Generalized Likelihood Ratio Detector Research Articles

Generalized likelihood ratio detector with horizontal linear array in presence of interference in uncertain shallow-water environment

Environmental uncertainties and interference are the main factors affecting the detection performance for detection problems in a shallow-water environment. To obtain robust performance, an interference and environmental uncertainties-constrained generalized likelihood ratio detector (IEU-GLRD) is proposed based on a horizontal linear array (HLA). The uncertainty sets of signal and interference wavefronts are used by IEU-GLRD, which contain different uncertainties when the interference source bearing relative to the HLA is known a priori. Due to the difference in the uncertainties, the signal, which is not in the uncertainty set of the interference, can be detected, while the interference is suppressed under different environmental parameters. The performance of IEU-GLRD is robust when the signal wavefront is approximately orthogonal to any interference wavefronts. The interference immunity of IEU-GLRD is mainly determined by the bearing of the interference source and the sediment sound speed, which is stronger when the interference source tends to the broad side and the sediment sound speed is lower.

Distributed Detection With Generalized Locally Most Powerful Fusion of Compressed Local Multi-Frame Test Statistics

Distributed radar multi-frame detection (DR-MFD) can detect dim targets through a longer fusion period of multi-radar observations. However, communication cost in the DR-MFD is usually huge, causing a heavy hardware burden in the real application. This paper investigates the dim target detection problem with the DR-MFD system and aims to realize the DR-MFD with a good detection performance and a low communication cost. To compress local data, local test statistics formed at each frame are quantized by the Fisher Information maximization-based quantization (FIMQ), and the quantized outputs are transmitted to a fusion center (FC). A generalized locally most powerful (GLMP) detector is derived to fuse the received multi-frame quantized outputs at the FC. It is proved that the FIMQ is asymptotically optimal for the GLMP detector in the sense of detection performance. A closed-form solution is provided to find the local quantization thresholds of the FIMQ. Simulation results indicate that the GLMP detector outperforms the generalized likelihood ratio detector in most situations. The asymptotic optimality of the FIMQ is also corroborated. In addition, for the GLMP detector with 3-bit FIMQ, the signal-to-noise ratio loss caused by data quantization can reach a 0.11 dB level.

A Unified Theory of Adaptive Subspace Detection Part II: Numerical Examples

This paper is devoted to the performance analysis of the detectors proposed in the companion paper where a comprehensive design framework is presented for the adaptive detection of subspace signals. The framework addresses four variations on subspace detection: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior probability distribution. In this paper, Monte Carlo simulations are used to compare the generalized likelihood ratio (GLR) detectors derived in [1] with estimate-and-plug (EP) approximations of the GLR detectors. Remarkably, the EP approximations appear here for the first time (at least to the best of the authors' knowledge). The numerical examples indicate that GLR detectors are effective for the detection of partially-known signals affected by inherent uncertainties due to the system or the operating environment. In particular, if the signal subspace is known, GLR detectors tend to outperform EP detectors. If, instead, the signal subspace is known only by its dimension, the performance of GLR and EP detectors is very similar.

A Unified Theory of Adaptive Subspace Detection Part I: Detector Designs

This paper addresses the problem of detecting multidimensional subspace signals, which model range-spread targets, in noise of unknown covariance. It is assumed that a primary channel of measurements, possibly consisting of signal plus noise, is augmented with a secondary channel of measurements containing only noise. The noises in these two channels share a common covariance matrix, up to a scale, which may be known or unknown. The signal model is a subspace model with variations: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior distribution. As a consequence, there are four general classes of detectors and, within each class, there is a detector for the case where the scale between the primary and secondary channels is known, and for the case where this scale is unknown. The generalized likelihood ratio (GLR) based detectors derived in this paper, when organized with previously published GLR detectors, comprise a unified theory of adaptive subspace detection from primary and secondary channels of measurements.

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.

Scale-Invariant Subspace Detectors Based on First- and Second-Order Statistical Models

The problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a dimension-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.

Adaptive Radar Detection in Gaussian Disturbance With Structured Covariance Matrix via Invariance Theory

This paper deals with adaptive radar detection of targets in the presence of Gaussian disturbance sharing a block-diagonal covariance structure. The problem is formulated according to a very general signal model, which contains the point-like, range-spread, and subspace target (or targets) as special instances. Hence, a unified study on the resulting adaptive detection problem is handled with the use of the invariance theory. The obtained results, including an appropriate transformation group, a maximal invariant and an induced maximal invariant, are proven consistent with those existing in the literature for some simple scenarios. Meanwhile, since the widely-used generalized likelihood ratio detector does not admit a closed form expression, new invariant detectors and their CFAR versions are proposed in this general scenario. Finally, their detection performance is assessed and validated via numerical examples.

Multiple Antenna Spectrum Sensing Based on GLR Detector in Cognitive Radios

As is known, eigenvalue based spectrum sensing for multi-antenna cognitive radio systems is a highly preferred method because it requires no priori knowledge concerning the signal to be sensed. The performance of the method depends on the most accurate calculation of the test statistic and the threshold value. Regaining of the threshold values was aimed in this study in order to increase performance in generalized likelihood ratio detection based sensing. While the threshold value was calculated, the probability of false detection (Pfa) and the probability of detection were regained by using a new probability distribution function for Wishart matrices. The simulations were performed under noise uncertainty for MIMO–OFDM systems, and a noticeable performance increase was observed with the new threshold value in comparison with conventional methods.

Adaptive GLR-, Rao- and Wald-based CFAR detectors for a subspace signal embedded in structured Gaussian interference

The problem of detecting a subspace signal embedded in subspace Gaussian interference and thermal noise is studied in this paper. In this problem, both the signal-independent and signal-dependent interferences are assumed to be present, therefore the overall interference subspace covers the signal subspace. The approach of this paper extends previous works involving either of those two kinds of interferences. A set of secondary data containing only interference plus noise is employed to estimate the interference covariance matrix and the noise power. Three new detectors are designed via the generalized likelihood ratio (GLR), Rao and Wald tests, respectively. Their probabilities of false alarms (PFAs) and detections are analytically derived. The PFAs show that the new detectors have the constant false alarm rate (CFAR) property against the interference and noise. Numerical results show that the new detectors outperform their counterparts for the studied problem. Furthermore, the new detectors are less sensitive to the secondary data size and to the mismatched subspace signal than some other detectors, such as the GLR detector (GLRD), the adaptive matched filter (AMF), the adaptive subspace detector (ASD), etc.

High-Performance GLR Detector for Moving Target Detection in OFDM Radar-Based Vehicular Networks

Nowadays, orthogonal frequency division multiplexing (OFDM) radars have been used in many applications such as target detection and recognition in vehicular networks and surveillance systems, according to their frequency diversity property. The model of the received signal in an OFDM radar based on target’s parameters has a non-linear form with respect to unknown velocity and scattering coefficients, so there is no possibility of achieving a closed form solution for Maximum Likelihood Estimation of the unknown parameters and so the Neyman–Pearson detector. Therefore, in all published works, the generalized likelihood ratio (GLR) detector is obtained for the target with known velocity, or in case of simultaneous unknown velocity and scattering coefficients, only a wide two-dimensional grid search over all possible values of the unknown parameters is considered to maximize the Likelihood ratio. In this paper, a new method is proposed for simultaneous estimations of target velocity and scattering coefficients using a coordinate descent approach, which reduces the above nonlinear problem to two linear problems, and makes the implementation of GLR detector efficient. The simulation results confirm the efficiency of the proposed method.

Spectrum sensing based on Bayesian generalised likelihood ratio for cognitive radio systems with multiple antennas

In this paper, the spectrum sensing problem is addressed via using multiple antennas in cognitive radio systems when the noise and the primary user signal are independent. The problem of optimal detection is considered, and an estimation framework is presented where the primary user signal is a complex zero-mean Gaussian distribution. This paper discusses the generalized likelihood ratio detector (GLRT) when the sample size is a finite number and derive the corresponding GLRT detector of the spectrum sensing problem in a multiantenna framework by utilizing the statistics of the received signal, the channel information and the prior information of the noise. The scenario involves the assumption that the noise variance is unknown while the channel matrix gain is known for the secondary user (SU). The simulation results show that the proposed Bayesian GLRT detector is optimal even under a limited number of samples and more importantly also clarify that the proposed detector outperforms other the state-of-the-art detectors.

Detecting Abnormal Power Emission for Orderly Spectrum Usage

This correspondence investigates the detection of a common kind of spectrum misuse behaviors, i.e., abnormal power emission, which may be induced by various factors, e.g., device fault, selfish motivation, or malicious attack. This problem is challenging due to the lack of prior information on specific abnormal behaviors and the uncertainty on real-time normal spectrum states. In this paper, we first formulate the detection of abnormal power emission as a composite binary hypothesis test. Then, a generalized likelihood ratio detector is derived to achieve the Neyman–Pearson criterion. Further, to simplify the detector and facilitate the performance analysis, a two-step detector called Normal before Abnormal detector is developed, and the corresponding detection performance and decision region are theoretically analyzed. Finally, simulation results show that the proposed detectors can well distinguish states with abnormal powers from normal spectrum states.

Dimension-reduced generalized likelihood ratio detection based on sampling of normal modes in deep ocean

In this paper, two generalized likelihood ratio (GLR) detectors are presented for the case of multiple snapshots of test data to detect the presence of an underwater acoustic source in the deep ocean. The two GLR detectors are termed the eigenvalue detector (EVD) and the constant false alarm rate eigenvalue detector (CFAR EVD), respectively. Theoretical analysis and numerical results show that for a given input signal-to-noise ratio (SNR) of the array, the GLR detectors achieve higher output SNRs when the spatial dimension of test data decreases. To further enhance the detection performances of the GLR detectors, we propose a dimension-reduced (DR-GLR) method based on array sampling of modal information. This DR-GLR method combines the characteristics of sound propagation and array receiving. According to normal mode theory, acoustic signals emitted from the acoustic source lie in the modal space spanned by the sampled modal information of the array. Resulting from the restriction of the array size, it often occurs in deep ocean when the dimension of " effective modal subspace” is less than that of the test data which is equivalent to the number of hydrophones. Based on this phenomenon, we reconstruct the modal information by merely retaining the " effective modal subspace” to formulate the dimension reduction matrix. The DR-GLR test statistics is deduced by employing the dimension reduction matrix when using the vertical linear array (VLA) and the horizontal linear array (HLA), respectively. The DR-GLR detectors when using an HLA require more computational amount than when using a VLA. Simulation experiments are conducted to analyze the detection performances of the two GLR detectors, and verify the performance improvement effects of DR-GLR detectors. The numerical results show that the CFAR EVD presents good robustness to the uncertainty of the noise power and the DR-GLR detectors outperform the GLR detectors in detection performance. It also turns out the acoustic signals received by the HLA lie in a lower-dimensional " effective modal subspace” than by the VLA, and thus when using an HLA the DR-GLR detectors present higher detection probabilities than using a VLA. Moreover, the smaller the dimension of the " effective modal subspace”, the better the performance improvement of the DR-GLR detectors will be. The dimension of the " effective modal subspace” increases with hydrophone spacing and/or the source frequency increasing.

Generalized Likelihood Ratio Detection Schemes for Forward Scatter Radar

This paper introduces innovative detection schemes for forward scatter radar (FSR) based on the generalized likelihood ratio test (GLRT) for both cases, where a fixed threshold can be used and where a fully adaptive CFAR scheme is desired. The detection performance of the newly proposed detectors is characterized analytically and compared to the performance of the standard detection scheme. This shows that the new detectors always outperform the standard FSR detector. In most cases the improvement has an upper bound of 3 dB, but there are specific cases where the standard FSR detector shows significant losses, while the new GLRT schemes suffer a much smaller degradation. Finally, simplified equivalent SNR expressions are introduced that relate the GLRT detection performance to the main parameters describing the FSR observation geometry and the target size and motion. These expressions are shown to be useful for the design of effective FSR geometries that guarantee desired detection performance for specific targets.

Target Detection in Analog Terrestrial TV-Based Passive Radar Sensor: Joint Delay-Doppler Estimation

Due to 64- $\mu \text{s}$ line fly-back time of the analog television (ATV) signal producing a range ambiguity at ranges corresponding to the multiples of 19.2 km, it seems that we cannot determine the targets’ ranges in ATV-based passive bistatic radars (PBRs). Based on this standpoint, all discovered works on a target-detection problem in an ATV-based PBR have focused on the Doppler information in echoes of the television video carrier signal not range information. To cope with the severe range ambiguity of the ATV signal and make it possible to jointly estimate targets’ delays and Doppler shifts, we propose a new detector performing target detection in a layered manner. In each layer, one target is detected. Detection in each layer is done using a generalized likelihood ratio detector. Interference due to the detected target in the first layer is estimated and subtracted from the received signal. From the first layer’s interference canceled signal, another target (if exist) is detected in the second layer. The interference due to the second layer’s detected target is estimated and subtracted. These detection and interference cancellation steps are carried out in each layer, until all the targets are detected. The proposed detector is also implemented based on the chirp z-transform to efficiently obtain targets’ Doppler shifts over a limited range of Doppler frequencies. To obtain an effective cancellation of the strong interfering targets as well as off-grid targets, a robust version of resulting algorithm is also presented. Extensive simulation results are provided to demonstrate the high performance of the resulting target-detection algorithms.

Resilient Control for Networked Control Systems Subject to Cyber/Physical Attacks

In this paper, we investigate a resilient control strategy for networked control systems (NCSs) subject to zero dynamic attacks which are stealthy false-data injection attacks that are designed so that they cannot be detected based on control input and measurement data. Cyber resilience represents the ability of systems or network architectures to continue providing their intended behavior during attack and recovery. When a cyber attack on the control signal of a networked control system is computed to remain undetectable from passive model-based fault detection and isolation schemes, we show that the consequence of a zero dynamic attack on the state variable of the plant is undetectable during attack but it becomes apparent after the end of the attack. A resilient linear quadratic Gaussian controller, having the ability to quickly recover the nominal behavior of the closed-loop system after the attack end, is designed by updating online the Kalman filter from information given by an active version of the generalized likelihood ratio detector.

Multiantenna GLR Detection of Rank-One Signals With Known Power Spectral Shape Under Spatially Uncorrelated Noise

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and unknown rank-one spatial signature in additive white Gaussian noise with an unknown diagonal spatial correlation matrix. This is motivated by spectrum sensing problems in dynamic spectrum access, in which the temporal correlation of the primary signal can be assumed known up to a scaling, and where the noise is due to an uncalibrated receive array. For spatially independent identically distributed (i.i.d.) noise, the corresponding GLR test reduces to a scalar optimization problem, whereas the GLR detector in the general non-i.i.d. case yields a more involved expression, which can be computed via alternating optimization methods. Low signal-to-noise ratio (SNR) approximations to the detectors are given, together with an asymptotic analysis showing the influence on detection performance of the signal power spectrum and SNR distribution across antennas. Under spatial rank- $P$ conditions, we show that the rank-one GLR detectors are consistent with a statistical criterion that maximizes the output energy of a beamformer operating on filtered data. Simulation results support our theoretical findings in that exploiting prior knowledge on the signal power spectrum can result in significant performance improvement.

Generalized Wald Test for Binary Composite Hypothesis Test

This letter provides a generalization of the well-known Wald test. The proposed generalized Wald test (GWT) is a Separating Function Estimation Test (SFET) which is a type of detector recently introduced for a wide class of composite problems. The test statistics of an SFET is an estimate of a real-valued Separating Function (SF). It is already proved that a Minimum Variance Unbiased Estimator of any SF leads to the optimal Uniformly Most Powerful unbiased detector. In many practical cases, such an optimal detector does not exist; hence, suboptimal ones are used, instead. Selecting an SF with a guaranteed performance is still an open problem which is investigated in this letter. First, we derive a lower bound for the detection probability of the SFET in terms of corresponding SF and the Fisher Information Matrix. Then we optimize the proposed bound with respect to the SF. The solution of the optimization problem leads to a generalization of the Wald test which is asymptotically optimal and reduces to the Wald detector in some special cases. Simulation results show the superiority of the proposed GWT over its counterparts, namely, the Wald test and GLR detector in some examples.

Wind noise suppression using compact arrays of infrasound sensors

This presentation describes how a compact array (aperture much less than the shortest wavelengths of interest) of infrasound sensors can be used to significantly enhance signal detection and waveform estimation in the presence of high levels of wind noise without the use of unwieldy mechanical screening. The methodology's effectiveness is founded on the fact that wind noise can be highly correlated on short spatiotemporal scales. This correlation structure is adaptively estimated from data and is used to formulate a generalized likelihood ratio detection problem and a minimum mean squared error waveform estimation problem. The infrasoudnic waveform is explicitly represented by a user-definable, parametrically characterized, stochastic prior distribution. Choice of this prior can enhance detection of anticipated signals and suppress others and thus more than one prior can be utilized in order to perform some level of classification. The presentation provides typical performance results from a range of application scenarios. Application to more traditional infrasound arrays is also presented, illustrating that exploitation of only the temporal correlation properties of wind noise is also beneficial in the context of the stochastic models and estimation techniques utilized.

Active GLR detector for resilient LQG controller in networked control systems

In computing science, resilience is the ability of system or network architecture to recover normal operation after a brutal crash. When malicious cyber act on control signals of a Networked Control System (NCS) is designed to remain undetectable from passive model-based Fault Detection and Isolation (FDI) schemes, we show that the unobservable consequence on the state variable of the plant becomes brutally observable after the disappearance of the damaging action. In order to quickly recover the nominal behavior of the Linear Quadratic Gaussian (LQG) controller, a resilient LQG controller is obtained from an active version of the Generalized Likelihood Ratio (GLR) test designed to detect the disappearance of the malicious act and to increase the tracking ability of the Kalman filter at detection time.