# Power Optimization in Multi-Tier Heterogeneous Networks Using Genetic Algorithm
## 4 System Model
### SIR Calculation with and without Interference Cancellation Technique  
The cellular user link comprises two stages: the connection from the AP to the RN and the connection from the RN to the CU. In this context, we determine the SINR for the first link between the AP and RN. The received signal at \(R_{i}\) is a combination of the desired signal plus all the interference from the surrounding RNs. \[IRI=\sqrt{\rho_{R_{i}}}P_{R,R}\alpha^{-\frac{7}{2}}\parallel H_{R_{j},R_{i}} \parallel x_{R_{j}} \tag{1}\]  
\[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]  
\[DS=\sqrt{\rho_{AP_{i}}}P_{A,R}\alpha^{-\frac{7}{2}}\parallel H_{AP_{i},R_{i}} \parallel x_{AP_{i}} \tag{3}\]  
\[y_{R_{i}}=DS+RSI+IRI+\eta_{R_{i}} \tag{4}\]  
The first part of the equation represents the desired signal from \(AP_{i}\) plus the noise received at \(R_{i}\); the second part represents the RSI, and the third part represents the inter-relay interference (IRI) from the neighboring relay node \(R_{j}\). Given the received signal, the SINR at \(R_{i}\) is calculatedas  
\[SINR_{R_{i}}=\frac{\rho_{AP_{i}}P_{A,R}\alpha_{i}^{-7}\parallel H_{AP_{i},R_{i }}\parallel^{2}}{I_{R_{i}}+\eta_{R_{i}}} \tag{5}\]  
where \(I_{R_{i}}\) is the total interference at \(R_{i}\), which includes both the RSI and IRI. \[I_{R_{i}}=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}}+ \sqrt{\rho_{R_{j}}}P_{R,R}\alpha^{-\frac{7}{2}}\parallel H_{R_{j},R_{i}} \parallel x_{R_{j}} \tag{6}\]  
For the second hop, from the RN to the CU, the received signal at \(CU_{i}\) is composed of the desired signal from \(R_{i}\) plus the noise received, the relay-to-user interference (RUI)  
Figure 1: Multi-tier heterogeneous network. from \(R_{j}\), the cellular-to-cellular interference (CCI) from \(CU_{j}\), and the cellular-to-device interference (CDI) from \(D_{j}\). The SINR at \(CU_{i}\) is determined from the received signal. \[SINR_{CU_{i}}=\frac{\rho_{R_{i}}P_{R_{C}}h_{i}^{-\gamma}\parallel H_{R_{j},CU_{i }}\parallel^{2}}{I_{CU_{i}}+\eta_{CU_{i}}} \tag{7}\]  
where \(I_{CU_{i}}\) is the total interference at \(CU_{i}\), which encompasses the RUI [34], the CCI, and the CDI [35; 36]. The SINR is calculated as the ratio of the desired signal to the interference from various network elements. The RUI, CDI, and CCI are estimated as  
\[RUI=\sqrt{\rho_{R_{j}}}P_{R_{C}}h^{-\gamma/2}\parallel H_{R_{j},CU_{i}} \parallel x_{R_{j}} \tag{8}\]  
\[CDI=\sum_{y_{j}\in\lambda_{CU}}\sqrt{\rho_{CU_{j}}}P_{C,D}f^{-\gamma/2} \parallel H_{CU_{j}}\text{CU}_{i}\parallel y_{D_{j}} \tag{9}\]  
\[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]0  
\[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]1  
For a given network, The total SINR at \(CU_{i}\) is the cumulative product of the SINR at \(R_{i}\) and \(CU_{i}\) and can be represented as  
\[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]2  
In our network, due to several interferences from nearby devices, the environment is considered to be interference-limited; therefore, noise can be neglected. \[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]3  
\[RSI=\sqrt{\rho_{R_{i}}}\parallel H_{R_{i},R_{i}}\parallel x_{R_{i}} \tag{2}\]4 Block diagram of the SIC technique. where \(I_{TCU_{i}}\) is the combination of all the interferences from the other relay nodes, D2D users, and cellular users. \(H_{o}\) is the combination of \(H_{AP_{i}R_{i}}\) and \(H_{R_{i}CU_{i}}\). The SIR for the interference cancellation technique is estimated by examining its impact on cellular users \(CU_{i}\). The total interference at \(CU_{i}\) includes the summation of the RUI, CCI, and CDI. As the \(k\) strongest equivalent interferers have been canceled, the received SIR at the cellular user can be estimated by comparing it with Equation (13).