Aleksandar Dogandzic

Maximum Likelihood Estimation of Compound-Gaussian Clutter and Target Parameters

Compound-Gaussian models are used in radar signal processing to describe heavy-tailed clutter distributions. The important problems in compound-Gaussian clutter modeling are choosing the texture distribution, and estimating its parameters. Many texture distributions have been studied, and their parameters are typically estimated using statistically suboptimal approaches. We develop maximum likelihood (ML) methods for jointly estimating the target and clutter parameters in compound-Gaussian clutter using radar array measurements. In particular, we estimate i) the complex target amplitudes, ii) a spatial and temporal covariance matrix of the speckle component, and iii) texture distribution parameters. Parameter-expanded expectation-maximization (PX-EM) algorithms are developed to compute the ML estimates of the unknown parameters. We also derived the Cramer-Rao bounds (CRBs) and related bounds for these parameters. We first derive general CRB expressions under an arbitrary texture model then simplify them for specific texture distributions. We consider the widely used gamma texture model, and propose an inverse-gamma texture model, leading to a complex multivariate t clutter distribution and closed-form expressions of the CRB. We study the performance of the proposed methods via numerical simulations

Distributed Estimation and Detection for Sensor Networks Using Hidden Markov Random Field Models

We develop a hidden Markov random field (HMRF) framework for distributed signal processing in sensor-network environments. Under this framework, spatially distributed observations collected at the sensors form a noisy realization of an underlying random field that has a simple structure with Markovian dependence. We derive iterated conditional modes (ICM) algorithms for distributed estimation of the hidden random field from the noisy measurements. We consider both parametric and nonparametric measurement-error models. The proposed distributed estimators are computationally simple, applicable to a wide range of sensing environments, and localized, implying that the nodes communicate only with their neighbors to obtain the desired results. We also develop a calibration method for estimating Markov random field model parameters from training data and discuss initialization of the ICM algorithms. The HMRF framework and ICM algorithms are applied to event-region detection. Numerical simulations demonstrate the performance of the proposed approach

Space-time fading channel estimation and symbol detection in unknown spatially correlated noise

We present maximum likelihood (ML) methods for space-time fading channel estimation with an antenna array in spatially correlated noise having unknown covariance; the results are applied to symbol detection. The received signal is modeled as a linear combination of multipath-delayed and Doppler-shifted copies of the transmitted waveform. We consider structured and unstructured array response models and derive the Cramer-Rao bound (CRB) for the unknown directions of arrival, time delays, and Doppler shifts. We also develop methods for spatial and temporal interference suppression. Finally, we propose coherent matched-filter and concentrated-likelihood receivers that account for the spatial noise covariance and analyze their performance.

Decentralized Random-Field Estimation for Sensor Networks Using Quantized Spatially Correlated Data and Fusion-Center Feedback

In large-scale wireless sensor networks, sensor-processor elements (nodes) are densely deployed to monitor the environment; consequently, their observations form a random field that is highly correlated in space. We consider a fusion sensor-network architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusion-center failures. We assume that the sensor observations follow a linear-regression model with known spatial covariances between any two locations within a region of interest. We propose a Bayesian framework for adaptive quantization, fusion-center feedback, and estimation of the random field and its parameters. We also derive a simple suboptimal scheme for estimating the unknown parameters, apply our estimation approach to the no-feedback scenario, discuss field prediction at arbitrary locations within the region of interest, and present numerical examples demonstrating the performance of the proposed methods.

Sparse Signal Reconstruction via ECME Hard Thresholding

We propose a probabilistic model for sparse signal reconstruction and develop several novel algorithms for computing the maximum likelihood (ML) parameter estimates under this model. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. Our reconstruction schemes are based on an expectation-conditional maximization either (ECME) iteration that aims at maximizing the likelihood function with respect to the unknown parameters for a given signal sparsity level. Compared with the existing iterative hard thresholding (IHT) method, the ECME algorithm contains an additional multiplicative term and guarantees monotonic convergence for a wide range of sensing (regression) matrices. We propose a double overrelaxation (DORE) thresholding scheme for accelerating the ECME iteration. We prove that, under certain mild conditions, the ECME and DORE iterations converge to local maxima of the likelihood function. The ECME and DORE iterations can be implemented exactly in small-scale applications and for the important class of large-scale sensing operators with orthonormal rows used e.g., partial fast Fourier transform (FFT). If the signal sparsity level is unknown, we introduce an unconstrained sparsity selection (USS) criterion and a tuning-free automatic double overrelaxation (ADORE) thresholding method that employs USS to estimate the sparsity level. We compare the proposed and existing sparse signal reconstruction methods via one-dimensional simulation and two-dimensional image reconstruction experiments using simulated and real X-ray CT data.

Variance-Component Based Sparse Signal Reconstruction and Model Selection

We propose a variance-component probabilistic model for sparse signal reconstruction and model selection. The measurements follow an underdetermined linear model, where the unknown regression vector (signal) is sparse or approximately sparse and noise covariance matrix is known up to a constant. The signal is composed of two disjoint parts: a part with significant signal elements and the complementary part with insignificant signal elements that have zero or small values. We assign distinct variance components to the candidates for the significant signal elements and a single variance component to the rest of the signal; consequently, the dimension of our models parameter space is proportional to the assumed sparsity level of the signal. We derive a generalized maximum-likelihood (GML) rule for selecting the most efficient parameter assignment and signal representation that strikes a balance between the accuracy of data fit and compactness of the parameterization. We prove that, under mild conditions, the GML-optimal index set of the distinct variance components coincides with the support set of the sparsest solution to the underlying underdetermined linear system. Finally, we propose an expansion-compression variance-component based method (ExCoV) that aims at maximizing the GML objective function and provides an approximate GML estimate of the significant signal element set and an empirical Bayesian signal estimate. The ExCoV method is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. We also develop a computationally and memory efficient approximate ExCoV scheme suitable for large-scale problems, apply the proposed methods to reconstruct one- and two-dimensional signals from compressive samples, and demonstrate their reconstruction performance via numerical simulations. Compared with the competing approaches, our schemes perform particularly well in challenging scenarios where the noise is large or the number of measurements is small.

Estimating range, velocity, and direction with a radar array

We present maximum likelihood (ML) methods for active estimation of range (time delay), velocity (Doppler shift), and direction of a point target with a radar array in spatially correlated noise with unknown covariance. We consider structured and unstructured array response models and compute the Cramer-Rao bound (CRB) for the time delay, Doppler shift, and direction of arrival. We derive ambiguity functions for the above models and discuss the relationship between identifiability, ambiguity, and the Fisher information matrix.

Maximum likelihood estimation of statistical properties of composite gamma-lognormal fading channels

We propose maximum likelihood (ML) methods for estimating the parameters of composite gamma-lognormal fading channels. Newton-Raphson and expectation-maximization (EM) algorithms are developed to compute the ML estimates of the mean and variance of the shadowing component, and the Nakagami-m parameter of the fading component. We also derive Crame/spl acute/r-Rao bounds (CRBs) for the unknown parameters. Numerical simulations demonstrate the performance of the proposed method.

Signal-strength based localization in wireless fading channels

We develop maximum likelihood (ML) methods for location estimation using spatio-temporal received-signal-strength (RSS) measurements in wireless fading channels. Fading and composite fading-shadowing scenarios with completely unknown and partially known source signals are considered. We adopt gamma (Nakagami-m) and lognormal models to describe fading and shadowing effects, respectively. We also derive Cramer-Rao bounds (CRBs) for the location parameters and discuss initialization of the proposed algorithms. Numerical simulations demonstrate the performance of our estimators.

Double overrelaxation thresholding methods for sparse signal reconstruction

We propose double overrelaxation (DORE) and automatic double overrelaxation (ADORE) thresholding methods for sparse signal reconstruction. The measurements follow an underdetermined linear model, where the regression-coefficient vector is a sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. We first introduce an expectation-conditional maximization either (ECME) algorithm for estimating the sparse signal and variance of the random signal component and then describe our DORE thresholding scheme. The DORE scheme interleaves two successive overrelaxation steps and ECME steps, with goal to accelerate the convergence of the ECME algorithm. Both ECME and DORE algorithms aim at finding the maximum likelihood (ML) estimates of the unknown parameters assuming that the signal sparsity level is known. If the signal sparsity level is unknown, we propose an unconstrained sparsity selection (USS) criterion and show that, under certain conditions, maximizing the USS objective function with respect to the signal sparsity level is equivalent to finding the sparsest solution of the underlying underdetermined linear system. Our ADORE scheme demands no prior knowledge about the signal sparsity level and estimates this level by applying a golden-section search to maximize the USS objective function. We employ the proposed methods to reconstruct images from sparse tomographic projections and compare them with existing approaches that are feasible for large-scale data. Our numerical examples show that DORE is significantly faster than the ECME and related iterative hard thresholding (IHT) algorithms.