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Thread Subject:
Wrap around technique, Hexagon mapping to torus

Subject: Wrap around technique, Hexagon mapping to torus

From: Olw

Date: 9 Aug, 2006 12:15:01

Message: 1 of 3

Hello,

Quite frequently in the analysis of cellular communications (and in
several other fields) a wrap around technique is used, where a set of
hexagonal cells are mapped onto a torus to avoid edge effects.

Is there a chance that somebody in this group has done such simulations
in Matlab and are willing to share some insight and or code?

I guess the number of cells has to be rhombic, i.e. #cells = i^2 + j^2
+i*j where i and j are integers. Then, for such a rhombic number of
cells, how is this implemented in Matlab?

Thanks,

Olw

Subject: Wrap around technique, Hexagon mapping to torus

From: Jeff

Date: 19 Jul, 2010 21:15:22

Message: 2 of 3

Did you figure this out? I am interested int he answer.

sana

"Olw" <anders@kommtek.com> wrote in message <1155150900.715234.253580@h48g2000cwc.googlegroups.com>...
> Hello,
>
> Quite frequently in the analysis of cellular communications (and in
> several other fields) a wrap around technique is used, where a set of
> hexagonal cells are mapped onto a torus to avoid edge effects.
>
> Is there a chance that somebody in this group has done such simulations
> in Matlab and are willing to share some insight and or code?
>
> I guess the number of cells has to be rhombic, i.e. #cells = i^2 + j^2
> +i*j where i and j are integers. Then, for such a rhombic number of
> cells, how is this implemented in Matlab?
>
> Thanks,
>
> Olw
>

Subject: Wrap around technique, Hexagon mapping to torus

From: Andreas Lobinger

Date: 20 Jul, 2010 17:57:13

Message: 3 of 3

Aloha,

On Mon, 19 Jul 2010 21:15:22 +0000, Jeff wrote:
> Did you figure this out? I am interested int he answer.
> "Olw" <anders@kommtek.com> wrote in message
> <1155150900.715234.253580@h48g2000cwc.googlegroups.com>...
>>
>> Quite frequently in the analysis of cellular communications (and in
>> several other fields) a wrap around technique is used, where a set of
>> hexagonal cells are mapped onto a torus to avoid edge effects.
>>
>> Is there a chance that somebody in this group has done such simulations
>> in Matlab and are willing to share some insight and or code?
>>
>> I guess the number of cells has to be rhombic, i.e. #cells = i^2 + j^2
>> +i*j where i and j are integers. Then, for such a rhombic number of
>> cells, how is this implemented in Matlab?

sorry no code, as this resides on another computer.

The insight:
- There are two methods in wrap around that are different
 a) keeping for a testpoint the network around the point (so in a cell-
  ular network, keeping the MS, wrapping the BS
 b) wrapping testpoints, that try 'leave' the network, around, so that
  they reenter the network on the other side

- for both methods you need a setup of the original network grid/layout
 and the positions of copys/mirrors of the network
- for hex cells and added n tiers, the wrap positions would be a hex grid,
 big enough, so that the border cells just touch (so 6 position and the
 original)
- for non-regular networks it's a little bit more complicated...

- for method a) you get all distances from the testpoint to all
(mirrored) BS and choose the shortest one
- for method b) you test if the testpoint plus all wrap positions lie
 inside the network border

Although i work in the communication industry myself and having
colleagues, who implemented a) or b) or both in simulations before,
it had cost me a few week understanding this in detail.

One of the only papers i know with good diagramm for a) is
http://www.ero.dk/F9669EF2-85DD-4F0C-92ED-F1A53D5DF907?frames=no&

Hope that helps.

Wishing a happy day,
LOBI

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