Performance of Statistical Tests for Single Source Detection using Random Matrix Theory

This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum Likelihood Test is studied and yields the analysis of the ratio between the maximum eigenvalue of the sampled covariance matrix and its normalized trace. Using recent results of random matrix theory, a practical way to evaluate the threshold and the $p$-value of the test is provided in the asymptotic regime where the number $K$ of sensors and the number $N$ of observations per sensor are large but have the same order of magnitude. The theoretical performance of the test is then analyzed in terms of Receiver Operating Characteristic (ROC) curve. It is in particular proved that both Type I and Type II error probabilities converge to zero exponentially as the dimensions increase at the same rate, and closed-form expressions are provided for the error exponents. These theoretical results rely on a precise description of the large deviations of the largest eigenvalue of spiked random matrix models, and establish that the presented test asymptotically outperforms the popular test based on the condition number of the sampled covariance matrix.Comment: 45 p. improved presentation; more proofs provide

Space-time reduced rank methods and CFAR signal detection algorithms with applications to HPRF radar

In radar applications, the statistical properties (covariance matrix) of the interference are typically unknown a priori and are estimated from a dataset with limited sample support. Often, the limited sample support leads to numerically ill-conditioned radar detectors. Under such circumstances, classical interference cancellation methods such as sample matrix inversion (SMI) do not perform satisfactorily. In these cases, innovative reduced-rank space-time adaptive processing (STAP) techniques outperform full-rank techniques. The high pulse repetition frequency (HPRF) radar problem is analyzed and it is shown that it is in the class of adaptive radar with limited sample support. Reduced-rank methods are studied for the HPRF radar problem. In particular, the method known as diagonally loaded covariance matrix SMI (L-SMI) is closely investigated. Diagonal loading improves the numerical conditioning of the estimated covariance matrix, and hence, is well suited to be applied in a limited sample support environment. The performance of L-SMI is obtained through a theoretical distribution of the output conditioned signal-to-noise ratio of the space-time array. Reduced-rank techniques are extended to constant false alarm rate (CFAR) detectors based on the generalized likelihood ratio test (GLRT). Two new modified CFAR GLRT detectors are considered and analyzed. The first is a subspace-based GLRT detector where subspace-based transformations are applied to the data prior to detection. A subspace transformation adds statistical stability which tends to improve performance at the expense of an additional SNR loss. The second detector is a modified GLRT detector that incorporates a diagonally loaded covariance matrix. Both detectors show improved performance over the traditional GLRT

Spectrum sensing algorithms and software-defined radio implementation for cognitive radio system

The scarcity of spectral resources in wireless communications, due to a fixed frequency allocation policy, is a strong limitation to the increasing demand for higher data rates. However, measurements showed that a large part of frequency channels are underutilized or almost unoccupied. The cognitive radio paradigm arises as a tempting solution to the spectral congestion problem. A cognitive radio must be able to identify transmission opportunities in unused channels and to avoid generating harmful interference with the licensed primary users. Its key enabling technology is the spectrum sensing unit, whose ultimate goal consists in providing an indication whether a primary transmission is taking place in the observed channel. Such indication is determined as the result of a binary hypothesis testing experiment wherein null hypothesis (alternate hypothesis) corresponds to the absence (presence) of the primary signal. The first parts of this thesis describes the spectrum sensing problem and presents some of the best performing detection techniques. Energy Detection and multi-antenna Eigenvalue-Based Detection algorithms are considered. Important aspects are taken into account, like the impact of noise estimation or the effect of primary user traffic. The performance of each detector is assessed in terms of false alarm probability and detection probability. In most experimental research, cognitive radio techniques are deployed in software-defined radio systems, radio transceivers that allow operating parameters (like modulation type, bandwidth, output power, etc.) to be set or altered by software.In the second part of the thesis, we introduce the software-defined radio concept. Then, we focus on the implementation of Energy Detection and Eigenvalue-Based Detection algorithms: first, the used software platform, GNU Radio, is described, secondly, the implementation of a parallel energy detector and a multi-antenna eigenbased detector is illustrated and details on the used methodologies are given. Finally, we present the deployed experimental cognitive testbeds and the used radio peripherals. The obtained algorithmic results along with the software-defined radio implementation may offer a set of tools able to create a realistic cognitive radio system with real-time spectrum sensing capabilities

Bayesian approach for the spectrum sensing mimo-cognitive radio network with presence of the uncertainty

A cognitive radio technique has the ability to learn. This system not only can observe the surrounding environment, adapt to environmental conditions, but also efficiently use the radio spectrum. This technique allows the secondary users (SUs) to employ the primary users (PUs) spectrum during the band is not being utilized by the user. Cognitive radio has three main steps: sensing of the spectrum, deciding and acting. In the spectrum sensing technique, the channel occupancy is determined with a spectrum sensing approach to detect unused spectrum. In the decision process, sensing results are evaluated and the decision process is then obtained based on these results. In the final process which is called the acting process, the scholar determines how to adjust the parameters of transmission to achieve great performance for the cognitive radio network

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

A subpixel target detection algorithm for hyperspectral imagery

The goal of this research is to develop a new algorithm for the detection of subpixel scale target materials on the hyperspectral imagery. The signal decision theory is typically to decide the existence of a target signal embedded in the random noise. This implies that the detection problem can be mathematically formalized by signal decision theory based on the statistical hypothesis test. In particular, since any target signature provided by airborne/spaceborne sensors is embedded in a structured noise such as background or clutter signatures as well as broad band unstructured noise, the problem becomes more complicated, and particularly much more under the unknown noise structure. The approach is based on the statistical hypothesis method known as Generalized Likelihood Ratio Test (GLRT). The use of GLRT requires estimating the unknown parameters, and assumes the prior information of two subspaces describing target variation and background variation respectively. Therefore, this research consists of two parts, the implementation of GLRT and the characterization of two subspaces through new approaches. Results obtained from computer simulation, HYDICE image and AVI RIS image show that this approach is feasible

Individual camera device identification from JPEG images

International audienceThe goal of this paper is to investigate the problem of source camera device identification for natural images in JPEG format. We propose an improved signal-dependent noise model describing the statistical distribution of pixels from a JPEG image. The noise model relies on the heteroscedastic noise parameters, that relates the variance of pixels’ noise with the expectation considered as unique fingerprints. It is also shown in the present paper that, non-linear response of pixels can be captured by characterizing the linear relation because those heteroscedastic parameters, which are used to identify source camera device. The identification problem is cast within the framework of hypothesis testing theory. In an ideal context where all model parameters are perfectly known, the Likelihood Ratio Test (LRT) is presented and its performance is theoretically established. The statistical performance of LRT serves as an upper bound of the detection power. In a practical identification, when the nuisance parameters are unknown, two generalized LRTs based on estimation of those parameters are established. Numerical results on simulated data and real natural images highlight the relevance of our proposed approach. While those results show a first positive proof of concept of the method, it still requires to be extended for a relevant comparison with PRNU-based approaches that benefit from years of experience

Environmentally adaptive noise estimation for active sonar

Noise is frequently encountered when processing data from the natural environment, and is of particular concern for remote-sensing applications where the accuracy of data gathered is limited by the noise present. Rather than merely accepting that sonar noise results in unavoidable error in active sonar systems, this research explores various methodologies to reduce the detrimental effect of noise. Our approach is to analyse the statistics of sonar noise in trial data, collected by a long-range active sonar system in a shallow water environment, and apply this knowledge to target detection. Our detectors are evaluated against imulated targets in simulated noise, simulated targets embedded in noise-only trial data, and trial data containing real targets. First, we demonstrate that the Weibull and K-distributions offer good models of sonar noise in a cluttered environment, and that the K-distribution achieves the greatest accuracy in the tail of the distribution. We demonstrate the limitations of the Kolmogorov-Smirnov goodness-of-fit test in the context of detection by thresholding, and investigate the upper-tail Anderson-Darling test for goodness-of-fit analysis. The upper-tail Anderson-Darling test is shown to be more suitable in the context of detection by thresholding, as it is sensitive to the far-right tail of the distribution, which is of particular interest for detection at low false alarm rates. We have also produced tables of critical values for K-distributed data evaluated by the upper-tail Anderson-Darling test. Having established suitable models for sonar noise, we develop a number of detection statistics. These are based on the box-car detector, and the generalized likelihood ratio test with a Rician target model. Our performance analysis shows that both types of detector benefit from the use of the noise model provided by the K-distribution. We also demonstrate that for weak signals, our GLRT detectors are able to achieve greater probability of detection than the box-car detectors. The GLRT detectors are also easily extended to use more than one sample in a single test, an approach that we show to increase probability of detection when processing simulated targets. A fundamental difficulty in estimating model parameters is the small sample size. Many of the pings in our trial data overlap, covering the same region of the sea. It is therefore possible to make use of samples from multiple pings of a region, increasing the sample size. For static targets, the GLRT detector is easily extended to multi-ping processing, but this is not as easy for moving targets. We derive a new method of combining noise estimates over multiple pings. This calculation can be applied to either static or moving targets, and is also shown to be useful for generating clutter maps. We then perform a brief performance analysis on trial data containing real targets, where we show that in order to perform well, the GLRT detector requires a more accurate model of the target than the Rician distribution is able to provide. Despite this, we show that both GLRT and box-car detectors, when using the K-distribution as a noise model, can achieve a small improvement in the probability of detection by combining estimates of the noise parameters over multiple pings.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust $M$-estimator of mean vector and scatter matrix when no a-priori information on the density generator is available. A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$-estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on Signal Processin