Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Exact Distribution of Poisson-Voronoi Area in $K$-tier HetNets with
  Generalized Association Rule   This letter characterizes the exact distribution function of a typical
Voronoi area in a $K$-tier Poisson network. The users obey a generalized
association (GA) rule, which is a superset of nearest base station association
and maximum received power based association (with arbitrary fading) rules that
are commonly adopted in the literature. Combining the Robbins' theorem and the
probability generating functional of a Poisson point process, we obtain the
exact moments of a typical $k$-th tier Voronoi area, $k \in \{1,...,K\}$ under
the GA rule. We apply this result in several special cases. For example, we
prove that in multi-tier networks with the GA rule, the mean of $k$-th tier
Voronoi area can exactly be expressed in a closed-form. We also obtain
simplified expressions of its higher-order moments for both average and
instantaneous received power based user association. In single-tier networks
with exponential fading, the later association rule provides closed-form
expression of the second-order moment of a typical Voronoi area. We numerically
evaluate this exact expression and compare it with an approximated result.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th