C802.20-05
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IEEE C802.20-05/15
Project
IEEE 802.20 Working Group on Mobile Broadband Wireless Access
<http://grouper.ieee.org/groups/802/20/>
Title
Clarification on the Wrap-Around Hexagon Network Structure
Date
Submitted
2005-03-13
Source(s)
David Huo
67 Whippany Road
Whippany, NJ 07981
Re:
Evaluation criteria.
Abstract
This document discusses the wrap-around hexagon network structure and proposes some
text change.
Purpose
Discuss and adopt.
Notice
This document has been prepared to assist the IEEE 802.20 Working Group. It is offered as
a basis for discussion and is not binding on the contributing individual(s) or
organization(s). The material in this document is subject to change in form and content
after further study. The contributor(s) reserve(s) the right to add, amend or withdraw
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by IEEE 802.20.
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Email: dhuo@lucent.com
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1. Introduction
Appendix B of the Evaluation Criteria Document[1] contains some text about the wraparound cellular structure, which fails to provide sufficient information on why and how
the wrap-around is introduced and deployed. This contribution attempts to clarify the
rational and provide new text for it.
The basic simulation assumption for the system level evaluation is the hexagonal
structure of cells, which again consist of cells, each is an area confined by a hexagon. In
abstract term, each cell can be reduced to a node, so that the network topology is given by
a network of nodes and the network takes the shape of a hexagon as shown in Fig.1
Exam ple of Netw ork of Nodes
Fig.1: Hexagonal Network of 2 Tier of Nodes
When mobiles are dropped into this network, they will start to communicate with the base
station that provides it the best radio condition. Due to the frequency reuse, it, however,
frequently occurs that a mobile receiver or base station receiver are interfered with other
mobiles and base stations. Therefore, in the simulation environment given by the hexagon
of finite nodes, the statistic condition with regard to the interference is not equivalent for
all cells. This is different to the case where a network consists of infinite number of cells,
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and where the statistic is the same for every cell, and in every cell it is symmetrical from
all 12 directions. To understand this, we can look into the mathematical structure of the
hexagon. From the group theory, and particularly from its application to the physics, it is
well known that a regular n-sided polygon on a plane can be described by a dihedral
group Dn and it has 2n elements. In particular, the hexagon is a D6 dihedral group with
2*6 elements, i.e. it possesses 6 rotations and 6 reflections, as shown in Fig.2. In
specifics, this group has 12 elements {r0, r1,r2,r3, r4, r5, s1, s2, s3, v1, v2, v3 }
Figure 2: Symmetries of the Hexagon.
The symmetry means that one would not notice the difference when standing in the
middle of the hexagon, while the hexagon is rotated or reflected accordingly. Therefore,
for a finite set of nodes contained in the network of 2 tiers, only the center cell enjoys
such symmetry. Thus, only in the center cell can we collect data that is statistically
equivalent to a network consisting of infinite cells. As simulation consumes resource, it
is desirable to utilize the drops in the cells others than the center one to speed up the data
collection. Particularly, when studying the reverse link, it is necessary to address mobiles
that are on the boundary between two cells. To account for all these needs of having more
cells be involved into the data collection, the notion of wrap-around is introduced. The
concept can be best described as a displacement of the hexagon along the three rotation
symmetrical axis. The distance of the displacement is determined by the size of the
hexagon in terms of the nodes, a quantity equivalent to the re-use factor in TDMA
network planning. It can be determined as the coordinates in the skewed Cartesian
coordination system, where the two axis are 60 degree to each other instead of
orthogonal, see Fig.3.
3
J
I
Figure 3: Skewed Cartesian Coordination System and the Displacement, where unit of I
an J is normalized by the inter-call distance.
For a network of 2 tiers, the point of a displacement is found in this coordination system
to be I=3, J=2, as shown in Fig.3. The first copy of the center hexagon can be therefore
generated by
H1=H+(I,J),
where H denotes the hexagon of 2 tiers of nodes given in Fig.1. To avoid having to
determine the coordinates for all copies, we can rotate H1 by the 6 rotations pertaining to
the dihedral group D6. The result is a cluster of hexagons as shown in Fig.4, where the
center hexagon is H surrounded by 6 copies H1, H2, H3, H4, H5 and H6.
Each node within Hi, (i=1,2,…,6) can be associated to a cell in H uniquely, so that a
mobile dropped in H experiences a boundless but finite cellular network. The symmetries
in all nodes are identical and one can collect data from all sectors, as they are identical in
terms of symmetry.
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Cluster of Hexagons
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2
Copies
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-8
-6
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Original
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Figure 4: Displaced 2-tier hexagons and the original center hexagon
2. Proposal
Having explained the rational and construction of the wrap-around cellular network, we
propose the following text for that section in [1], replacing the current text.
===============================================================
Proposed New Text for Appendix B of the Evaluation Criteria Document
===============================================================
Appendix B: 19 Cell Wrap-Around Implementation.
In order to allow for data collection in all cells within the hexagonal network, it is
necessary to extend the network to a cluster of network consisting of 7 copies of the
original hexagonal network, with the original hexagonal network in the middle while the
other 6 copies are attached to it symmetrically on 6 sides, as shown in Fig.10. The
cluster can be thought of as 6 displacements of the original hexagon. There is a one-toone mapping between cells/sectors of the center hexagon and cells/sectors of each copy,
5
so that every cell in the extended network is identified with one of the cells in the central
(original) hexagonal network. Those corresponding cells have thus the same antenna
configuration, traffic, fading etc. except the location. The correspondence of those
cells/sectors is illustrated in Fig.10.
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Figure 10: An example of wrap-around hexagonal network of sectorized cells
with the antenna orientations for each sector; the arrows in the Figure show the
direction of the antenna.
3.Reference
[1] IEEE802.20 Evaluation Criteria Document
6
