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 networks these cells are often assumed to be hexagonal. 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. Clustering patterns and the corresponding frequency bands are re-used in a regular fashion over the entire service area.

In Long-Term Evolution(LTE), the smallest radio resource that can be allocated to a user is one RB (Resource Block) which is consisting of 12 subcarriers of 15kHz each. Therefore, the RB bandwidth is equal to 180kHz. In downlink, considering that each user is allocated one RB and the carrier frequnecy 2.6GHz, the Signal to Interference plus Noise Ratio $SINR_k^c$ of each user k on RB c can be computed as follows:

$SINR_{k}^c$ = $\frac{P_{Tx}\cdot PL(r_k)\cdot G_{Tx}(\theta_k)\cdot G_{Rx}\cdot \alpha_{sh}}{I+N}$

where: Antenna transmission power = $P_{Tx}$ [dBm]

pathloss = $PL(r_k)$ = $10\cdot \log_{10}(\frac{\lambda}{4\cdot \pi\cdot r_k})^\gamma$ [$\gamma$=2 corresponds to free space]

Antenna Gain = $G_{Tx}(\theta_k)$ =$G_{Rx}$= 1

For a 3-sector cell, $G_{Tx}(\theta_k)$ = $-min[12(\frac{\theta_k}{\theta_{3dB}})^2,A_m];$ where $\theta_k$ is angle w.r.t main Antenna Lobe,3-dB beamwidth $\theta_{3dB}$=70$^{\circ}$, Front-to-back power ration $A_m$=20 dB;

shadow fading = $\alpha_{sh}$

Interference= $I$ = $\sum\limits_{i=1}^{N_{BS}} P_{Tx,i}\cdot PL(r_i)\cdot G_{Tx}(\theta_i)\cdot G_{Rx}\cdot \alpha_{sh}$; where $N_{BS}$ is the number of interfering base stations and $P_{Tx,i}$ is the radiated power per base station using the same frequency band.

Noise = N = $K(boltzmann constant) \cdot T \cdot Bandwidth$ = -121.42 dBm