Why the cell structure is used as hexogonal shape in mobile communication?
Answer:
In the cellular concept, frequencies allocated to the service are re-used in a regular pattern of areas, called 'cells', each covered by one base station. In mobile-telephone nets these cells are usually hexagonal. In radio broadcasting, a similar concept has been developed based on rhombic cells.
To ensure that the mutual interference between users remains below a harmful level, adjacent cells use different frequencies. In fact, a set of C different frequencies {f1, ..., fC} are used for each cluster of C adjacent cells. Cluster patterns and the corresponding frequencies are re-used in a regular pattern over the entire service area.
In real mobile phone systems, the cells are not hexagonal, because of wide variations in terrain and demand. However, assume a simple system in which all the cells are the same size and all the base stations have the same power and are evenly spaced.
Since each base station antenna is omnidirectional, its polar diagram is a circle. And since we want the entire area to be covered with a minimum signal level, these circles must overlap, or there would be small areas (triangles with curved sides) where signal was below the minimum required.
It's a simple geometric fact that if you take a lot of overlapping, identical, evenly spaced circles and join the points where they meet, you get a grid of hexagons. These can then be used to define the theoretical coverage of each base station for purposes of frequency allocation.
You could define other shaped cells, but the closest approach to uniform coverage comes from overlapping circles and the resulting hexagons.
Although, as I say, it's much more complicated in reality.
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