**What is cellular frequency reuse ?**

A group of radio channel is allocated a separate circular base station to be used within a small geographic area called cell.

The design method of selecting and allocating channel groups for all cellular base station within a system called as frequency reuse.

Here we have to use hexagonal geometry is used in the design of cellular system.

we have to better to understand frequency reuse concept in cellular system having S duplex channel then, and if n channel is less than S (n<S) and is S channel are divided among N cell into unique and disjoint channel groups with each having the same number of channels, then the total number of available radio channel is define as :

S = nN

Total number of duplex channel C can be defined as :

C = mnN = mS

The capacity of cellular system is directly proportional to the number of times a cluster repeated in a fixed service area, the factor N is called as the cluster size

For maximum capacity, the smallest possible value of N is desired. 1/N is called as the frequency reuse factor as each cell within the cluster is only assigned 1/N times of the total available channels.

The geometry of hexagon is such that the number of cell per cluster N can have values that satisfy the equation,

N = i

^{2}+ij + j^{2}Where i and j are non negative integer

So here we have to calculate the possible cluster size above this equation :

i=1, j=1 so N=3

i=2, j=0 so N=4

i=2, j=2 so N=12

i=2, j=3 so N=19