# Interference Avoidance Using TDMA-Beamforming in Location Aware Small Cell Systems
## 2 System Modelling and Problem Formulation  
Crucial challenges and limitations in terms of the practicality of any simulation-based wireless communication system, need to be addressed especially channel and network representations. Here, the realisation of the channel and the annotations used in this simulation are introduced. As highlighted earlier, indoor facilities are expected to embrace the greatest portion of data exchange since higher frequencies are assumed to be effective within indoor capacities. Therefore, all simulation parameters including channel modelling parameters are tailored with respect to line-of-sight indoor environments.  
In this paper, the set of small cells is denoted by \(\mathcal{S}\) whereby each small cell is assigned \(\mathcal{K}\) subchannels. The set of users associated to each small cell is denoted by \(\mathcal{U}\). Moreover, \(\mathcal{P}^{-}\) and \(\mathcal{P}^{+}\) describe the maximum transmission power and the received power of each small cell, respectively. Without loss of generality, the necessary assumptions used in this paper are described below:  
* Small scale fading (Rayleigh fading) is represented by the instantaneous received signal strength, which varies frequently in response to the separation between the transmitter and receiver. This is theoretically modelled using zeros-mean exponential distribution with unity deviation. However, for more practical analysis, [PERSON]'s model [27] can be taken into account because it considers multipath, subchannel frequency, and the user speed.
* The service area (single indoor facility) is virtually controlled by small cell management system (ScMS) that is later connected to the LTE core network through the packets gateway (P-GW) [28].
* The network bandwidth \(\mathcal{B}=20\) MHz.
* The locations of small cells and users are entirely random (random distribution) in the simulation. However, once the locations of the small cells are generated, they remain unchanged until the iteration cycle completes. It later changes when the number of users is changed. Moreover, all locations and angles are assumed to be known to the ScMS.  
Other simulation parameters are described in Table 1.  
Signal propagation in the given scenario is dominated by line-of-sight path whereby any other reflected, scattered, or refracted signals are entirely neglected. Therefore, the channel gain \(g_{\kappa\mu}\) between small cell and a user that are separated by a distance \(d_{\mu\mu}\) is obtained by the following [31]:  
\[g_{\kappa\mu}=-[\mathcal{P}^{\mathcal{L}}_{\kappa\mu}+\mathcal{L}^{\mathcal{H} }_{\kappa\mu}+\mathcal{L}^{F}_{\kappa\mu}] \tag{1}\]  
whereby \(\mathcal{P}^{\mathcal{L}}_{\kappa\mu}\) is the pathloss that is calculated by \(127+30 log_{10}d_{\mu\mu}\)[31], \(\mathcal{P}^{\mathcal{H}}_{\kappa\mu}\) is the shadowing loss, and \(\mathcal{P}^{\mathcal{F}}_{\kappa\mu}\) is the fading loss. It is also important to state that noise is Gaussian [31] whereby it equals to:  
\[\mathcal{N}=\mathcal{N}_{0}\times\mathcal{N}_{d}\times\mathcal{B}^{-} \tag{2}\]  
\(\mathcal{N}_{0}\) is the noise factor \(\approx\)2.5, \(\mathcal{N}_{d}\) is the noise spectral density \(\approx\)\(-\)174 dBm/Hz, and \(\mathcal{B}^{-}\) is the subchannel bandwidth \(\approx\)180 kHz.  
Additionally, the simulation of the array antenna with respect to the parameters of Table 1 gives a beamwidth of \(40^{\circ}\) in which the main lobe is directed towards the desired user at a specific angle. The antenna polar beam pattern is presented in Figure 1.