wald test. It is found that the Rao test does not exist, whereas the two-step Wald test shares the same form as the two-step GLRT. Numerical examples show that the robustness of the proposed detectors is better than that of their counterparts in general. In particular, the proposed one-step GLRT is the most robust in most cases, and the proposed two-step GLRT and one-step Wald test can be more robust than the one-step GLRT in the case where the number of training data is small.

Persymmetric Adaptive Detection With Reduced-Dimension Approach

For target detection in Gaussian noise with unknown covariance matrix, usually sufficient training data are needed to form a nonsingular estimate of the noise covariance matrix. However sufficient training data could not be satisfied in practice. Aiming to design a detector with small training data size, this letter proposes a reduced-dimension detector by incorporating the persymmetric structure of received data. Based on the persymmetric structure, a reduced-dimension approach of subspace transformation-based detector is adopted. Then, the criterion of the generalized likelihood ratio test is used to design the detector. The proposed detector is shown to possess the constant false alarm rate property with respect to noise covariance matrix. Compared with existing detectors, such as conventional polarization-space-time generalized likelihood ratio detector, persymmetric polarization-space-time generalized likelihood ratio detector and subspace transformation-based detector, simulation results demonstrate that the proposed one has better detection performance, especially in the circumstance of limited training data.

Adaptive Persymmetric Subspace Detectors in the Partially Homogeneous Environment

This paper addresses the adaptive detection of subspace signals in the noise whose covariance matrix is unknown. The partially homogeneous scenario, where the primary data have the same noise covariance matrix with the training data up to an unknown scaling factor is considered. We exploit the persymmetric structure of the noise covariance matrix to enhance the matched detection performance in the case of limited number of training data. Three persymmetric subspace detectors are proposed by applying the generalized likelihood ratio (GLR), Rao and Wald design criteria, respectively. It is proved that the three persymmetric subspace detectors can ensure the constant false alarm rate (CFAR) property. Experimental results show that the new persymmetric subspace detectors significantly outperform the conventional subspace detector in terms of the matched detection performance. Compared with the persymmetric rank-one signal detectors, the proposed persymmetric subspace detectors are more robust in the mismatched signal case.

Persymmetric subspace adaptive detection and performance analysis

This study deals with the problem of detecting a subspace signal in coloured Gaussian noise, where the subspace signal belongs to a known subspace, but with unknown coordinates. The authors exploit the persymmetric structure of the covariance matrix by a unitary transform and then devise a persymmetric subspace detector based on two-step design procedure. By exploiting the persymmetric structure of the covariance matrix, the proposed detector can reduce training data requirements. Additionally, approximate expressions for the probabilities of false alarm and detection of the proposed detector are derived. Numerical results demonstrate that the proposed detector can offer significantly enhanced detection performance in comparison with the conventional counterparts when the amount of training data is limited.

Persymmetric generalised adaptive matched filter for range‐spread targets in homogeneous environment

This study deals with the problem of adaptively detecting range-spread targets in Gaussian environment, by assuming a persymmetric structure of covariance matrix. A persymmetric detector based on the two-step generalised likelihood ratio test design scheme is devised to reduce secondary data requirement, which ensures the constant false alarm rate property. Moreover, the general closed-form expressions of the probabilities of the false alarm and detection for the proposed detector are derived, in both cases of deterministic and fluctuating scatter models. Furthermore, the compact versions of forenamed expressions are presented in a special case when the joint space-time dimension of the received signal is odd. Finally, the numerical results of these derived statistical expressions are confirmed with those of Monte Carlo trials.

One-Step Persymmetric GLRT for Subspace Signals

We exploit persymmetric structures to design a generalized likelihood ratio test for detecting subspace signals in homogeneous Gaussian clutter with unknown covariance matrix. The subspace model is employed to account for mismatches in the target steering vector. An exact but finite-sum expression for the probability of false alarm of the proposed detector is derived, which is verified using Monte Carlo simulations. This expression is irrelevant to the clutter covariance matrix, indicating that the proposed detector exhibits a constant false alarm rate property against the clutter covariance matrix. Numerical examples show that the proposed detector has strong robustness to the target steering vector mismatch.

Persymmetric Rao test for MIMO radar in Gaussian disturbance

This paper considers the target detection problem in multiple-input multiple-output radar where the disturbance covariance matrix is unknown. Based on the Rao criterion, a persymmetric Rao test is designed by exploiting the persymmetric structure of the disturbance covariance matrix. Particularly, the proposed detector does not require training data, and exhibits strong selectivity to mismatched signals. Another contribution in this paper is to propose a two-stage detector whose second stage coincides with the proposed persymmetric Rao test. The selectivity or robustness of the two-stage detector can be tuned by selecting different threshold pairs.

Persymmetric Subspace Detection in Structured Interference and Non-Homogeneous Disturbance

This letter addresses the problem of distributed target detection in structured interference and non-homogeneous disturbance. The target signal and interference locate in two linearly independent subspaces with unknown coordinates, while the disturbance is partially homogeneous with an unknown covariance matrix. By incorporating the persymmetric structure of received data, we propose a persymmetric subspace detector for a distributed target, which includes the detector for a point-like target as a special case. Remarkably, the proposed detector is shown to ensure a constant false alarm rate property with respect to both the covariance matrix structure and the power scaling factor. In addition, analytical expressions for the probabilities of false alarm and detection of the special case of the proposed detector for point-like targets are derived, which are verified by Monte Carlo trials. Numerical examples illustrate that the proposed detector can achieve better detection performance, as well as anti-interference ability in training-limited situations.

Low-Rank Structured Covariance Matrix Estimation

The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.

Persymmetric adaptive subspace detectors for range-spread targets

This paper investigates the problem of adaptive detection of a range-spread target in colored Gaussian disturbance. The range-spread target is described by a multi-rank subspace model, which lies in a subspace but with unknown coordinates. The disturbance, usually including clutter and thermal noise, has an unknown covariance matrix. Under the above assumption, we design the Rao and generalized likelihood ratio test (GLRT) detectors by the two-step procedure, which incorporates persymmetric structure of received data. The two detectors are shown to coincide with each other. Remarkably, the proposed detector ensures constant false alarm rate property. Experimental results conducted by both simulation and real data verify that the proposed detector outperforms the existing counterparts in training-limited scenarios.

Knowledge-Aided Structured Covariance Matrix Estimator Applied for Radar Sensor Signal Detection.

This study deals with the problem of covariance matrix estimation for radar sensor signal detection applications with insufficient secondary data in non-Gaussian clutter. According to the Euclidean mean, the authors combined an available prior covariance matrix with the persymmetric structure covariance estimator, symmetric structure covariance estimator, and Toeplitz structure covariance estimator, respectively, to derive three knowledge-aided structured covariance estimators. At the analysis stage, the authors assess the performance of the proposed estimators in estimation accuracy and detection probability. The analysis is conducted both on the simulated data and real sea clutter data collected by the IPIX radar sensor system. The results show that the knowledge-aided Toeplitz structure covariance estimator (KA-T) has the best performance both in estimation and detection, and the knowledge-aided persymmetric structure covariance estimator (KA-P) has similar performance with the knowledge-aided symmetric structure covariance estimator (KA-S). Moreover, compared with existing knowledge-aided estimator, the proposed estimators can obtain better performance when secondary data are insufficient.

Persymmetric Adaptive Detection of Subspace Signals: Algorithms and Performance Analysis

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated by incorporating persymmetric structure of received data. The signal of interest is described with a subspace model, namely, it belongs to a subspace spanned by the columns of a known matrix, but with unknown coordinates. We propose a persymmetric detector with two tunable parameters, which includes many existing persymmetric detectors as special cases. Approximate expressions for the probabilities of false alarm and detection of the proposed detector are derived, which are verified via Monte Carlo simulations. Numerical results reveal that the exploitation of the persymmetric structure leads to a significant gain in the detection performance, especially in the case of limited training data. In addition, a further gain in the detection performance can be obtained by optimally selecting the tunable parameters.

Persymmetric GLRT Detection in MIMO Radar

The problem of target detection in colocated multiple-input multiple-output radar with unknown disturbance covariance matrix is considered. According to the generalized likelihood ratio test, we design an adaptive detector by exploiting the persymmetric structure of the covariance matrix. In particular, training data are not required in the proposed adaptive detector. Analytical expressions for the probability of false alarm and detection probability are derived, which are confirmed by Monte Carlo simulations. The expression for the probability of false alarm shows that the proposed detector exhibits a constant false alarm rate property against the disturbance covariance matrix. Numerical examples based on both simulated and experimental data confirm that the proposed detector has better detection performance than its counterparts.