7,391 research outputs found
On Channel Reciprocity to Activate Uplink Channel Training for Downlink Wireless Transmission in Tactile Internet Applications
We determine, for the first time, the requirement on channel reciprocity to
activate uplink channel training, instead of downlink channel training, to
achieve a higher data rate for the downlink transmission from a multi-antenna
base station to a single-antenna user. We first derive novel closed-form
expressions for the lower bounds on the data rates achieved by the two channel
training strategies by considering the impact of finite blocklength. The
performance comparison result of these two strategies is determined by the
amount of channel reciprocity that is utilized in the uplink channel training.
We then derive an approximated expression for the minimum channel reciprocity
that enables the uplink channel training to outperform the downlink channel
training. Through numerical results, we demonstrate that this minimum channel
reciprocity decreases as the blocklength decreases or the number of transmit
antennas increases, which shows the necessity and benefits of activating the
uplink channel training for short-packet communications with multiple transmit
antennas. This work provides pivotal and unprecedented guidelines on choosing
channel training strategies and channel reciprocity calibrations, offering
valuable insights into latency reduction in the Tactile Internet applications.Comment: 6 pages, 3 figures, Submitted to IEEE ICC 2018 Worksho
Spherical Tiling by 12 Congruent Pentagons
The tilings of the 2-dimensional sphere by congruent triangles have been
extensively studied, and the edge-to-edge tilings have been completely
classified. However, not much is known about the tilings by other congruent
polygons. In this paper, we classify the simplest case, which is the
edge-to-edge tilings of the 2-dimensional sphere by 12 congruent pentagons. We
find one major class allowing two independent continuous parameters and four
classes of isolated examples. The classification is done by first separately
classifying the combinatorial, edge length, and angle aspects, and then
combining the respective classifications together.Comment: 53 pages, 40 figures, spherical geometr
Parameter constraints in a near-equipartition model with multi-frequency \emph{NuSTAR}, \emph{Swift} and \emph{Fermi-LAT} data from 3C 279
Precise spectra of 3C 279 in the 0.5-70 keV range, obtained during two epochs
of
\emph{Swift} and \emph{NuSTAR} observations, are analyzed using a
near-equipartition model. We apply a one-zone leptonic model with a
three-parameter log-parabola electron energy distribution (EED) to fit the
\emph{Swift} and \emph{NuSTAR} X-ray data, as well as simultaneous optical and
\emph{Fermi}-LAT -ray data. The Markov Chain Monte Carlo (MCMC)
technique is used to search the high-dimensional parameter space and evaluate
the uncertainties on model parameters. We show that the two spectra can be
successfully fit in near-equipartition conditions, defined by the ratio of the
energy density of relativistic electrons to magnetic field
being close to unity. In both spectra, the observed X-rays are dominated by
synchrotron-self Compton photons, and the observed rays are dominated
by Compton scattering of external infrared photons from a surrounding dusty
torus.
Model parameters are well constrained. From the low state to the high state,
both the curvature of the log-parabola width parameter and the synchrotron peak
frequency significantly increase. The derived magnetic fields in the two states
are nearly identical (\ G), but the Doppler factor in the high state is
larger than that in the low state (28 versus 18). We derive that
the gamma-ray emission site takes place outside the broad-line region, at
0.1 pc from the black hole, but within the dusty torus. Implications
for 3C 279 as a source of high-energy cosmic-rays are discussed.Comment: accepted by MNRA
Graphical condensation of plane graphs: a combinatorial approach
The method of graphical vertex-condensation for enumerating perfect matchings
of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003),
267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57)
and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113-125). In this
paper, by a purely combinatorial method some explicit identities on graphical
vertex-condensation for enumerating perfect matchings of plane graphs (which do
not need to be bipartite) are obtained. As applications of our results, some
results on graphical edge-condensation for enumerating perfect matchings are
proved, and we count the sum of weights of perfect matchings of weighted Aztec
diamond.Comment: 13 pages, 5 figures. accepted by Theoretial Computer Scienc
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