1,472 research outputs found
A Multichannel Spatial Compressed Sensing Approach for Direction of Arrival Estimation
The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-15995-4_57ESPRC Leadership Fellowship EP/G007144/1EPSRC Platform Grant EP/045235/1EU FET-Open Project FP7-ICT-225913\"SMALL
On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization
The use of multichannel data in line spectral estimation (or frequency
estimation) is common for improving the estimation accuracy in array
processing, structural health monitoring, wireless communications, and more.
Recently proposed atomic norm methods have attracted considerable attention due
to their provable superiority in accuracy, flexibility and robustness compared
with conventional approaches. In this paper, we analyze atomic norm
minimization for multichannel frequency estimation from noiseless compressive
data, showing that the sample size per channel that ensures exact estimation
decreases with the increase of the number of channels under mild conditions. In
particular, given channels, order samples per channel, selected randomly from
equispaced samples, suffice to ensure with high probability exact
estimation of frequencies that are normalized and mutually separated by at
least . Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor
Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization
We consider multichannel sparse recovery problem where the objective is to
find good recovery of jointly sparse unknown signal vectors from the given
multiple measurement vectors which are different linear combinations of the
same known elementary vectors. Many popular greedy or convex algorithms perform
poorly under non-Gaussian heavy-tailed noise conditions or in the face of
outliers. In this paper, we propose the usage of mixed norms on
data fidelity (residual matrix) term and the conventional -norm
constraint on the signal matrix to promote row-sparsity. We devise a greedy
pursuit algorithm based on simultaneous normalized iterative hard thresholding
(SNIHT) algorithm. Simulation studies highlight the effectiveness of the
proposed approaches to cope with different noise environments (i.i.d., row
i.i.d, etc) and outliers. Usefulness of the methods are illustrated in source
localization application with sensor arrays.Comment: Paper appears in Proc. European Signal Processing Conference
(EUSIPCO'15), Nice, France, Aug 31 -- Sep 4, 201
Time Delay Estimation from Low Rate Samples: A Union of Subspaces Approach
Time delay estimation arises in many applications in which a multipath medium
has to be identified from pulses transmitted through the channel. Various
approaches have been proposed in the literature to identify time delays
introduced by multipath environments. However, these methods either operate on
the analog received signal, or require high sampling rates in order to achieve
reasonable time resolution. In this paper, our goal is to develop a unified
approach to time delay estimation from low rate samples of the output of a
multipath channel. Our methods result in perfect recovery of the multipath
delays from samples of the channel output at the lowest possible rate, even in
the presence of overlapping transmitted pulses. This rate depends only on the
number of multipath components and the transmission rate, but not on the
bandwidth of the probing signal. In addition, our development allows for a
variety of different sampling methods. By properly manipulating the low-rate
samples, we show that the time delays can be recovered using the well-known
ESPRIT algorithm. Combining results from sampling theory with those obtained in
the context of direction of arrival estimation methods, we develop necessary
and sufficient conditions on the transmitted pulse and the sampling functions
in order to ensure perfect recovery of the channel parameters at the minimal
possible rate. Our results can be viewed in a broader context, as a sampling
theorem for analog signals defined over an infinite union of subspaces
Multiband Spectrum Access: Great Promises for Future Cognitive Radio Networks
Cognitive radio has been widely considered as one of the prominent solutions
to tackle the spectrum scarcity. While the majority of existing research has
focused on single-band cognitive radio, multiband cognitive radio represents
great promises towards implementing efficient cognitive networks compared to
single-based networks. Multiband cognitive radio networks (MB-CRNs) are
expected to significantly enhance the network's throughput and provide better
channel maintenance by reducing handoff frequency. Nevertheless, the wideband
front-end and the multiband spectrum access impose a number of challenges yet
to overcome. This paper provides an in-depth analysis on the recent
advancements in multiband spectrum sensing techniques, their limitations, and
possible future directions to improve them. We study cooperative communications
for MB-CRNs to tackle a fundamental limit on diversity and sampling. We also
investigate several limits and tradeoffs of various design parameters for
MB-CRNs. In addition, we explore the key MB-CRNs performance metrics that
differ from the conventional metrics used for single-band based networks.Comment: 22 pages, 13 figures; published in the Proceedings of the IEEE
Journal, Special Issue on Future Radio Spectrum Access, March 201
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
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