57,056 research outputs found
Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks
The performance of cellular system significantly depends on its network
topology, where the spatial deployment of base stations (BSs) plays a key role
in the downlink scenario. Moreover, cellular networks are undergoing a
heterogeneous evolution, which introduces unplanned deployment of smaller BSs,
thus complicating the performance evaluation even further. In this paper, based
on large amount of real BS locations data, we present a comprehensive analysis
on the spatial modeling of cellular network structure. Unlike the related
works, we divide the BSs into different subsets according to geographical
factor (e.g. urban or rural) and functional type (e.g. macrocells or
microcells), and perform detailed spatial analysis to each subset. After
examining the accuracy of Poisson point process (PPP) in BS locations modeling,
we take into account the Gibbs point processes as well as Neyman-Scott point
processes and compare their accuracy in view of large-scale modeling test.
Finally, we declare the inaccuracy of the PPP model, and reveal the general
clustering nature of BSs deployment, which distinctly violates the traditional
assumption. This paper carries out a first large-scale identification regarding
available literatures, and provides more realistic and more general results to
contribute to the performance analysis for the forthcoming heterogeneous
cellular networks
The Aemulus Project III: Emulation of the Galaxy Correlation Function
Using the N-body simulations of the AEMULUS Project, we construct an emulator
for the non-linear clustering of galaxies in real and redshift space. We
construct our model of galaxy bias using the halo occupation framework,
accounting for possible velocity bias. The model includes 15 parameters,
including both cosmological and galaxy bias parameters. We demonstrate that our
emulator achieves ~ 1% precision at the scales of interest, 0.1<r<10 h^{-1}
Mpc, and recovers the true cosmology when tested against independent
simulations. Our primary parameters of interest are related to the growth rate
of structure, f, and its degenerate combination fsigma_8. Using this emulator,
we show that the constraining power on these parameters monotonically increases
as smaller scales are included in the analysis, all the way down to 0.1 h^{-1}
Mpc. For a BOSS-like survey, the constraints on fsigma_8 from r<30 h^{-1} Mpc
scales alone are more than a factor of two tighter than those from the fiducial
BOSS analysis of redshift-space clustering using perturbation theory at larger
scales. The combination of real- and redshift-space clustering allows us to
break the degeneracy between f and sigma_8, yielding a 9% constraint on f alone
for a BOSS-like analysis. The current AEMULUS simulations limit this model to
surveys of massive galaxies. Future simulations will allow this framework to be
extended to all galaxy target types, including emission-line galaxies.Comment: 14 pages, 8 figures, 1 table; submitted to ApJ; the project webpage
is available at https://aemulusproject.github.io ; typo in Figure 7 and
caption updated, results unchange
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
The Extreme Small Scales: Do Satellite Galaxies Trace Dark Matter?
We investigate the radial distribution of galaxies within their host dark
matter halos by modeling their small-scale clustering, as measured in the Sloan
Digital Sky Survey. Specifically, we model the Jiang et al. (2011) measurements
of the galaxy two-point correlation function down to very small projected
separations (10 < r < 400 kpc/h), in a wide range of luminosity threshold
samples (absolute r-band magnitudes of -18 up to -23). We use a halo occupation
distribution (HOD) framework with free parameters that specify both the number
and spatial distribution of galaxies within their host dark matter halos. We
assume that the first galaxy in each halo lives at the halo center and that
additional satellite galaxies follow a radial density profile similar to the
dark matter Navarro-Frenk-White (NFW) profile, except that the concentration
and inner slope are allowed to vary. We find that in low luminosity samples,
satellite galaxies have radial profiles that are consistent with NFW. M_r < -20
and brighter satellite galaxies have radial profiles with significantly steeper
inner slopes than NFW (we find inner logarithmic slopes ranging from -1.6 to
-2.1, as opposed to -1 for NFW). We define a useful metric of concentration,
M_(1/10), which is the fraction of satellite galaxies (or mass) that are
enclosed within one tenth of the virial radius of a halo. We find that M_(1/10)
for low luminosity satellite galaxies agrees with NFW, whereas for luminous
galaxies it is 2.5-4 times higher, demonstrating that these galaxies are
substantially more centrally concentrated within their dark matter halos than
the dark matter itself. Our results therefore suggest that the processes that
govern the spatial distribution of galaxies, once they have merged into larger
halos, must be luminosity dependent, such that luminous galaxies become poor
tracers of the underlying dark matter.Comment: 12 pages, 6 figures, Accepted to Ap
Two-tier Spatial Modeling of Base Stations in Cellular Networks
Poisson Point Process (PPP) has been widely adopted as an efficient model for
the spatial distribution of base stations (BSs) in cellular networks. However,
real BSs deployment are rarely completely random, due to environmental impact
on actual site planning. Particularly, for multi-tier heterogeneous cellular
networks, operators have to place different BSs according to local coverage and
capacity requirement, and the diversity of BSs' functions may result in
different spatial patterns on each networking tier. In this paper, we consider
a two-tier scenario that consists of macrocell and microcell BSs in cellular
networks. By analyzing these two tiers separately and applying both classical
statistics and network performance as evaluation metrics, we obtain accurate
spatial model of BSs deployment for each tier. Basically, we verify the
inaccuracy of using PPP in BS locations modeling for either macrocells or
microcells. Specifically, we find that the first tier with macrocell BSs is
dispersed and can be precisely modelled by Strauss point process, while Matern
cluster process captures the second tier's aggregation nature very well. These
statistical models coincide with the inherent properties of macrocell and
microcell BSs respectively, thus providing a new perspective in understanding
the relationship between spatial structure and operational functions of BSs
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