181 research outputs found
Orthogonal Matching Pursuit: A Brownian Motion Analysis
A well-known analysis of Tropp and Gilbert shows that orthogonal matching
pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n)
noise-free linear measurements obtained through a random Gaussian measurement
matrix with a probability that approaches one as n approaches infinity. This
work strengthens this result by showing that a lower number of measurements, 2
k log(n - k), is in fact sufficient for asymptotic recovery. More generally,
when the sparsity level satisfies kmin <= k <= kmax but is unknown, 2 kmax
log(n - kmin) measurements is sufficient. Furthermore, this number of
measurements is also sufficient for detection of the sparsity pattern (support)
of the vector with measurement errors provided the signal-to-noise ratio (SNR)
scales to infinity. The scaling 2 k log(n - k) exactly matches the number of
measurements required by the more complex lasso method for signal recovery with
a similar SNR scaling.Comment: 11 pages, 2 figure
60 GHz Blockage Study Using Phased Arrays
The millimeter wave (mmWave) frequencies offer the potential for enormous
capacity wireless links. However, designing robust communication systems at
these frequencies requires that we understand the channel dynamics over both
time and space: mmWave signals are extremely vulnerable to blocking and the
channel can thus rapidly appear and disappear with small movement of obstacles
and reflectors. In rich scattering environments, different paths may experience
different blocking trajectories and understanding these multi-path blocking
dynamics is essential for developing and assessing beamforming and
beam-tracking algorithms. This paper presents the design and experimental
results of a novel measurement system which uses phased arrays to perform
mmWave dynamic channel measurements. Specifically, human blockage and its
effects across multiple paths are investigated with only several microseconds
between successive measurements. From these measurements we develop a modeling
technique which uses low-rank tensor factorization to separate the available
paths so that their joint statistics can be understood.Comment: To appear in the Proceedings of the 51st Asilomar Conference on
Signals, Systems, and Computers, 201
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