10,215 research outputs found
Cooperative Wideband Spectrum Sensing Based on Joint Sparsity
COOPERATIVE WIDEBAND SPECTRUM SENSING BASED ON JOINT SPARSITY
By Ghazaleh Jowkar, Master of Science
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at Virginia Commonwealth University
Virginia Commonwealth University 2017
Major Director: Dr. Ruixin Niu, Associate Professor of Department of Electrical and Computer Engineering
In this thesis, the problem of wideband spectrum sensing in cognitive radio (CR) networks using sub-Nyquist sampling and sparse signal processing techniques is investigated. To mitigate multi-path fading, it is assumed that a group of spatially dispersed SUs collaborate for wideband spectrum sensing, to determine whether or not a channel is occupied by a primary user (PU). Due to the underutilization of the spectrum by the PUs, the spectrum matrix has only a small number of non-zero rows. In existing state-of-the-art approaches, the spectrum sensing problem was solved using the low-rank matrix completion technique involving matrix nuclear-norm minimization. Motivated by the fact that the spectrum matrix is not only low-rank, but also sparse, a spectrum sensing approach is proposed based on minimizing a mixed-norm of the spectrum matrix instead of low-rank matrix completion to promote the joint sparsity among the column vectors of the spectrum matrix. Simulation results are obtained, which demonstrate that the proposed mixed-norm minimization approach outperforms the low-rank matrix completion based approach, in terms of the PU detection performance. Further we used mixed-norm minimization model in multi time frame detection. Simulation results shows that increasing the number of time frames will increase the detection performance, however, by increasing the number of time frames after a number of times the performance decrease dramatically
Bayesian Nonstationary Spatial Modeling for Very Large Datasets
With the proliferation of modern high-resolution measuring instruments
mounted on satellites, planes, ground-based vehicles and monitoring stations, a
need has arisen for statistical methods suitable for the analysis of large
spatial datasets observed on large spatial domains. Statistical analyses of
such datasets provide two main challenges: First, traditional
spatial-statistical techniques are often unable to handle large numbers of
observations in a computationally feasible way. Second, for large and
heterogeneous spatial domains, it is often not appropriate to assume that a
process of interest is stationary over the entire domain.
We address the first challenge by using a model combining a low-rank
component, which allows for flexible modeling of medium-to-long-range
dependence via a set of spatial basis functions, with a tapered remainder
component, which allows for modeling of local dependence using a compactly
supported covariance function. Addressing the second challenge, we propose two
extensions to this model that result in increased flexibility: First, the model
is parameterized based on a nonstationary Matern covariance, where the
parameters vary smoothly across space. Second, in our fully Bayesian model, all
components and parameters are considered random, including the number,
locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil
measurements, we show that both extensions can result in substantial
improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure
Likelihood-informed dimension reduction for nonlinear inverse problems
The intrinsic dimensionality of an inverse problem is affected by prior
information, the accuracy and number of observations, and the smoothing
properties of the forward operator. From a Bayesian perspective, changes from
the prior to the posterior may, in many problems, be confined to a relatively
low-dimensional subspace of the parameter space. We present a dimension
reduction approach that defines and identifies such a subspace, called the
"likelihood-informed subspace" (LIS), by characterizing the relative influences
of the prior and the likelihood over the support of the posterior distribution.
This identification enables new and more efficient computational methods for
Bayesian inference with nonlinear forward models and Gaussian priors. In
particular, we approximate the posterior distribution as the product of a
lower-dimensional posterior defined on the LIS and the prior distribution
marginalized onto the complementary subspace. Markov chain Monte Carlo sampling
can then proceed in lower dimensions, with significant gains in computational
efficiency. We also introduce a Rao-Blackwellization strategy that
de-randomizes Monte Carlo estimates of posterior expectations for additional
variance reduction. We demonstrate the efficiency of our methods using two
numerical examples: inference of permeability in a groundwater system governed
by an elliptic PDE, and an atmospheric remote sensing problem based on Global
Ozone Monitoring System (GOMOS) observations
On the probability that all eigenvalues of Gaussian, Wishart, and double Wishart random matrices lie within an interval
We derive the probability that all eigenvalues of a random matrix lie
within an arbitrary interval ,
, when is a real or complex finite dimensional Wishart,
double Wishart, or Gaussian symmetric/Hermitian matrix. We give efficient
recursive formulas allowing the exact evaluation of for Wishart
matrices, even with large number of variates and degrees of freedom. We also
prove that the probability that all eigenvalues are within the limiting
spectral support (given by the Mar{\v{c}}enko-Pastur or the semicircle laws)
tends for large dimensions to the universal values and for
the real and complex cases, respectively. Applications include improved bounds
for the probability that a Gaussian measurement matrix has a given restricted
isometry constant in compressed sensing.Comment: IEEE Transactions on Information Theory, 201
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