1,109 research outputs found
MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter
Multiple-input multiple-output (MIMO) radar has become a thriving subject of
research during the past decades. In the MIMO radar context, it is sometimes
more accurate to model the radar clutter as a non-Gaussian process, more
specifically, by using the spherically invariant random process (SIRP) model.
In this paper, we focus on the estimation and performance analysis of the
angular spacing between two targets for the MIMO radar under the SIRP clutter.
First, we propose an iterative maximum likelihood as well as an iterative
maximum a posteriori estimator, for the target's spacing parameter estimation
in the SIRP clutter context. Then we derive and compare various
Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we
address the problem of target resolvability by using the concept of angular
resolution limit (ARL), and derive an analytical, closed-form expression of the
ARL based on Smith's criterion, between two closely spaced targets in a MIMO
radar context under SIRP clutter. For this aim we also obtain the non-matrix,
closed-form expressions for each of the CRLBs. Finally, we provide numerical
simulations to assess the performance of the proposed algorithms, the validity
of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure
Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case
In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix does not depend on this matrix and is fully specified by the matrix dimension and the number of independent training samples . Since this p.d.f. could therefore be pre-calculated for any a priori known , one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario () while Part 2 deals with the under-sampled scenario ()
Detection of an unknown rank-one component in white noise
We consider the detection of an unknown and arbitrary rank-one signal in a spatial sector scanned by a small number of beams. We address the problem of finding the maximal invariant for the problem at hand and show that it consists of the ratio of the eigenvalues of a Wishart matrix to its trace. Next, we derive the generalized-likelihood ratio test (GLRT) along with expressions for its probability density function (pdf) under both hypotheses. Special attention is paid to the case m= 2, where the GLRT is shown to be a uniformly most powerful invariant (UMPI). Numerical simulations attest to the validity of the theoretical analysis and illustrate the detection performance of the GLRT
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Model Order Selection Rules For Covariance Structure Classification
The adaptive classification of the interference covariance matrix structure
for radar signal processing applications is addressed in this paper. This
represents a key issue because many detection architectures are synthesized
assuming a specific covariance structure which may not necessarily coincide
with the actual one due to the joint action of the system and environment
uncertainties. The considered classification problem is cast in terms of a
multiple hypotheses test with some nested alternatives and the theory of Model
Order Selection (MOS) is exploited to devise suitable decision rules. Several
MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria
are adopted and the corresponding merits and drawbacks are discussed. At the
analysis stage, illustrating examples for the probability of correct model
selection are presented showing the effectiveness of the proposed rules
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