135 research outputs found
5G Positioning and Mapping with Diffuse Multipath
5G mmWave communication is useful for positioning due to the geometric
connection between the propagation channel and the propagation environment.
Channel estimation methods can exploit the resulting sparsity to estimate
parameters(delay and angles) of each propagation path, which in turn can be
exploited for positioning and mapping. When paths exhibit significant spread in
either angle or delay, these methods breakdown or lead to significant biases.
We present a novel tensor-based method for channel estimation that allows
estimation of mmWave channel parameters in a non-parametric form. The method is
able to accurately estimate the channel, even in the absence of a specular
component. This in turn enables positioning and mapping using only diffuse
multipath. Simulation results are provided to demonstrate the efficacy of the
proposed approach
A Tour of Constrained Tensor Canonical Polyadic Decomposition
This paper surveys the use of constraints in tensor decomposition models. Constrained tensor decompositions have been extensively applied to chemometrics and array processing, but there is a growing interest in understanding these methods independently of the application of interest. We suggest a formalism that unifies various instances of constrained tensor decomposition, while shedding light on some possible extensions of existing methods
Subspace Methods for Joint Sparse Recovery
We propose robust and efficient algorithms for the joint sparse recovery
problem in compressed sensing, which simultaneously recover the supports of
jointly sparse signals from their multiple measurement vectors obtained through
a common sensing matrix. In a favorable situation, the unknown matrix, which
consists of the jointly sparse signals, has linearly independent nonzero rows.
In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally
proposed by Schmidt for the direction of arrival problem in sensor array
processing and later proposed and analyzed for joint sparse recovery by Feng
and Bresler, provides a guarantee with the minimum number of measurements. We
focus instead on the unfavorable but practically significant case of
rank-defect or ill-conditioning. This situation arises with limited number of
measurement vectors, or with highly correlated signal components. In this case
MUSIC fails, and in practice none of the existing methods can consistently
approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC),
which improves on MUSIC so that the support is reliably recovered under such
unfavorable conditions. Combined with subspace-based greedy algorithms also
proposed and analyzed in this paper, SA-MUSIC provides a computationally
efficient algorithm with a performance guarantee. The performance guarantees
are given in terms of a version of restricted isometry property. In particular,
we also present a non-asymptotic perturbation analysis of the signal subspace
estimation that has been missing in the previous study of MUSIC.Comment: submitted to IEEE transactions on Information Theory, revised versio
Robust L1-norm Singular-Value Decomposition and Estimation
Singular-Value Decomposition (SVD) is a ubiquitous data analysis method in engineering, science, and statistics. Singular-value estimation, in particular, is of critical importance in an array of engineering applications, such as channel estimation in communication systems, EMG signal analysis, and image compression, to name just a few. Conventional SVD of a data matrix coincides with standard Principal-Component Analysis (PCA). The L2-norm (sum of squared values) formulation of PCA promotes peripheral data points and, thus, makes PCA sensitive against outliers. Naturally, SVD inherits this outlier sensitivity. In this work, we present a novel robust method for SVD based on a L1-norm (sum of absolute values) formulation, namely L1-norm compact Singular-Value Decomposition (L1-cSVD). We then propose a closed-form algorithm to solve this problem and find the robust singular values with cost . Accordingly, the proposed method demonstrates sturdy resistance against outliers, especially for singular values estimation, and can facilitate more reliable data analysis and processing in a wide range of engineering applications
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