Generalized Likelihood Ratio Criterion Research Articles

Adaptive Radar Detection in the Presence of Missing-data

This article deals with the problem of adaptive radar detection in a missing-data context, where the complete observations (i.e., downstream information loss mechanisms) are characterized by homogeneous Gaussian disturbance with an unknown but possibly structured covariance matrix. The detection problem, formulated as a composite hypothesis test, is tackled by resorting to suboptimal design strategies, leveraging the generalized likelihood ratio criterion demanding appropriate maximum likelihood estimates (MLEs) of the unknowns under both hypotheses. Capitalizing on some possible <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge about the interference covariance matrix structure, the optimization problems involved in the MLE computation are handled by employing the expectation–maximization (EM) algorithm or its expectation–conditional maximization and multicycle EM variants. At the analysis stage, the performance of the devised architectures is assessed both via Monte Carlo simulations and on measured data for some covariance matrix structures of practical interest.

Distributed Target Detection in Partially Homogeneous Environment When Signal Mismatch Occurs

This paper investigates the problem of detecting a distributed target in the presence of signal mismatch in a partially homogeneous environment. To design a selective detector, we modify the original hypothesis test by injecting a fictitious interference under the null hypothesis test. The fictitious interference is assumed to be orthogonal to the nominal signal in the whitened subspace. Then, according to the generalized likelihood ratio criterion, we obtain a detector that has the constant false alarm rate property and is more selective than existing detectors. However, the proposed detector works only in the case of large number of training data. To overcome this limitation, we introduce a tunable detector, which is parameterized by a tunable parameter. It can work under a very loose constraint on a number of training data. More importantly, the directivity property (robustness and selectivity) of the tunable detector can be flexibly adjusted through the tunable parameter. In addition, the tunable detector can achieve roughly the same detection performance as the corresponding generalized likelihood ratio test when no signal mismatch occurs. Numerical examples are given to demonstrate the effectiveness of the proposed detectors.

Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks.

Detecting the signals of the primary users in the wideband spectrum is a key issue for cognitive radio networks. In this paper, we consider the multi-antenna based signal detection in a wideband spectrum scenario where the noise statistical characteristics are assumed to be unknown. We reason that the covariance matrices of the spectrum subbands have structural constraints and that they describe a manifold in the signal space. Thus, we propose a novel signal detection algorithm based on Riemannian distance and Riemannian mean which is different from the traditional eigenvalue-based detector (EBD) derived with the generalized likelihood ratio criterion. Using the moment matching method, we obtain the closed expression of the decision threshold. From the considered simulation settings, it is shown that the proposed Riemannian distance detector (RDD) has a better performance than the traditional EBD in wideband spectrum sensing.

Multi-source Signal Detection With Arbitrary Noise Covariance

Detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing. In this paper, we consider multi-antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown. We address this problem in the context of cognitive radio, where a multiple-primary-user detector is analyzed. This detector is known as Wilks' detector in statistics literature, which was derived under the generalized likelihood ratio criterion. We calculate the moments of Wilks' detector, which lead to simple and accurate approximate analytical formulae for the false alarm probability, the detection probability and the receiver operating characteristic. From the considered simulation settings, performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users.

The stochastically curtailed generalized likelihood ratio: A new termination criterion for variable-length computerized classification tests.

Computerized classification tests (CCTs) are used to classify examinees into categories in the context of professional certification testing. The term "variable-length" refers to CCTs that terminate (i.e., cease administering items to the examinee) when a classification can be made with a prespecified level of certainty. The sequential probability ratio test (SPRT) is a common criterion for terminating variable-length CCTs, but recent research has proposed more efficient methods. Specifically, the stochastically curtailed SPRT (SCSPRT) and the generalized likelihood ratio criterion (GLR) have been shown to classify examinees with accuracy similar to the SPRT while using fewer items. This article shows that the GLR criterion itself may be stochastically curtailed, resulting in a new termination criterion, the stochastically curtailed GLR (SCGLR). All four criteria-the SPRT, SCSPRT, GLR, and the new SCGLR-were compared using a simulation study. In this study, we examined the criteria in testing conditions that varied several CCT design features, including item bank characteristics, pass/fail threshold, and examinee ability distribution. In each condition, the termination criteria were evaluated according to their accuracy (proportion of examinees classified correctly), efficiency (test length), and loss (a single statistic combing both accuracy and efficiency). The simulation results showed that the SCGLR can yield increased efficiency without sacrificing accuracy, relative to the SPRT, SCSPRT, and GLR in a wide variety of CCT designs.

GLRT-Based Combining Schemes for PPM IR-UWB Systems with Multiple Receive Antennas

This paper deals with impulse-radio ultra wide-band systems with multiple receive antennas. For binary PPM modulations, we propose various combining/detection schemes derived by the generalized likelihood ratio criterion. These schemes first combine delayed versions of the waveforms received at the different antennas and then compute the energies of the resulting signal over intervals smaller than half the symbol period. The decision statistic is finally obtained by a linear combination of these energies. The proposed algorithms can be implemented using currently available technology. They outperform a detection scheme that simply combines the decision statistics obtained (at each antenna) by means of a conventional energy-based detector. Their advantage increases with the number of antennas.

A statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors from supernova SN 1987 A

A detailed statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors on UT 07∶35, 2/23'87 is carried out. Distribution functions of the mean scattering angles in the reactions\(\bar \upsilon _e p \to e^ + n\) andve→ve are constructed with account taken of the multiple Coulomb scattering and the experimental angular errors. The Smirnov and Wald-Wolfowitz run tests are used to test the hypothesis that the angular distributions of events from the two detectors agree with each other. We test with the use of the Kolmogorov and Mises statistical criterions the hypothesis that the recorded events all represent\(\bar \upsilon _e p \to e^ + n\) inelastic scatterings. Then the Neyman-Pearson test is applied to each event in testing the hypothesis\(\bar \upsilon _e p \to e^ + n\) against the alternativeve→ve. The hypotheses that the number of elastic events equalss=0, 1, 2, ... against the alternativess≠0, 1, 2, ... are tested on the basis of the generalized likelihood ratio criterion. The confidence intervals for the number of elastic events are also constructed. The current supernova models fail to give a satisfactory account of the angular distribution data.