Generalized Likelihood Ratio Test Detector Research Articles

Adaptive radar target detection in nonzero-mean compound Gaussian sea clutter with random texture

This paper deals with the radar target detecting problem in nonzero-mean compound Gaussian sea clutter with random texture. The texture is considered to be an inverse Gamma, Gamma, or inverse Gaussian variable. Three novel adaptive detectors using the two-step maximum a posteriori (MAP) generalized likelihood ratio test (GLRT) are proposed. More precisely, we derive the test statistics of the proposed detectors for known mean vector (MV) and speckle covariance matrix (CM) in the first step. In the second step, unbiased and consistent estimators are proposed to estimate the MV and CM in nonzero-mean compound Gaussian circumstances. We acquire the fully adaptive nonzero-mean GLRT detectors by substituting the estimates into the test statistics. Then, the constant false alarm rate (CFAR) properties of the proposed detectors with respect to (w.r.t.) the speckle CM are proved. Finally, the performance of three proposed detectors is verified by simulation experiments using the synthetic and real sea clutter data.

Mixture texture model with weighted generalized inverse Gaussian distribution for target detection

With the improvement of radar resolution, the amplitude distribution of sea clutter has begun to exhibit significant heavy-tailed characteristics. Existing models for sea clutter amplitude distribution do not sufficiently solve this problem, which results in a diminished target detection probability in two-step generalized likelihood ratio test (GLRT) based target detectors. To address this issue and to enhance the radar target detection capabilities, we propose a new compound-Gaussian clutter model based on a weighted mixture of generalized inverse Gaussian distributions to model the texture. The CG-WGIG model demonstrates greater flexibility and effectively captures the characteristics of sea clutter amplitude distributions with heavy tails, thus affording a better fit. We combine this model with the two-step GLRT criterion to propose a GLRT detector endowed with a weighted generalized inverse Gaussian texture (GLRT-WGIG), specifically tailored for detecting range-spread targets (RSTs). We have conducted a rigorous mathematical proof to demonstrate that the constant false alarm rate (CFAR) characteristic of the proposed GLRT-WGIG detector is independent of the covariance matrix, thereby ensuring its robustness in various operational scenarios. Using measured data, we demonstrate that the proposed model and detector are flexible and outperform the existing methods in terms of fitting and detection performance, where we obtain a mean 12.02% MSE of fitting performance promotion.

The knowledge-aided generalized multipath adaptive detector

In urban environments, the challenges brought about by multipath propagation are significant for traditional adaptive radar detection problems. To tackle this issue, a generalized multipath signal model combined with environmental geometric prior information (EGPI) is developed. This model can be utilized regardless of whether the multipath signals are fully, partially, or partially-resolvable in the range domain. During the process of designing a detector using the criteria of the one-step generalized likelihood ratio test (GLRT), an attempt to find a closed-form expression for the maximum likelihood estimator of the unknown parameters was unsuccessful. However, by utilizing an adaptive configuration for the initial value, a cyclic optimization algorithm was able to obtain the estimated value within just a few iterations, demonstrating a rapid convergence rate. Furthermore, a detector based on the two-step GLRT criteria is proposed. Compared to traditional detectors, the newly developed detectors make more efficient use of the energy in multipath signals, resulting in improved detection performance. It has been demonstrated that when the whitened angles between subspaces are set to two specific values, the GLRT detectors exhibit the Constant False Alarm Probability (CFAR) property. Simulation results show that the false alarm probability(Pfa) at these two specific angles provides upper and lower bounds of Pfa.

Adaptive Jamming Attack Detection Under Noise Uncertainty in mmWave Massive MIMO Systems

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

Iterative multi-target detection for PA-FDA dual-mode radar

In this paper, the multi-target detection for joint phased array (PA) and frequency diverse array (FDA) radars, referred to as PA-FDA dual-mode radar, is investigated by exploiting the high transmit power efficiency of PA as well as wide spatial coverage of FDA. The PA-FDA dual-mode radar is formulated in a signal-level fusion manner by combining the PA and the FDA, which enables us to exploit the joint information in the PA-FDA dual-mode radar. In the sequel, an iterative multi-target detection method is devised with two main steps: i) the generalized likelihood ratio test (GLRT) is performed, which provides the knowledge of target parameters, and ii) the conditional-cancelation-before-detection GLRT (CCBD-GLRT) detector is carried out, which detects other targets based on the previous detection knowledge. At the analysis stage, the optimal detector is provided for the signal-level fusion of PA and FDA radars. Moreover, the corresponding analytical expressions of the probabilities of detection as well as the probabilities of false alarm with respect to both the developed GLRT and CCBD-GLRT detectors are derived for multi-target detection. Simulation results demonstrate that the proposed multi-target detection method is effective and the PA-FDA dual-mode radar outperforms the PA and the FDA radars.

Weak Signal Detection With Low-Bit Quantization in Colocated MIMO Radar

This paper addresses the weak signal detection problem in a massive colocated multiple-input multiple-output (MIMO) radar. To cope with the sheer amount of data produced by the large-scale antennas, a low-bit quantizer is introduced in the sampling process to enable both for hardware limitations and a high detection performance. The generalized likelihood ratio test (GLRT) detector is proposed for the quantized data, with the batch gradient descent algorithm being introduced to form an estimate of the unknown parameters. Furthermore, as a low-complexity alternative to the GLRT detector, we propose a multi-bit Rao detector, yielding a closed-form test statistic, whose theoretical distribution is also presented. Finally, we refine the design of the quantizer by optimizing the quantization thresholds, which are obtained using the particle swarm optimization algorithm. Results from simulation and experimental data demonstrate the performance of the detectors using both unquantized and quantized data. They corroborate the theoretical analyses and show that the performance with 3-bit quantization yields a performance that approaches the cases without quantization, while reducing the overall complexity of the system substantially.

Impedance Variation Detection at MISO Receivers

Techniques have been proposed to estimate unknown antenna impedance due to time-varying near-field loading conditions at multiple-input single-output (MISO) receivers. However, it remains unclear when a change occurs and impedance estimation becomes necessary. In this letter, we address this problem by formulating it as a hypothesis test. Our contributions include deriving a generalized likelihood-ratio test (GLRT) detector to decide if the antenna impedance has changed over two groups of packets. This GLRT formulation leads to a novel optimization problem, but we propose a binary search based algorithm to solve it efficiently. Our derived GLRT detector enjoys a better detection and false alarm trade-off when compared with a well-known, reference detector in simulations. As one result, more transmit diversity significantly improves detection accuracy at a given false alarm rate, especially in slow fading channels.

A Neural Network-Prepended GLRT Framework for Signal Detection Under Nonlinear Distortions

Many communications and sensing applications hinge on the detection of a signal in a noisy, interference-heavy environment. Signal processing theory yields techniques such as the generalized likelihood ratio test (GLRT) to perform detection when the received samples correspond to a linear observation model. Numerous practical applications exist, however, where the received signal has passed through a nonlinearity, causing significant performance degradation of the GLRT. In this work, we propose prepending the GLRT detector with a neural network classifier capable of identifying the particular nonlinear time samples in a received signal. We show that pre-processing received nonlinear signals using our trained classifier to eliminate excessively nonlinear samples (i) improves the detection performance of the GLRT on nonlinear signals and (ii) retains the theoretical guarantees provided by the GLRT on linear observation models for accurate signal detection.

Optimum and Near-Optimum Coherent CFAR Detection of Radar Targets in Compound-Gaussian Clutter With Generalized Inverse Gaussian Texture

In this article, we propose optimum and near-optimum adaptive coherent detectors of radar targets in compound-Gaussian clutter with generalized inverse Gaussian texture (CG-GIG clutter). The target amplitude and the speckle covariance matrix are modeled as unknown quantities to be estimated. On the basis of the two-step generalized likelihood ratio test (GLRT) and the estimate of the speckle covariance matrix, the optimum coherent detector and its adaptive version are designed in this article. It is demonstrated that the proposed optimum coherent detector contains three common detectors, which are the optimum K detector, the generalized likelihood ratio test linear-threshold detector (GLRT-LTD), and the GLRT detector for compound-Gaussian clutter with inverse Gaussian texture. Due to the existence of the modified Bessel function depending on data, the optimum coherent detector is computationally unrealizable. Therefore, a near-optimum coherent detector with a new structure named $\alpha$ matched filter ($\alpha$-MF) detector and its adaptive version are proposed, which decreases the computational cost. The proposed near-optimum coherent detector contains two common detectors, the GLRT-LTD and the $\alpha$-MF detector in K-distributed clutter, and has a comparable detection performance of the near-optimum detector in compound-Gaussian clutter with inverse Gaussian texture, which was proposed before. Theoretical analysis and numerical experiments illustrate that the proposed two detectors for CG-GIG clutter have the constant false alarm ratio property relative to the estimate of the speckle covariance matrix and the Doppler steering vector. Moreover, the detection performance of the two coherent detectors are evaluated by the simulated and real data.

Facing the SNR Wall Detection in Full Duplex Cognitive Radio Networks Using a GLRT Multipath-Based Detector

Recently, with the advances in self-interference cancellation, full-duplex (FD) techniques have become a feasible approach to improve the spectrum usage in new generation wireless systems. In particular, in cognitive radio networks, FD allows a secondary user to simultaneously sense the spectrum and transmit, improving the network efficiency. However, the residual self interference (RSI) arising from an imperfect cancellation, represents a bottleneck for the spectrum sensing performance. This paper analytically demonstrates that RSI represents a colored noise which leads to the SNR Wall phenomenon making the typical OFDM signal detectors no longer robust. To overcome this drawback, we propose a generalized likelihood ratio test detector exploiting the multipath correlation due to the primary user’s (PU) channel. It is proven that the proposed method is not affected by the SNR Wall, hence it is robust w.r.t an imperfect self-interference cancellation. Specifically, best detection performance is achieved when an approximated knowledge of the maximum delay spread of the PU channel is available, otherwise it is shown that a limited performance degradation occurs. Moreover, provided results highlight that our approach outperforms the classical alternatives in different scenarios, including when PU employs a mixed numerology OFDM signal, which characterizes the 5G New Radio waveform.

Protecting GNSS Open Service Navigation Message Authentication Against Distance-Decreasing Attacks

As the security of global navigation satellite systems (GNSSs) for civilian usage is increasingly important, navigation message authentication (NMA) significantly improves resilience to spoofing attacks. However, not all attacks can be effectively countered: a strong variant of replay/relay attacks, distance-decreasing (DD) attacks, can shorten pseudorange measurements, without manipulating the cryptographically protected navigation message, thus manipulating the position, velocity, and time solution undetected. First, we discuss how DD attacks can tamper with GNSS signals, demonstrating the attack effectiveness on a recorded Galileo signal. DD attacks might introduce bit errors to the forged signals, but the adversary can keep this error rate very low with proper attack parameter settings. Then, based on our mathematical model of the prompt correlator output of the tracking phase at the victim receiver, we find that the correlator output distribution changes in the presence of DD attacks. This leads us to apply hypothesis testing to detect DD attacks, notably a goodness-of-fit (GoF) test and a generalized likelihood ratio test (GLRT), depending on the victim’s knowledge on the DD attacks. Monte Carlo simulations are used to evaluate the detection probability and the receiver operating characteristic curves for two tests, for different adversary configuration and noise settings. Then, we evaluate the effectiveness of the GoF test and the GLRT with a synthesized DD signal. Both tests can detect DD attacks with similar performance in high-signal-to-noise-ratio (SNR) environments. The GLRT detection probability is approximately 20% higher than that of the GoF test in low-SNR environments.

Assessing the Effectiveness of Generalized Likelihood Ratio Test Detector Schemes in Seismic Event Detection and the Avoidance of Nontarget Signals

ABSTRACT Cross-correlation techniques have played a long-standing and pivotal role in seismic event monitoring. However, the performance of correlation-based detectors is challenged by nuisance seismicity, or nontarget signals. Such detections are a problem when the mission is to automatically map events to the correct source region. Using aftershocks of the 2014 Mw 6.0 South Napa, California, earthquake, we demonstrate the effectiveness of utilizing a dynamic correlation processor framework in a generalized likelihood ratio test (GLRT) detector configuration to minimize nontarget detections. A GLRT maximizes a detection statistic with respect to one or more unknown parameters. In this case, the detection statistic is a template signal match against the waveform in a window sliding over a data stream, and the unknown parameter is an index variable indicating group membership of the template event or events. Detected events are assigned to the event group that yields the largest detection statistic. Our results show that a GLRT detector will outperform a suite of independently operating correlation and subspace detectors in terms of having a lower nontarget detection rate at a given missed detection rate. We also show that a GLRT detector composed of a few high-rank subspace detectors has a slightly higher nontarget detection rate, but a significantly lower missed detection rate, than a GLRT detector composed of many low-rank subspace detectors. The high-rank GLRT configuration produced impressive results even with marginal data (single channel, single station, and very low time bandwidth product), which bodes well for the utility of building efficient aftershock classification systems and global monitoring systems at larger scales. However, future work is required to assess performance at the regional scale and to assess the performance of the system at detecting target events not used in the detector template creation.

A Joint Sonar-Communication System Based on Multicarrier Waveforms

Jointdetection and communication systems demonstrate their unique efficiencies in both spectrum and cost. In this letter, we propose a sonar-communication (SonarCom) system for underwater scenarios based on two multicarrier (MC) waveforms, which are orthogonal frequency division multiplexing (OFDM) and orthogonal chirp division multiplexing (OCDM) waveforms. Different types of waveforms provide flexibilities to deal with various underwater environments. Furthermore, a generalized likelihood ratio test (GLRT) is proposed for detection to deal with multipath channels. Time aliasing techniques are applied to leverage the signal structure. Moreover, a minimum mean square error (MMSE) equalizer is developed for communication to counter frequency-selective fading. Simulation results show that the GLRT detector for the SonarCom system outperforms the existing matched filter (MF). The OCDM scheme maintains better communication performance than the OFDM one.

Phase-Based GLRT Detection of Moving Targets with Pixel Tracking in Low-Resolution SAR Image Sequences

Spaceborne synthetic aperture radar (SAR) can provide ground area monitoring with large coverage. However, achieving a wide observation scope comes at the cost of resolution reduction owing to the trade-off between these parameters in conventional SAR. In low-resolution imaging, the moving target appears unresolved, weakly scattered, and slow moving in the image sequence, which can be generated by the subaperture technique. This article proposes a novel moving target detection method. First, interferometric phase statistics are combined with the generalized likelihood ratio test detector. A pixel tracking strategy is further exploited to determine whether a motion signal is present. These methods rely on the approximation of both clutter and noise statistics using Gaussian distributions in a low-resolution scenario. In addition, the motion signals are imaged with a subpixel offset. The proposed method is primarily validated using four real image sequences from TerraSAR-X data, which represent two types of homogeneous areas. The results reveal that moving targets can be detected in nearby areas using this strategy. The method is compared with the stack averaged coherence change detection and particle-filter-based tracking strategies.

Extended GLRT Detection of Moving Targets for Multichannel SAR Based on Generalized Steering Vector.

A generalized likelihood ratio test (GLRT) with the constant false alarm rate (CFAR) property was recently developed for adaptive detection of moving targets in focusing synthetic aperture radar (SAR) images. However, in the multichannel SAR-ground moving-target indication (SAR-GMTI) system, image defocus is inevitable, which will remarkably degrade the performance of the GLRT detector, especially for the lower radar cross-section (RCS) and slower radial velocity moving targets. To address this issue, based on the generalized steering vector (GSV), an extended GLRT detector is proposed and its performance is evaluated by the optimum likelihood ratio test (LRT) in the Neyman-Pearson (NP) criterion. The joint data vector formulated by the current cell and its adjacent cells is used to obtain the GSV, and then the extended GLRT is derived, which coherently integrates signal and accomplishes moving-target detection and parameter estimation. Theoretical analysis and simulated SAR data demonstrate the effectiveness and robustness of the proposed detector in the defocusing SAR images.

Persymmetric detection of subspace signals based on multiple observations in the presence of subspace interference

The problem of detecting subspace signals in the presence of subspace interference and Gaussian noise is examined by using multiple observations collected from multiple range cells, bands, and/or coherent processing intervals. We exploit persymmetry to propose one-step and two-step detectors, according to the criterion of generalized likelihood ratio test (GLRT). Both the proposed detectors exhibit constant false alarm rate properties against the noise covariance matrix. Moreover, the statistical characterizations of the proposed one-step detector are obtained. We derive exact expressions for the probability of false alarm (PFA) of the proposed one-step detector in six cases where the signal subspace dimension is no more than 4 or the number of observations is no more than 2. In other cases, we derive an approximate expression for the PFA of the proposed one-step detector. Numerical examples illustrate that the proposed detectors outperform their counterparts, especially when the number of training data is small. In addition, the proposed one-step GLRT detector generally has better detection performance than the two-step detector.

Absorptive Weak Plume Detection on Gaussian and Non-Gaussian Background Clutter

For additive signals on Gaussian clutter, the optimal detector is a linear matched filter that is adapted to the known signal and the covariance of the background. This adaptive matched filter is widely used for gas-phase plume detection, even though the effect of the plume on the background is not strictly additive. Here, a derivation of the matched filter for a strictly absorptive plume produces, in the weak plume limit, a quadratic filter. This quadratic matched filter is extended in two ways: an elliptically-contoured multivariate t distribution is used to generalize the Gaussian background clutter, and a generalized likelihood ratio test detector is derived to extend applicability to stronger plumes. In addition to detectors whose purpose is to identify presence versus absence of a plume, expressions are also derived for estimating plume strength. The performance of these various detectors is evaluated by implanting simulated plume into background images that are either real hyperspectral images or simulated images based on different (Gaussian, multivariate t, and lognormal) clutter distributions.

Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations

Integration of Information and Communication Technology (ICT) in modern smart grids (SGs) offers many advantages including the use of renewables and an effective way to protect, control and monitor the energy transmission and distribution. To reach an optimal operation of future energy systems, availability, integrity and confidentiality of data should be guaranteed. Research on the cyber-physical security of electrical substations based on IEC 61850 is still at an early stage. In the present work, we first model the network traffic data in electrical substations, then, we present a statistical Anomaly Detection (AD) method to detect Denial of Service (DoS) attacks against the Generic Object Oriented Substation Event (GOOSE) network communication. According to interpretations on the self-similarity and the Long-Range Dependency (LRD) of the data, an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model was shown to describe well the GOOSE communication in the substation process network. Based on this ARFIMA-model and in view of cyber-physical security, an effective model-based AD method is developed and analyzed. Two variants of the statistical AD considering statistical hypothesis testing based on the Generalized Likelihood Ratio Test (GLRT) and the cumulative sum (CUSUM) are presented to detect flooding attacks that might affect the availability of the data. Our work presents a novel AD method, with two different variants, tailored to the specific features of the GOOSE traffic in IEC 61850 substations. The statistical AD is capable of detecting anomalies at unknown change times under the realistic assumption of unknown model parameters. The performance of both variants of the AD method is validated and assessed using data collected from a simulation case study. We perform several Monte-Carlo simulations under different noise variances. The detection delay is provided for each detector and it represents the number of discrete time samples after which an anomaly is detected. In fact, our statistical AD method with both variants (CUSUM and GLRT) has around half the false positive rate and a smaller detection delay when compared with two of the closest works found in the literature. Our AD approach based on the GLRT detector has the smallest false positive rate among all considered approaches. Whereas, our AD approach based on the CUSUM test has the lowest false negative rate thus the best detection rate. Depending on the requirements as well as the costs of false alarms or missed anomalies, both variants of our statistical detection method can be used and are further analyzed using composite detection metrics.

Distributed Parameter Detection in Massive MIMO Wireless Sensor Networks Relying on Imperfect CSI

Distributed parameter detection is conceived for massive multiple-input multiple-output (MIMO) wireless sensor networks (WSNs), where multiple sensors collaborate to detect the presence/ absence of a spatially correlated parameter. Neyman-Pearson (NP) and generalized likelihood ratio test (GLRT)-based detectors are developed at the fusion center (FC) for known and unknown parameter detection scenarios, respectively. More explicitly, the GLRT detector also has to estimate the unknown parameter value. Closed-form expressions are derived for the probabilities of detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) and false alarm (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ) in order to characterize the performance of the proposed schemes. Furthermore, the optimal sensor transmit gains are determined for maximising the detection performance attained. An asymptotic performance analysis is carried out for determining the gain scaling laws for the massive MIMO WSN considered, when the number of antennas tends to infinity. The proposed framework is also extended to the realistic imperfect channel knowledge scenario at the FC, followed by the development of the associated fusion rules and analytical results to characterize the performance. Our simulation results closely tally the theoretical findings.

Distributed Target Detection in Communication Interference and Noise Using OFDM Radar

In this letter, the distributed target detection in a mixture of unknown communication interference and noise using the orthogonal frequency division multiplexing (OFDM) radar is considered. A closed-form detector is not tractable, instead, an efficient expectation maximization-based generalized likelihood ratio test (GLRT) detector is developed. The ideal GLRT detector with the complete knowledge of communication signal is also derived as a contrast. Besides, an information theoretic waveform design method by maximizing Kullback-Leibler divergence is addressed to improve the detection performance, in which the subcarrier power ratio is used as a constraint. Simulations show the superiority of the addressed detectors and method.