## 2 System Model and Problem Formulation
### User Clustering Problem Formulation  
To ensure that the SIC operation can be implemented successfully at the users' receivers, the power used by the BS for the downlink transmission requires a careful allocation. The SIC condition for power allocation for cluster \(i\) can be expressed as:  
\[G\ \ {{}_{n-1,m}}\left({{p_{n,m}}-\sum\limits_{i=1}^{N-1}{{p_{i,m}}}}\right)\geq{ {p_{SIC}}},\ n=2,\ 3,\ \ldots,\ N,\ \forall m\in\mathcal{M}_{i} \tag{7}\]  
where \({p_{SIC}}\) is the minimum power difference necessitated by a user \(n\) to distinguish between the intended decodable signal and unwanted nondecodable signals from superposed signals sent by the BS. Let the user clustering indicator set of a user \(n\) be \(\theta_{n}=\left\{{\theta_{n,m}^{1},\theta_{n,m}^{2},\ldots,\theta_{n,m}^{C}} \right\}\), \(\forall m\in\mathcal{M}\) where \(\theta_{n,m}^{i}\) is the clustering Boolean variable such that \(\theta_{n,m}^{i}=1\) if a user n is grouped into a cluster i sharing a subcarrier \(m\), otherwise \(\theta_{n,m}^{i}=0\). Concretely, the K-user clustering indicator set can be denoted as \(\theta=\left\{{\theta_{1},\theta_{2},\ldots,\theta_{Q}}\right\}\). The power allocation strategy for the BS to all users can be represented by the power allocation vector \(P=\left\{{{p_{1,m}},{p_{2,m}},\ldots,{p_{K,m}}}\right\}\), \(\forall m\in\mathcal{M}\). By optimally selecting the clustering and power allocation strategies, the sum throughput of the NOMA system can be maximized subject to various constraints. The throughput maximization problem is formulated as  
\[\max\limits_{\theta,\ P}\sum\limits_{i=1}^{C}{\sum\limits_{n=1}^{N}{\sum \limits_{m=1}^{M}{\theta_{n,m}^{i}Blog_{2}}}}{\left[{1+\frac{{{p_{n,m}}G_{n,m} }}{{{\sum\
olimits_{q=1}^{n-1}{{p_{q,m}}G_{q,m}}+1}}}}\right]} \tag{8a}\] \begin{table}
\begin{tabular}{c l} \hline \hline
**Notations** & **Description** \\ \hline \(B_{K}\) & Bell number to partition \(K\) number of users \\ \(N\) & Cluster size \\ \(U\) & User set \\ \(i\) & Cluster index \\ \(C\) & Total of cluster number formed \\ \({p_{min}}\) & Minimum power difference \\ \({p_{c}}\) & Maximum downlink transmission power for a cluster \\ A & Minimum power variance required to perform SIC \\ \({y_{n,m}}\) & Received signal at \({U_{n,m}}\) \\ \({x_{n,m}}\) & Transmitted signal from the BS to \({U_{n,m}}\) \\ \({\gamma_{n,m}}\) & Signal-to-interference-plus-noise ratio (SINR) for \({U_{n,m}}\) \\ \({R_{n,m}}\) & Achievable throughput for \({U_{n,m}}\) \\ \({R_{i}}\) & Achievable throughput for cluster \(i\) \\ \(R\) & Total system throughput \\ \(I\) & Number of input layer nodes \\ \(I\) & Number of hidden layers \\ \(V\) & Number of output layer nodes \\ \(x\) & Input vector of DNN-UC \\ \(z\) & Output vector of DNN-UC \\ \(q\) & Hidden layer index \\ \(N\) & Number of hidden layer nodes \\ \(W^{(t)}\) & Weight matrix that links (\(q\)-1) th layer to the \(q\)-th layer \\ \(f^{q}(\cdot)\) & Activation function for the \(q\)th layer \\ \(b^{q}\) & Bias vector for the \(q\)th layer \\ \(a^{q}\) & Output vector of hidden layer \\ \(z\) & Predicted UC at the output of DNN-UC \\ \(J(\theta)\) & Cost function \\ \(\eta\) & Step size \\ \(S\) & Total number of samples \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._\[\sum_{m=1}^{M}R_{n,m}\geq R_{min},\;\forall n=1,2,\ldots,K \tag{8b}\] \[G_{n-1,m}\Bigg{(}p_{n,m}-\sum_{i=1}^{N-1}p_{i,m}\Bigg{)}\geq p_{SIC},\;n=2,\;3, \;\ldots,\;N,\;\forall m\in\mathcal{M}_{i}\] (8c) \[\sum_{i=1}^{C}\sum_{m=1}^{M}\theta_{n,m}^{i}\leq 1,\;\forall n=1,2,3, \ldots,K \tag{8d}\]  
The maximization in (8) is subject to constraints (8a)-(8d). Constraint (8a) limits the total power allocation to the available power budget at the BS while constraint (8b) ensures all users achieve the minimum required throughput, \(R_{min}\) on their allocated subcarriers. Furthermore, constraint (8c) defines the SIC conditions that must be enforced in every cluster, and constraint (8d) guarantees that one user can be assigned to one cluster only.