# Interference Avoidance Using TDMA-Beamforming in Location Aware Small Cell Systems
## 2 System Modelling and Problem Formulation
### Evaluation Metrics
At the ScMS, the base station transmission can now be described in terms of time and angle whereby the transmission of small cell \(s\) is set with respect to Table 2. Note that in Table 2 subchannels are considered in the transmission whereby the transmission is said to be in the downlink only i.e., only the small cells are instructed to adjust the transmission. For two interfering small cells \(s\) and \(i\), and after \(\tau_{su}\) is set according to Equation (8), \(\beta_{iu}\) is updated if user \(u\) is not receiving small cell \(s\) i.e., no interference. This is shown in Algorithm 2. It can now be claimed that the maximum \(SINR_{s}\) is obtained if \(\sum_{i\in\mathcal{S}/\{s\}}\beta_{iu}=0\). However, enhancements can be obtained if \(\beta_{iu}\) is minimised. Therefore, the \(SINR_{s}\) in Equation (3) can now be obtained by the following:  
\[\begin{split}\arg\max& SINR_{\mathcal{S}}\\ &=\sum_{u\in\mathcal{U}}\sum_{\xi\in\mathcal{K}}\frac{\mathcal{P} ^{+}_{s\xi\xi}\beta_{s\xi}\times\beta_  
coverage and mobility. Therefore, the SCon/off-DS scheme achieves downlink interference avoidance, and mitigation at the macrocell and the small cells, respectively. The LASO scheme improves the throughput by adjusting the power offset in downlink transmission by effectively locating the users. The authors have categorised the coverage area into two categories, namely: the non-dominantly interfered region (NDIR), and the interfered region (IR). The users in the NDIR experience high SINR, whereby the users in the IR experience low SINR. Additionally, beamforming scheme without TDMA technique is referred to as PI-beamforming, the proposed algorithm is referred to as SI-beamforming. Subsequently, the fairness of the beamforming schemes is later compared with baseline (BL) scheme in which interference is assumed to be zero i.e., the best performance, which is used to assess the feasibility and reliability of the proposed algorithm. Simulation results presented in this section are in-line with the assumptions of \(\mathcal{U}=\)[10-100] users, 20 MHz bandwidth, \(B^{-}=180\) kHz, service area \(=100\) m \(\times\) 100 m, and 100 iterations. The user throughput performance is illustrated in Figure 2a. Although the throughput achieved by the SCon/off-DS and the LASO in NDIR is relatively high when there are 10 users, the number quickly degrades as the number of users increase. However, both the PI-beamforming and the SI-beamforming schemes maintain a throughput level of approximately 16 Mbps and 18 Mbps, respectively. This is because the beams are effectively redirected towards the desired users only. Thus, reduces the interference to other users. This is evidenced by the SINR levels shown in Figure 2b whereby the superiority of the beamforming schemes is clear. This shows how significantly can the beamforming schemes reduce the interference in comparison to the other schemes. However, interference can still occur when the number of users increase due to the proximity of users. Figure 3 shows the fairness level obtained by the SI-beamforming. It is noteworthy to mention that the fairness results are compared to the BL scheme because the fairness was not evaluated in [29]. Nevertheless, the SI-beamforming is able to perform better than the PI-beamforming because narrower beamwidth and TDMA leads to less interference. Therefore, the SI-beamforming is able to achieve about 95% fairness levels for 100 users. The overall performance of the SI-beamforming promotes it as an efficient interference mitigation paradigm for future communication systems where the number of base stations is expected to increase. Figure 2: Throughput and SINR comparison when increasing the number of users in the service area for all schemes.