stds-80220-eval-criteria: FW: Non-member submission from [<shankar@research.att.com>]
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h6UG19bv021201
As promised at the July meeting, here is
a reference on "hexagonally wrapped"
cellular topologies. This paper is available
on IEEE Explore. This paper talks
about general cases, including the specific
case of 19 cells. The specific case
of 19 cells is also discussed in the
appendix of the 1xEV-DV document in the
drop-box.
If the simulation involves
full simulation of all bases and mobiles
(as opposed to some abstracted cumulative
interference from boundary cells), there
is no difference in complexity or time
between the wrapped and non-wrapped simulations.
The advantage of wrapping is that there are
more (19x times) results and that increases
the statistical efficiency of each run.
The number of cells simulated in the
wrapped case is still 19.
For each receiver, the transmitter position
may get transformed to another "wrapped" position
such that every receiver appears to have
two tiers of 6+12=18 interferers around it.
As discussed in the meeting, there
may be subtle issues if the relative positions
of the mobiles/bases have some
complex inter-dependencies.
The question to ask is: If a transmitter T1
appears at one place for receiver R1, and
appears to be at another place for receiver R2,
(at no point will any one receiver see multiple
signals from T1), does that affect R1, R2,
or some third-party R3 that is trying to
manage multiple things. It may mess up some kind
of referred/derived topology map if
R2 were to later communicate to R1 about its
perceived location of T1.
By the way, note that 19 is a prime number.
If the reuse pattern involves a cluster
of 3 or 4 or 7 cells, then there is an
issue of the pattern not repeating itself.
- N. K. Shankar
=============
Symmetric cellular network embeddings on a torus
Iridon, M. Matula, D.W.
This paper appears in: Computer Communications and Networks, 1998.
Proceedings. 7th International Conference on
Meeting Date: 10/12/1998 -10/15/1998
Publication Date: 12-15 Oct 1998
Location: Lafayette, LA , USA
On page(s): 732-736
References Cited: 9
IEEE Catalog Number: 98EX226
Number of Pages: xxii+929
INSPEC Accession Number: 6220023
------------------------------------------------------------------------
Abstract:
Infinite planar cellular networks are embedded on a torus to obtain a
symmetric regular finite network sample region for performance analysis.
We show that a "hexagonal wrap" toroidal embedding preserves
translational and rotational symmetry on all three axes of a hexagonal
lattice and is preferable to a "Cartesian wrap" embedding. Hexagonal
tilings and embeddings are obtained for all rhombic tile sizes. Certain
tilings are shown to provide modular based neighbor addressing schemes
that simplify distributed channel assignment algorithms. Hierarchical
"hexagons within a hexagon" tilings are illustrated with the large
hexagon exhibiting the sample repeat and comprising a multiplicity of
channel frequency repeat small hexagonal the clusters. The symmetric
hexagonal sample region repeat embeddings are noted to be useful for
probabilistic analysis of high utilization channel assignment
performance both theoretically and by simulation