• In communication system, Frequency reuse or frequency planning is a method of reusing frequencies and channels to improve the capacity and spectral efficiency. It is one of the basic concepts that involve the parting of an RF radiating area into cells. It means that frequency allocated the service are reused in a regular pattern of cells where each covered by one base station.
• The repeating well-ordered pattern of cells is called cluster. There are several cells that use the same set of frequencies. These calls are called co-channel cells and the interference between signals from these cells is called co-channel interference. As we know, Interference is the limiting factor in the presentation of cellular systems. This interference can happen from encounter with another mobile in the same cell or because of a call in the adjacent cell.
• The interference can be divide into two parts that are co-channel interference and adjacent channel interference. To reduce these intrusion in co-channel cells must be physically separated by a minimum distance to provide sufficient isolation due to propagation. When the size of each cell is roughly same then the co-channel interference ratio (Q) is independent of the transmitted power and becomes a function of radius of the cell (R) and the distance between centers of the nearest co-channel cells (D).
• As we know that the co-channel reuse ratio (Q) is also associated to the cluster size (N).

$\large{Q= \dfrac{D}{ R} = {\sqrt{3N}}} \cdots\mathrm{(Equation \ 1)} $

• As we know, cluster size N equals to

$\large{N= {{i^2} + ij+ {j^2}}} \cdots\mathrm{(Equation \ 2)}$

Where i and j are the non-negative integers which are used to find nearest co-channel neighbours of a particular cell and also help to find out the co-channel reuse ratio as shown in below table.

• A small value of Q furnishes larger capacity since the cluster size, N is small. Whereas a large value of Q improves the transmission quality, due to the smaller level of co-channel interference. As we know, path loss exponent (n) typically ranges between 2 to 4 in urban cellular systems. When transmit power of each base station is equal and the path loss exponent is same all over the coverage area, then signal to interference (S/I) for mobile can be roughly as,

      $\large\dfrac{S}{I}=\dfrac{S}{\Sigma_{i=1}{i=0} {I_i}} \cdots\mathrm{(Equation \ 3)}$        

Where S is the desired signal power from the desired base station and $I_i $ is the interference power caused by the ith  interfering co-channel cell base station. If the signal levels of co-channel cells are known, then S/I ratio for the forward link can be discovered using equation 3.

 When the transmit power of each base station is equal and the path loss exponent is the same all over the coverage area.

S/I for a mobile can be roughly as

   $\large\dfrac{S}{I}=\dfrac{R^{-n}}{\Sigma_{i=1}{i=0} {D_i^{-n}}}\cdots\mathrm{(Equation \ 4)}$   

• Observing only first layer of interfering cells, if all the interfering base stations are at the same distance from the desired base station and if this distance is equal to the distance D between cell centers, then equation 4 simplifies to

      $\large\dfrac{S}{I}=\dfrac{{\dfrac{D}{R}}^n}{i_0} = \cdots\mathrm{(Equation \ 5)}$ 

using equation 1, it becomes

$\large\dfrac{S}{I}=\dfrac{{\sqrt{3}{N}}^n}{i_0} = \cdots\mathrm{(Equation \ 6)}$

Here,  $i_0$ be no .of co-channel interfering cells.

Therefore, equation 6 relates the S/I to the cluster size (N), which in turn decides the overall capacity of the system.