## 3 System Model
### Clustered PD-NOMA  
1. _The user will send their respective channel state information (CSI) to the corresponding SBS, and the SBS forms the CSI set 'I', within the threshold value 'T', where T 1._
2. _The SBS finds the channel gain difference based on the correlation between the users linked with the same SBS._
3. _The SBS calculates the distance_ \(d_{j,n}\) _as the channel gain difference between the jth and kth user._ \(I_{j,k}=\left\{d_{j,k}\rightarrow\ \mid\left|\,h_{j}\right|\ -\ \left|\,h_{k}\,\right|\ |\ ;\text{corresponding}\ \left(j,u\right) \rightarrow\ \left(\,\left|\,h_{j},h_{k}\,\right|\,/\left|\,h_{j}\,\right|\,\left|\,h_{ k}\,\right|\,\right)>\rho\right\}\)_, Where '_\(\rho\)_' represents a pre-defined real value (_\(0\leq\rho\leq 1\)_)._
4. _The SBS forms the cluster with users having the maximum channel gain difference. (_\(j,k\)_)* = argmax_ \(\left\{d_{j,k}\right\}\)_,_ \(T\) = \(T\) - \(\left(d_{j,k}\right)\) _until the difference with the nth user is computed._
5. _Among the residual users, users with the most significant channel gain difference will be selected by the SBS, eventually improving system capacity._ \(\forall(j,k)_{n}\) _the users will be evaluated based on the respective channel gain difference._  
The SBSs share the bandwidth '\(W\)' using the OFDMA scheme. Assuming downlink transmission, let \(U_{s}\supset\bigcap\ (U_{H}\cup U_{L})\), where \(U_{s}\) represents the set of all SBS users sharing '\(W\)' under the NOMA scheme, and \(U_{H}\) and \(U_{L}\) represent the categorization of users of HSBS and LSBS, respectively. Let \(S\supset\bigcap\ (S_{H}\cup S_{L})\) denote the set of all SBSs, with \(S_{H}=\left\{1,2,\,\ldots,\,S_{H}\right\}\) as a set of HSBS, and \(S_{L}=\left\{1,2,\,\ldots,\,S_{L}\right\}\) representing the set of LSBS. Consider \(C_{s}\supset\bigcap\ (C_{H}\cup C_{L})\) as the set of sub-channels, where \(C_{H}=\left\{1,\,2,\,\ldots,\,C_{n}\right\}\) and \(C_{L}=\left\{1,2,\,\ldots,\,C_{n}\right\}\) represent the sub-channels assigned to the \(S_{H}\) and \(S_{L}\), respectively. Considering only the small-cell network, each user is connected to either an HSBS or an LSBS, as \(U_{s}\) and \(C_{s}\) represent the set of SBS users linked with the set of sub-channels, respectively. Let \(P_{uc}\) be the power allocated to user \(u\) on sub-channel \(c\), and \(h_{uc}\) be the channel gain between the SBS \(s\) and user \(u\) on sub channel \(c\), where \(P_{uc}>0\). Therefore, the SINR of user \(u\) on sub-channel \(c\) can be given as:  
\[SINR_{uc}=\frac{p_{uc}h_{uc}}{\sum_{i\in U_{s}}\ p_{uc}h_{uc}+No} \tag{1}\]  
where \(i\) represent the interfering signals intended for users belonging to set \(U_{s}\), and \(h_{uc}\) represents the channel gain. If '\(X\)' (where \(X=x_{usc}\)) represents the user association matrix, such that, \(\forall\ s\in S,\,u\in U_{s}\), and \(c\in C_{s}\), then  
\[x_{usc}= \begin{array}{ll}1,&if\ ^{\prime}s^{\prime}\ \text{is transmitted to}\ ^{\prime}u^{\prime}\ \text{over}\ ^{\prime}c^{\prime}\\ 0,&otherwise\end{array}  \tag{2}\]  
The user association '\(X\)' should guarantee that the total number of associated users has increased, and the sub channels are efficiently allocated, as shown in Figure 3. The user interference is managed using the SIC technique at the receiver's side [7; 31]. The optimal decoding in the downlink channel can be attained by organizing users according to the normalized channel gain \(\left|\,h_{usc}\,\right|\,^{2}/\sigma^{2}\), where \(\sigma^{2}\) is the variance of the additive white Gaussian noise (AWGN), and \(\left|\,h_{usc}\,\right|\) is the modulus of channel gain between user '\(u\)' and SBS '\(s\)'. SIC is used for detection and decoding in the accompanying NOMA scheme with a normalized channel gain. NOMA reduces the inter-user interference that occurs when densely deployed BSs and users operate in the same vicinity.