102 research outputs found
Generalized Sparse Covariance-based Estimation
In this work, we extend the sparse iterative covariance-based estimator
(SPICE), by generalizing the formulation to allow for different norm
constraints on the signal and noise parameters in the covariance model. For a
given norm, the resulting extended SPICE method enjoys the same benefits as the
regular SPICE method, including being hyper-parameter free, although the choice
of norms are shown to govern the sparsity in the resulting solution.
Furthermore, we show that solving the extended SPICE method is equivalent to
solving a penalized regression problem, which provides an alternative
interpretation of the proposed method and a deeper insight on the differences
in sparsity between the extended and the original SPICE formulation. We examine
the performance of the method for different choices of norms, and compare the
results to the original SPICE method, showing the benefits of using the
extended formulation. We also provide two ways of solving the extended SPICE
method; one grid-based method, for which an efficient implementation is given,
and a gridless method for the sinusoidal case, which results in a semi-definite
programming problem
A Compact Formulation for the Mixed-Norm Minimization Problem
Parameter estimation from multiple measurement vectors (MMVs) is a
fundamental problem in many signal processing applications, e.g., spectral
analysis and direction-of- arrival estimation. Recently, this problem has been
address using prior information in form of a jointly sparse signal structure. A
prominent approach for exploiting joint sparsity considers mixed-norm
minimization in which, however, the problem size grows with the number of
measurements and the desired resolution, respectively. In this work we derive
an equivalent, compact reformulation of the mixed-norm
minimization problem which provides new insights on the relation between
different existing approaches for jointly sparse signal reconstruction. The
reformulation builds upon a compact parameterization, which models the
row-norms of the sparse signal representation as parameters of interest,
resulting in a significant reduction of the MMV problem size. Given the sparse
vector of row-norms, the jointly sparse signal can be computed from the MMVs in
closed form. For the special case of uniform linear sampling, we present an
extension of the compact formulation for gridless parameter estimation by means
of semidefinite programming. Furthermore, we derive in this case from our
compact problem formulation the exact equivalence between the
mixed-norm minimization and the atomic-norm minimization. Additionally, for the
case of irregular sampling or a large number of samples, we present a low
complexity, grid-based implementation based on the coordinate descent method
Frequency-Selective Vandermonde Decomposition of Toeplitz Matrices with Applications
The classical result of Vandermonde decomposition of positive semidefinite
Toeplitz matrices, which dates back to the early twentieth century, forms the
basis of modern subspace and recent atomic norm methods for frequency
estimation. In this paper, we study the Vandermonde decomposition in which the
frequencies are restricted to lie in a given interval, referred to as
frequency-selective Vandermonde decomposition. The existence and uniqueness of
the decomposition are studied under explicit conditions on the Toeplitz matrix.
The new result is connected by duality to the positive real lemma for
trigonometric polynomials nonnegative on the same frequency interval. Its
applications in the theory of moments and line spectral estimation are
illustrated. In particular, it provides a solution to the truncated
trigonometric -moment problem. It is used to derive a primal semidefinite
program formulation of the frequency-selective atomic norm in which the
frequencies are known {\em a priori} to lie in certain frequency bands.
Numerical examples are also provided.Comment: 23 pages, accepted by Signal Processin
Atomic Norm decomposition for sparse model reconstruction applied to positioning and wireless communications
This thesis explores the recovery of sparse signals, arising in the wireless communication and radar system fields, via atomic norm decomposition. Particularly, we
focus on compressed sensing gridless methodologies, which avoid the always existing
error due to the discretization of a continuous space in on-grid methods. We define
the sparse signal by means of a linear combination of so called atoms defined in a
continuous parametrical atom set with infinite cardinality. Those atoms are fully
characterized by a multi-dimensional parameter containing very relevant information
about the application scenario itself. Also, the number of composite atoms is
much lower than the dimension of the problem, which yields sparsity. We address
a gridless optimization solution enforcing sparsity via atomic norm minimization to
extract the parameters that characterize the atom from an observed measurement
of the model, which enables model recovery. We also study a machine learning approach to estimate the number of composite atoms that construct the model, given
that in certain scenarios this number is unknown.
The applications studied in the thesis lay on the field of wireless communications,
particularly on MIMO mmWave channels, which due to their natural properties can
be modeled as sparse. We apply the proposed methods to positioning in automotive
pulse radar working in the mmWave range, where we extract relevant information
such as angle of arrival (AoA), distance and velocity from the received echoes of
objects or targets. Next we study the design of a hybrid precoder for mmWave
channels which allows the reduction of hardware cost in the system by minimizing
as much as possible the number of required RF chains. Last, we explore full channel
estimation by finding the angular parameters that model the channel. For all
the applications we provide a numerical analysis where we compare our proposed
method with state-of-the-art techniques, showing that our proposal outperforms the
alternative methods.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Juan José Murillo Fuentes.- Secretario: Pablo Martínez Olmos.- Vocal: David Luengo Garcí
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