14,045 research outputs found
The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC
Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
Recovery under Side Constraints
This paper addresses sparse signal reconstruction under various types of
structural side constraints with applications in multi-antenna systems. Side
constraints may result from prior information on the measurement system and the
sparse signal structure. They may involve the structure of the sensing matrix,
the structure of the non-zero support values, the temporal structure of the
sparse representationvector, and the nonlinear measurement structure. First, we
demonstrate how a priori information in form of structural side constraints
influence recovery guarantees (null space properties) using L1-minimization.
Furthermore, for constant modulus signals, signals with row-, block- and
rank-sparsity, as well as non-circular signals, we illustrate how structural
prior information can be used to devise efficient algorithms with improved
recovery performance and reduced computational complexity. Finally, we address
the measurement system design for linear and nonlinear measurements of sparse
signals. Moreover, we discuss the linear mixing matrix design based on
coherence minimization. Then we extend our focus to nonlinear measurement
systems where we design parallel optimization algorithms to efficiently compute
stationary points in the sparse phase retrieval problem with and without
dictionary learning
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