# Joint User-Slice Pairing and Association Framework Based on H-NOMA in RAN Slicing
## 2 System Model
### Signalling Model  
Two types of interferences should be considered in the proposed multi-cell H-NOMA system. Firstly, the inter-BS interference is generated by the signals transmitted from the un-associated BSs. Secondly, the intra-BS interference is produced by the co-channel interference of H-NOMA schemes. In any coalition, the received signal at user \(u\) is shown as follows [33; 34] in Figure 3:  
\[y_{tu}^{mm}=\underbrace{\sum_{h\in\mathrm{B}\setminus\{b\}}\sum_{\hat{u}\in\{k +1,\ldots,U\}\setminus\{u\}}\sqrt{a_{hu}^{mm}\;\;p_{b}^{m}\;\hat{p}_{hu}^{mm} \;x_{uu}^{mm}\;x_{uu}^{mm}}}_{\text{inter-BS interference}}+\underbrace{\sum_{b \in\mathrm{B}}\sum_{u\in U}\sqrt{(1-a_{bu}^{mm})\;p_{b}^{m}\;\hat{p}_{ku}^{mm} \;x_{uu}^{mm}}}_{\text{(Unnamed Spati- Remove using SC)}}^{\text{intra-BS interference}}+\underbrace{\sqrt{a_{hu}^{mm}\;p_{b}^{m}\;\hat{p}_{hu}^{mm}\;x_{uu}^{mm} \;x_{uu}^{mm}}}_{\text{(Unnamed Spati- Remove using SC)}}^{\text{intra-BS interference}}+\underbrace{\sqrt{a_{hu}^{mm}\;p_{b}^{m}\;\hat{p}_{hu}^{mm}\;x_{uu}^{mm} \;x_{uu}^{mm}}}_{\text{Wanted Signal}}^{\text{intra-BS interference}}+o^{2} \tag{3}\]  
where \(\mathrm{B}\setminus\{b\}\) is the collection of interfering nodes that utilise the same frequency channel, \(r_{bu}^{mm}\) the signal transmitted from the BS to the \(u\) UE, \(a_{bu}^{mm}\in[0,1]\) denotes the power allocation coefficient for the UE \(u\) associated with BS \(b\) on PRB \(n\); \(P_{b}^{n}\) denotes the transmit power of BS \(b\) over PRB \(n\) to UE \(u\); \(\mathcal{G}_{bu}^{nm}\) represents the channel gain between BS \(b\) and UE \(u\) at mini slot \(m\) and \((1-a_{bu}^{mm})\;P_{b}^{n}\;\mathcal{G}_{bu}^{nm}\) denote the received interference from the coexisting another user. Moreover, let \(\mathcal{G}_{u}=(\mathcal{G}_{1u},\mathcal{G}_{2u},\ \ldots,\ \mathcal{G}_{\mathrm{B}u})\in G\) with the perfect CSI. \(o^{2}\) is the additive noise power.  
When H-NOMA is applied, each PRB can mostly serve two different services UEs. Implementing H-NOMA brings more sophisticated co-channel interferences (CCI) to the existing networks; to optimize the main problem without CCI employing perfect SIC, both eMBB and uRLLC UEs receive the superimposed signal, and each UE executes SIC to decode its message [46]. We assume the stronger user is a uRLLC UE which only can decode and remove CCI from the weak user is eMBB UE. While the eMBB UE with weaker channel conditions cannot wholly eliminate the interference of uRLLC UEs' signals, which results in maximized throughput for the eMBB UE with contrast [40] and prove it with the results in Section 5 Because our approach is based on uRLLC UE is superimposed with eMBB UE through a few mini slots and assigned high power for eMBB UE to reduce the latency by providing a high rate to the paired uRLLC UEs at a mini slot and achieving high reliability. Thus, the effect of CCI on eMBB UE is less than if the conventional pairing is along a TTI.  
As well as, to guarantee inter-slice interference isolation between slices and ensure the QoS for each UE-slice according to H-NOMA technology, we assume \(\mathcal{A}_{sb}^{PN}\) is the reserved rate for each slice \(s\in\mathcal{S}=\{1,\ 2\}\) in each BS [47; 48]. The total rate of the cell is denoted as \(\mathcal{A}_{b}^{PN}\)=\(\mathcal{A}_{1b}^{PN}\)+ \(\mathcal{A}_{2b}^{PN}\); based on the average downlink physical data rate of LTE system is achieved by [49].  
Under the superposition scheme, the SINR \(\Gamma_{bu}^{mm}\) is received by the UE \(u\in U\) from a BS \(b\in\) B on a PRB \(n\in N_{b}^{s}\) per mini slot \(m\in\mathcal{M}\) as, can be as follows  
\[\Gamma_{bu}^{mm}=\frac{\alpha_{bu}^{mm}\ P_{b}^{n}\ g_{bu}^{mm}}{(1-\alpha_{bu}^{ mm})\ P_{b}^{n}\ g_{bu}^{mm}+\sum_{h\in\mathds{B}\left\{b\right\}}\alpha_{hu}^{ mm}\ P_{hu}^{n}\ g_{hu}^{mm}+\varrho^{2}}, \tag{4}\]