Frequency Reuse Concepts
Introduction:
The band of frequency allocated for cellular system use can be reused with different CLUSTERS. The configuration of cells over which the complete frequency band is divided and this configuration of cells is repeated over and over is called Cluster.
Cluster shapes:

Valid clusters are those that result in 6 cells with the same frequency of a particular cell located at equal distance from it(see figure5.1)
Figure 5.1(Frequency reuse) 
Several cluster shapes with different frequency reuse factors:
· Cell Frequency Reuse Cluster (Frequency Reuse Factor = 1) [Valid]:
· Cell Frequency Reuse Cluster [Invalid]:
· Cell Frequency Reuse Cluster (Frequency Reuse Factor = 1/3) [Valid]:
· Cell Frequency Reuse Cluster (Frequency Reuse Factor = 1/4) [Valid]:
· Cell Frequency Reuse Cluster (Frequency Reuse Factor = 1/5)[Invalid]:
Frequency Allocation Concepts
 Assume that the total frequency band allocated for a cellular system is BHz, and that each halfâ€duplex channel requires W Hz, the number of fullâ€duplex channels S thatthe total band supports (one channel for transmission and one for reception) is
S=B/2W
 Let the total number of fullâ€duplex channels be divided equally among N cells (in an Nâ€Cell Frequencyreuse system). The total number of channels k assigned to each cell becomes
k=S/N
 With a frequency reuse factorFRF given by
FRF=1/N
 The N cell over which the complete frequency band has been divided is called a CLUSTER. If this cluster is repeated M times over the coverage area, this gives a total number of fullâ€duplex channels in the Coverage area C equal to
C=MS=MkN
 The value C is strongly related to the capacity of the cellular system
 A larger C means higher capacity and higher number of calls that can take place at the same time
 A Lower C means lower capacity and lower number of calls that can take place at the same time.
Possible Cluster Sizes
 There are some cluster sizes that if repeated they will be able to cover the complete region. In fact, there following formula give the cluster sizes N that are possible
N=i^{2} ij j^{2}