16,562 research outputs found
Off-the-Grid Line Spectrum Denoising and Estimation with Multiple Measurement Vectors
Compressed Sensing suggests that the required number of samples for
reconstructing a signal can be greatly reduced if it is sparse in a known
discrete basis, yet many real-world signals are sparse in a continuous
dictionary. One example is the spectrally-sparse signal, which is composed of a
small number of spectral atoms with arbitrary frequencies on the unit interval.
In this paper we study the problem of line spectrum denoising and estimation
with an ensemble of spectrally-sparse signals composed of the same set of
continuous-valued frequencies from their partial and noisy observations. Two
approaches are developed based on atomic norm minimization and structured
covariance estimation, both of which can be solved efficiently via semidefinite
programming. The first approach aims to estimate and denoise the set of signals
from their partial and noisy observations via atomic norm minimization, and
recover the frequencies via examining the dual polynomial of the convex
program. We characterize the optimality condition of the proposed algorithm and
derive the expected convergence rate for denoising, demonstrating the benefit
of including multiple measurement vectors. The second approach aims to recover
the population covariance matrix from the partially observed sample covariance
matrix by motivating its low-rank Toeplitz structure without recovering the
signal ensemble. Performance guarantee is derived with a finite number of
measurement vectors. The frequencies can be recovered via conventional spectrum
estimation methods such as MUSIC from the estimated covariance matrix. Finally,
numerical examples are provided to validate the favorable performance of the
proposed algorithms, with comparisons against several existing approaches.Comment: 14 pages, 10 figure
Compressed Sensing of Analog Signals in Shift-Invariant Spaces
A traditional assumption underlying most data converters is that the signal
should be sampled at a rate exceeding twice the highest frequency. This
statement is based on a worst-case scenario in which the signal occupies the
entire available bandwidth. In practice, many signals are sparse so that only
part of the bandwidth is used. In this paper, we develop methods for low-rate
sampling of continuous-time sparse signals in shift-invariant (SI) spaces,
generated by m kernels with period T. We model sparsity by treating the case in
which only k out of the m generators are active, however, we do not know which
k are chosen. We show how to sample such signals at a rate much lower than m/T,
which is the minimal sampling rate without exploiting sparsity. Our approach
combines ideas from analog sampling in a subspace with a recently developed
block diagram that converts an infinite set of sparse equations to a finite
counterpart. Using these two components we formulate our problem within the
framework of finite compressed sensing (CS) and then rely on algorithms
developed in that context. The distinguishing feature of our results is that in
contrast to standard CS, which treats finite-length vectors, we consider
sampling of analog signals for which no underlying finite-dimensional model
exists. The proposed framework allows to extend much of the recent literature
on CS to the analog domain.Comment: to appear in IEEE Trans. on Signal Processin
Millimeter Wave MIMO Channel Estimation Based on Adaptive Compressed Sensing
Multiple-input multiple-output (MIMO) systems are well suited for
millimeter-wave (mmWave) wireless communications where large antenna arrays can
be integrated in small form factors due to tiny wavelengths, thereby providing
high array gains while supporting spatial multiplexing, beamforming, or antenna
diversity. It has been shown that mmWave channels exhibit sparsity due to the
limited number of dominant propagation paths, thus compressed sensing
techniques can be leveraged to conduct channel estimation at mmWave
frequencies. This paper presents a novel approach of constructing beamforming
dictionary matrices for sparse channel estimation using the continuous basis
pursuit (CBP) concept, and proposes two novel low-complexity algorithms to
exploit channel sparsity for adaptively estimating multipath channel parameters
in mmWave channels. We verify the performance of the proposed CBP-based
beamforming dictionary and the two algorithms using a simulator built upon a
three-dimensional mmWave statistical spatial channel model, NYUSIM, that is
based on real-world propagation measurements. Simulation results show that the
CBP-based dictionary offers substantially higher estimation accuracy and
greater spectral efficiency than the grid-based counterpart introduced by
previous researchers, and the algorithms proposed here render better
performance but require less computational effort compared with existing
algorithms.Comment: 7 pages, 5 figures, in 2017 IEEE International Conference on
Communications Workshop (ICCW), Paris, May 201
Linear Block Coding for Efficient Beam Discovery in Millimeter Wave Communication Networks
The surge in mobile broadband data demands is expected to surpass the
available spectrum capacity below 6 GHz. This expectation has prompted the
exploration of millimeter wave (mm-wave) frequency bands as a candidate
technology for next generation wireless networks. However, numerous challenges
to deploying mm-wave communication systems, including channel estimation, need
to be met before practical deployments are possible. This work addresses the
mm-wave channel estimation problem and treats it as a beam discovery problem in
which locating beams with strong path reflectors is analogous to locating
errors in linear block codes. We show that a significantly small number of
measurements (compared to the original dimensions of the channel matrix) is
sufficient to reliably estimate the channel. We also show that this can be
achieved using a simple and energy-efficient transceiver architecture.Comment: To appear in the proceedings of IEEE INFOCOM '1
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
Recursive Compressed Sensing
We introduce a recursive algorithm for performing compressed sensing on
streaming data. The approach consists of a) recursive encoding, where we sample
the input stream via overlapping windowing and make use of the previous
measurement in obtaining the next one, and b) recursive decoding, where the
signal estimate from the previous window is utilized in order to achieve faster
convergence in an iterative optimization scheme applied to decode the new one.
To remove estimation bias, a two-step estimation procedure is proposed
comprising support set detection and signal amplitude estimation. Estimation
accuracy is enhanced by a non-linear voting method and averaging estimates over
multiple windows. We analyze the computational complexity and estimation error,
and show that the normalized error variance asymptotically goes to zero for
sublinear sparsity. Our simulation results show speed up of an order of
magnitude over traditional CS, while obtaining significantly lower
reconstruction error under mild conditions on the signal magnitudes and the
noise level.Comment: Submitted to IEEE Transactions on Information Theor
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