1,222 research outputs found
Painless Breakups -- Efficient Demixing of Low Rank Matrices
Assume we are given a sum of linear measurements of different rank-
matrices of the form . When and under
which conditions is it possible to extract (demix) the individual matrices
from the single measurement vector ? And can we do the demixing
numerically efficiently? We present two computationally efficient algorithms
based on hard thresholding to solve this low rank demixing problem. We prove
that under suitable conditions these algorithms are guaranteed to converge to
the correct solution at a linear rate. We discuss applications in connection
with quantum tomography and the Internet-of-Things. Numerical simulations
demonstrate empirically the performance of the proposed algorithms
Regularized Gradient Descent: A Nonconvex Recipe for Fast Joint Blind Deconvolution and Demixing
We study the question of extracting a sequence of functions
from observing only the sum of
their convolutions, i.e., from . While convex optimization techniques
are able to solve this joint blind deconvolution-demixing problem provably and
robustly under certain conditions, for medium-size or large-size problems we
need computationally faster methods without sacrificing the benefits of
mathematical rigor that come with convex methods. In this paper, we present a
non-convex algorithm which guarantees exact recovery under conditions that are
competitive with convex optimization methods, with the additional advantage of
being computationally much more efficient. Our two-step algorithm converges to
the global minimum linearly and is also robust in the presence of additive
noise. While the derived performance bounds are suboptimal in terms of the
information-theoretic limit, numerical simulations show remarkable performance
even if the number of measurements is close to the number of degrees of
freedom. We discuss an application of the proposed framework in wireless
communications in connection with the Internet-of-Things.Comment: Accepted to Information and Inference: a Journal of the IM
Self-correcting multi-channel Bussgang blind deconvolution using expectation maximization (EM) algorithm and feedback
A Bussgang based blind deconvolution algorithm called self-correcting multi-channel Bussgang (SCMB) blind deconvolution algorithm was proposed. Unlike the original Bussgang blind deconvolution algorithm where the probability density function (pdf) of the signal being recovered is assumed to be completely known, the proposed SCMB blind deconvolution algorithm relaxes this restriction by parameterized the pdf with a Gaussian mixture model and expectation maximization (EM) algorithm, an iterative maximum likelihood approach, is employed to estimate the parameter side by side with the estimation of the equalization filters of the original Bussgang blind deconvolution algorithm. A feedback loop is also designed to compensate the effect of the parameter estimation error on the estimation of the equalization filters. Application of the SCMB blind deconvolution framework for binary image restoration, multi-pass synthetic aperture radar (SAR) autofocus and inverse synthetic aperture radar (ISAR) autofocus are exploited with great results.Ph.D.Committee Chair: Dr. Russell Mersereau; Committee Member: Dr. Doug Willams; Committee Member: Dr. Mark Richards; Committee Member: Dr. Xiaoming Huo; Committee Member: Dr. Ye (Geoffrey) L
Channel Sounding for the Masses: Low Complexity GNU 802.11b Channel Impulse Response Estimation
New techniques in cross-layer wireless networks are building demand for
ubiquitous channel sounding, that is, the capability to measure channel impulse
response (CIR) with any standard wireless network and node. Towards that goal,
we present a software-defined IEEE 802.11b receiver and CIR estimation system
with little additional computational complexity compared to 802.11b reception
alone. The system implementation, using the universal software radio peripheral
(USRP) and GNU Radio, is described and compared to previous work. By overcoming
computational limitations and performing direct-sequence spread-spectrum
(DS-SS) matched filtering on the USRP, we enable high-quality yet inexpensive
CIR estimation. We validate the channel sounder and present a drive test
campaign which measures hundreds of channels between WiFi access points and an
in-vehicle receiver in urban and suburban areas
Blind Demixing for Low-Latency Communication
In the next generation wireless networks, lowlatency communication is
critical to support emerging diversified applications, e.g., Tactile Internet
and Virtual Reality. In this paper, a novel blind demixing approach is
developed to reduce the channel signaling overhead, thereby supporting
low-latency communication. Specifically, we develop a low-rank approach to
recover the original information only based on a single observed vector without
any channel estimation. Unfortunately, this problem turns out to be a highly
intractable non-convex optimization problem due to the multiple non-convex
rankone constraints. To address the unique challenges, the quotient manifold
geometry of product of complex asymmetric rankone matrices is exploited by
equivalently reformulating original complex asymmetric matrices to the
Hermitian positive semidefinite matrices. We further generalize the geometric
concepts of the complex product manifolds via element-wise extension of the
geometric concepts of the individual manifolds. A scalable Riemannian
trust-region algorithm is then developed to solve the blind demixing problem
efficiently with fast convergence rates and low iteration cost. Numerical
results will demonstrate the algorithmic advantages and admirable performance
of the proposed algorithm compared with the state-of-art methods.Comment: 14 pages, accepted by IEEE Transaction on Wireless Communicatio
Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems
We study the feasibility of short finite impulse response (FIR) synthesis for
perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis
banks, we focus on the one with the minimum filter length. For filter banks
with oversampling factors of at least two, we provide prescriptions for the
shortest filter length of the synthesis bank that would guarantee PR almost
surely. The prescribed length is as short or shorter than the analysis filters
and has an approximate inverse relationship with the oversampling factor. Our
results are in form of necessary and sufficient statements that hold
generically, hence only fail for elaborately-designed nongeneric examples. We
provide extensive numerical verification of the theoretical results and
demonstrate that the gap between the derived filter length prescriptions and
the true minimum is small. The results have potential applications in synthesis
FB design problems, where the analysis bank is given, and for analysis of
fundamental limitations in blind signals reconstruction from data collected by
unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
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