Constant False Alarm Rate Property Research Articles

Constant false alarm rate detection method in mixed Weibull distribution sea clutter

In maritime surveillance, sea clutter represents a major obstacle to target detection accuracy due to missed or false alarms. Several methods have been proposed to find the most efficient. However, most of these methods have only been tested with simulated data, and their applicability and success in a real environment cannot be guaranteed. This work proposes constant false alarm rate (CFAR) detection techniques tailored to mixed Weibull-distributed sea clutter. The mixed Weibull distribution was used to model a mixture of Gaussian and non-Gaussian data. For CFAR detection in mixed Weibull distribution and Weibull clutter, the log t CFAR (logt-CFAR), Weber Haykin CFAR (WHCFAR), Geometric Mean Order Statistic CFAR (GMOS-CFAR), Trimmed Mean Order Statistic CFAR (TMOS-CFAR), Inclusion/Exclusion CFAR (IE-CFAR), and Weber Haykin Order Statistic CFAR (WHOS-CFAR) algorithms were performed. Both synthetic and actual ice multi-parameter imaging X-band (IPIX) radar data were used for experimental verification of this distribution. Simulation studies demonstrated that the proposed detectors maintain the CFAR property in Weibull-distributed clutter, making them effective in controlled scenarios, and confirming how better is the detection performance compared to other detection methods. This research bridges a critical gap in radar signal processing by significantly improving the detection of targets in challenging clutter environments.

GLRT‐based compressive subspace detectors in single‐frequency multistatic passive radar systems

AbstractThe authors study the problem of compressive target detection in a single‐frequency network (SFN)‐based multistatic passive radar system (MS‐PRS) consisting of multiple illuminators of opportunity (IOs) and one receiver. Firstly, a generalised likelihood ratio test (GLRT)‐based SFN‐based compressive subspace detector (SFN‐CSD) is derived by exploiting the sparsity of the target echoes for the case of known noise variance. When the noise variance is unknown, an SFN‐based unknown‐noise (UN) compressive subspace detector is proposed, referred to as the SFN‐UNCSD. Moreover, closed‐form expressions of the probability of false alarm and detection of the proposed detectors are deriived. It is proved that the SNF‐UNCSD has a constant false alarm rate (CFAR) property. Finally, numerical simulations are conducted to verify the theoretical analysis and illustrate the performance of the proposed detector relative to several benchmark detectors.

Adaptive double subspace target detection based on gradient test: Designs and comparisons

The issue of adaptive detection for double subspace (DOS) signals under the Gaussian noise background is investigated in this paper. The DOS signal has the special structure where the rows and columns of the matrix-valued signal lie in known subspaces with unknown coordinates. To deal with the DOS signal detection problem, two kinds of Gradient tests are proposed in homogeneous environments and partially homogeneous environments. Remarkably, the Durbin test, as well as its two-step version, is also used for the detector design, which is consistent with the existing methods. To evaluate the performance of the proposed methods, both simulated data and real data collected by IPIX radar are used. The results indicate that the Gradient tests ensure the constant false alarm rate property. Furthermore, the proposed detectors obtain relatively robust characteristics and achieve superior performance to existing competitors in some scenarios.

Robust moving target detection for FDA-MIMO radar with steering vector mismatches

This paper studies a robust moving target detection problem for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar with a target embedded in Gaussian clutter with an unknown covariance matrix. We focus on the case of signal mismatch where the errors exist in the transmit-receive vector and Doppler steering vector. To solve the above detection problem, we adopt the subspace approach, where the true and nominal transmit-receive and Doppler steering vectors are assumed to lie in four-dimensional and two-dimensional subspaces, respectively, for the special framework for FDA-MIMO radar. At the detector design stage, we propose three robust adaptive detectors based on the one-step generalized likelihood ratio test (GLRT), two-step GLRT, and Wald test, respectively, with the training data free. The proposed detectors own the constant false alarm rate (CFAR) property against the clutter covariance matrix. The numerical examples validate the effectiveness of the proposed detectors.

Persymmetric adaptive subspace detection in compound Gaussian sea clutter with generalized inverse Gaussian texture

This paper considers the detection problem of subspace targets in compound Gaussian sea clutter with generalized inverse Gaussian (GIG) texture. Based on the Wald test, the gradient test, and the Durbin test, we propose three novel subspace detectors. And the criterion above are first applied to the detection problem in compound Gaussian (CG) sea clutter with GIG texture. In the first step, assuming that the speckle covariance matrix (CM) and the texture component are unknown to obtain the test statistics of the proposed detectors. In the second step, we exploit the persymmetric property of speckle CM and the maximum a posteriori (MAP) criterion to obtain the estimation of speckle CM and the GIG texture parameters. Moreover, the constant false alarm rate (CFAR) properties of the three proposed detectors have been proven with respect to the speckle CM and the scale parameter of the texture component. We verify the detection performance of the three proposed detectors by the numerical experiments both in simulated data and real sea clutter data, and the simulated results show the proposed detectors are robust in the case of limited training and mismatched signals.

Resource-Efficient Low-Latency Modified Pietra-Ricci Index Detector for Spectrum Sensing in Cognitive Radio Networks

In this article, the modified Pietra-Ricci index detector (mPRIDe) is devised, and its field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) designs are reported. The mPRIDe attains lower implementation complexity with respect to its predecessor, without performance penalty. Moreover, the mPRIDe is blind, robust against time-varying noise and received signal powers, and exhibits the constant false alarm rate property. Two versions of the mPRIDe, namely mPRIDe v1 and mPRIDe v2, have been designed. The former privileges lower hardware complexity, whereas the latter aims lower latency, with both versions having a linear scalability with the number of sensors in cooperation. In comparison with the smallest area consumed by a state-of-the-art sensor, mPRIDe v1 and mPRIDe v2 consume 56.6% and 47.3% lower areas, respectively. The sensing times of the proposed sensors are 1.6 and 2.9 times better than the fastest sensing time of contemporary sensors. Moreover, the proposed designs deliver the lowest area-time-product and power-delay-product among state-of-the-art implementations. These metrics make both mPRIDe v1 and mPRIDe v2 the most hardware-efficient and power-efficient sensors reported in the literature.

A Tunable Adaptive Detector for Distributed Targets When Signal Mismatch Occurs

Aiming at the problem of detecting a distributed target when signal mismatch occurs, this paper proposes a tunable detector parameterized by an adjustable parameter. By adjusting the parameter, the tunable detector can achieve robust or selective detection of mismatched signals. Moreover, the proposed tunable detector, with a proper tunable parameter, can provide higher detection probability compared with existing detectors in the case of no signal mismatch. In addition, the proposed tunable detector possesses the constant false alarm rate property with the unknown noise covariance matrix.

Modified Gini Index Detector for Cooperative Spectrum Sensing over Line-of-Sight Channels

Recently, the Gini index detector (GID) has been proposed as an alternative for data-fusion cooperative spectrum sensing, being mostly suitable for channels with line-of-sight or dominant multi-path components. The GID is quite robust against time-varying noise and signal powers, has the constant false-alarm rate property, can outperform many the state-of-the-art robust detectors, and is one of the simplest detectors developed so far. The modified GID (mGID) is devised in this article. It inherits the attractive attributes of the GID, yet with a computational cost far below the GID. Specifically, the time complexity of the mGID obeys approximately the same run-time growth rate of the GID, but has a constant factor approximately 23.4 times smaller. Equivalently, the mGID takes approximately 4% of the computation time spent to calculate the GID test statistic, which brings a huge reduction in the latency of the spectrum sensing process. Moreover, this latency reduction comes with no performance loss with respect to the GID.

Range-Spread Target Detection Based on Adaptive Scattering Centers Estimation

Proper prior knowledge of target scattering centers (SCs) can help to obtain better detection performance of range-spread targets. However, target SCs are sensitive to the target’s attitude relative to the radar and vary significantly among different targets. The existing approaches that employ predetermined prior knowledge may suffer performance degradation when the prior information does not match the practical scenarios. A possible way to circumvent this drawback is to estimate the SCs of different targets adaptively and check the presence of a target utilizing the range cells occupied by the most likely target SCs. For this reason, this article develops a generalized likelihood ratio test based on adaptive SCs estimation (ASCE-GLRT) for range-spread target detection in compound-Gaussian clutter. Under the assumption that the target SCs are sparse, we model the problem of SCs estimation as a sparse signal representation. Moreover, since the sparse assumption may not always be satisfied in practice, a modified sparsity regularization method is proposed to enhance the robustness of the estimation performance of targets with different scattering characteristics. A theoretical analysis shows that the proposed detector can achieve the constant false alarm rate (CFAR) property. The performance assessments conducted by numerical simulation and field tests confirm the effectiveness and robustness of the proposed detector.

Adaptive detection for resolvable multipath signal under heterogeneous clutter

In the urban environment, the radar is easily affected by multipath (MP) returns. The problem of detecting point-like targets in the urban environment with the existence of resolvable MP returns under the background of heterogeneous clutter is addressed. Two adaptive detectors have been devised with a combination of prior information on the environment and echoes of target. The detectors can use the MP echoes in all MP prediction range cells for detection or in some available paths for signal detection by the available path selection algorithm that eliminates the weak signal propagation paths. Remarkably, the proposed decision schemes exhibit the desirable constant false alarm rate property with respect to the unknown parameters of the heterogeneous interference. The performance assessment, conducted on simulated data in terms of detection probability also in comparison with conventional solutions, highlights the effectiveness of the MP exploitation, while the MP signal is strong and shows the detection performance enhancement potential.

Wald Test for Adaptive Array Detection With General Configuration

Assume that a modern radar system has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. We consider the target detection problem for such array radar systems in Gaussian disturbance with unknown covariance matrix. An adaptive detector is proposed according to the criterion of Wald test. The statistical properties of the proposed detector are provided in the mismatched case, where the nominal target steering vector may not be aligned with the true target steering vector. An analytical expression for the probability of false alarm is derived, which reveals that the proposed detector has a constant false alarm rate property with respect to the disturbance covariance matrix. Moreover, a closed-form expression for the detection probability is obtained in the mismatched case. Simulation results demonstrate that the proposed detector exhibits strong robustness against the target steering vector mismatch.

GLRT-based detectors for FDA-MIMO radar with training data

In this paper, a frequency diverse array multi-input multi-output (FDA-MIMO) radar is used for moving target detection in unknown Gaussian noise. To solve the detection problem, we adopt the generalized likelihood ratio test (GLRT) and use the training data to estimate the unknown noise covariance matrix. We derive the GLRT both for the case of unknown target velocity and the case of known target velocity. We also derive the analytical expressions for the probabilities of detection (PDs) and the probabilities of false alarm (PFAs), which indicate that the proposed detectors have constant false alarm rate (CFAR) properties. Theoretical and simulation results show that the proposed detectors can provide higher PDs than the existing detectors which do not utilize training data.

Persymmetric subspace detector for distributed target in partially homogeneous environment

This paper deals with the problem of distributed target detection in partially homogeneous Gaussian clutter whose covariance matrix is unknown but persymmetric. It is assumed that primary data and training data share the same clutter covariance matrix structure but different power levels. The target signal is supposed to lie in a multi-rank subspace with unknown coordinates. A persymmetric subspace detector is designed based on the generalised likelihood ratio test criteria. It is theoretically demonstrated that the proposed detector possesses constant false alarm rate property with respect to the unknown clutter covariance matrix as well as the power level. Experimental results illustrate the performance advantage of the proposed detector over the existing competitors, especially in training-limited scenarios.

Target detection with persymmetric subspace models for steering vector mismatches in MIMO radars

In colocated multiple-input multiple-output radar, the problem of detecting a target embedded in Gaussian noise with unknown covariance matrix is examined for the mismatched case where the true transmit and receive steering vectors are not aligned with the nominal ones, respectively. We adopt subspace models to take into account the steering vector mismatches. With exploitation of persymmetry, adaptive detectors without requiring training data are proposed according to the criteria of generalized likelihood ratio test (GLRT), Wald test, and Rao test. The proposed GLRT and Wald test exhibit constant false alarm rate properties against the noise covariance matrix. Interestingly, we find out that the Rao test does not exist for the detection problem considered. Simulation results show that the proposed detectors bear stronger robustness to the steering vector mismatches than their counterparts.

Multichannel adaptive signal detection: basic theory and literature review

Multichannel adaptive signal detection uses test and training data jointly to form an adaptive detector to determine whether a target exists. The resulting adaptive detectors typically possess constant false alarm rate (CFAR) properties; thus, no additional CFAR processing is required. In addition, a filtering process is also not required because the filtering function is embedded in the adaptive detector. Adaptive detection typically exhibits better detection performance than the filtering-then-CFAR detection technique. It has been approximately 35 years since the first multichannel adaptive detector was proposed by Kelly in 1986. However, there are few overview articles on this topic. Thus, in this study, we present a tutorial overview of multichannel adaptive signal detection with an emphasis on the Gaussian background. We discuss the main design criteria for adaptive detectors, investigate the relationship between adaptive detection and filtering-then-CFAR detection techniques, investigate the relationship between adaptive detectors and adaptive filters, summarize typical adaptive detectors, present numerical examples, provide a comprehensive literature review, and discuss potential future research tracks.

Test Statistics for Reflection Symmetry: Applications to Quad-Polarimetric SAR Data for Detection of Man-Made Structures

In polarimetric synthetic aperture radar (SAR) images, speckle is removed by multilooking and the local covariance matrix is the main parameter of interest. In the covariance matrix from a backscatter with reflection symmetry, the terms <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\langle \boldsymbol{S}_{hh}\boldsymbol{S}_{hv}^*\rangle }$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\langle \boldsymbol{S}_{vv}\boldsymbol{S}_{hv}^*\rangle }$</tex-math></inline-formula> , and their complex conjugates are 0. The backscatter from natural covers, such as fields and forested areas, is typically reflection-symmetric, as these four elements have near-zero values. The backscatter from urban areas and man-made structures is substantially different, and the backscatter from buildings not aligned with the radar line of sight usually does not have reflection symmetry. A novel block-diagonality test statistic for reflection symmetry with a constant false alarm rate property is proposed. It is compared to an approximate test built on a change detection test statistic for Wishart-distributed covariance matrices. Their use on quad-polarimetric data in different situations shows their high potential for man-made structure detection. Applied after an orientation correction of the covariance matrices, these test statistics highlight with high-contrast buildings and urban areas. We also apply this test for ship detection at sea, and show that while the results are unconvincing at X-band, it can also be applied at longer wavelengths such as L-band.

A Nonparametric Approach to Signal Detection in Non-Gaussian Noise

This letter proposes a nonparametric detector, termed as Gini Correlation (GC), to solve the classical problem of detecting deterministic signals buried in impulsive noise. With the help of the popular Middleton’s Class-A impulsive noise (MCAN) model, we derive the expectation and variance of GC under alternative hypothesis and null hypothesis, which, along with the central limit theorem, are further employed for determining the detection probability and the detection threshold. The results show that the proposed detector possesses a constant false alarm rate property. Monte Carlo simulations verify not only the correctness of our theoretical findings but also the superiority of GC to other state-of-the-art methods in terms of receiver operating characteristic (ROC) curves and asymptotic relative efficiency (ARE) curves.

Persymmetric Detection of Radar Targets in Nonhomogeneous and Non-Gaussian Sea Clutter

This article addresses the detection problem of radar targets embedded in nonhomogeneous and non-Gaussian sea clutter. Nonhomogeneity leads to insufficiency of secondary data for estimating the clutter speckle covariance matrix, and non-Gaussianity causes sea clutter to become spiky. In this article, the persymmetry of the clutter covariance matrix is adopted to alleviate the requirement of secondary data, and the prior distribution of clutter texture is exploited to tackle the clutter non-Gaussianity. Based on such clutter knowledge, three adaptive detectors are proposed according to the principles of the generalized likelihood ratio test, the Wald test, and the Rao test. It is proven that three detectors ensure constant false alarm rate (CFAR) properties with respect to both the clutter speckle covariance matrix and the clutter power mean. Simulation experiments show that three detectors outperform their competitors.

Robust STAP Detection Based on Volume Cross-Correlation Function in Heterogeneous Environments

The performance of moving target detection in heterogeneous environments with the traditional space-time adaptive processing (STAP) may degrade when the real clutter environments deviate from the prior assumption on the clutter distribution. In this letter, a new detector for STAP applications based on volume cross-correlation function (VCF), namely VCF-STAP, is proposed to achieve robust performance of moving target detection in heterogeneous environments. In the new VCF-STAP, the VCF is used to form a distance measure between the sample signal subspace and the target subspace without modeling the clutter distribution. Then, a new robust STAP detection statistic is constructed using this distance measure. Simulation and experimental results show that the proposed VCF-STAP achieves robust performance of moving target detection in heterogeneous environments, especially it achieves much superior detection performance compared with existing STAP methods when the real clutter environments do not satisfy their prior assumptions. Besides, it is also shown that VCF-STAP has the constant false alarm rate (CFAR) property.

Adaptive Radar Detection in Gaussian Interference Using Clutter-Free Training Data

This paper addresses adaptive detection of range spread targets in the presence of thermal noise, jammer, and clutter. After motivating the study, a set of clutter-free training (CFT) data is considered to assist radar detection in absence of conventional secondary data sharing the same spectral properties as the interference of the cells under test. To this end, a maximum likelihood (ML) estimate of the unknown parameters is derived under the alternative hypothesis by leveraging the primary data and the CFT data simultaneously. Subsequently, the ML estimate is used to design decision rules based on generalized likelihood ratio, complex parameter Wald, and complex parameter Gradient test criteria. Furthermore, conditions guaranteeing the constant false alarm rate (CFAR) property of the proposed detectors are discussed. At the analysis stage, numerical examples are presented to evaluate the effectiveness of the proposed detectors in comparison with other detection schemes available in the literature.