# Joint User-Slice Pairing and Association Framework Based on H-NOMA in RAN Slicing
### Organization
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Notions** & **Definitions** & **Notions** & **Definitions** \\ \hline \(\mathcal{B}\) & Set of base stations & \(R_{\text{tr}}^{\text{min}}\) & Minimum DL required data rate for \(u\in U\) \\ \(\mathcal{L}\) & Set of uRLLC users & \(T_{\text{tr}}^{\text{max}}\) & Maximum DL tolerant delay on the system for \(l\in\mathcal{L}\) \\ \(E\) & Set of dMBB users & \(\mathcal{I}_{l}(t)\) & payload size for \(l\in\mathcal{L}\) \\ \(U\) & Set of eMBB and uRLLC users & \(\mathcal{A}_{l}\) & Arrival rate for \(l\in\mathcal{L}\) \\ \(\mathscr{M}\) & Number of mini slots in long TTI & \(\mathcal{C}_{ll}\) & Block-length code for \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(\mathcal{S}^{\prime}\) & Duration of a RAN time slot & \(\varepsilon\) & uRLLC reliability probability \\ \(\delta\) & Duration of a RAN mini slot & \(\mathcal{V}_{l}^{\text{min}}\) & Channel dispersion for \\ \(\delta\) & Set of slices per BS & \(T_{\text{bl}}^{\text{WBH}}\) & \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(l_{s}\) & Set of users in each slice s \(\in\delta\), BS \(b\in\mathbf{B}\) & \(T_{\text{bl}}^{\text{RAN}}\) & RAN mean transmission packet delay for \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(N_{l}^{\text{s}}\) & Set of virtual PRBs per BS’s slice \(s\in\delta\), \(b\in\mathbf{B}\) & SINR\({}_{\text{1B}}\) & Received SINR for a SBS from MBS \(b\in\mathbf{B}\), \(b\
eq 1\) \\ \(\alpha_{l}^{\text{min}}\) & Binary UE-slice association matrix & \(\eta_{\text{1B}}\) & Channel gain between MBS and SBS \(b\
eq 1\) \\ \(a_{\text{tr}}^{\text{min}}\) & Power allocation coefficient for \(u\in U\), \(b\in\mathbf{B}\) & \(\sigma^{2}\) & Noise power \\ \(\alpha_{\text{tr}}^{\text{max}}\) & Association decision variable, for & & \\ \(u\in U\), \(b\in\mathbf{B},n\in N_{b}^{\text{s}},m\in\mathscr{M}\) & \(SINR^{TH}\) & Threshold SINR of WBH network \\ \(\mathcal{X}^{U}\) & Binary Superposition matrix by H-NOMA & \(br_{\text{lu}}\) & Number of bits for a single successful WBH \\ \(x_{\text{tr}}^{\text{min}}\) & Superposition variable for \(l\in\mathcal{L}\), \(e\in\mathbb{E}\) on \(n\in N_{b}^{\text{s}},m\in\mathscr{M}\) & \(\tau^{\text{WBH}}\) & WBH time slot \\ \(\delta_{\text{lu}}^{\text{min}}\) & Integer number of mini slots for \(u\in U\), \(b\in\mathbf{B}\) & \(W^{\text{WBH}}\) & Bandwidth of the backhaul network \\ \(y_{\text{tr}}^{\text{min}}\) & Received signal by user \(u\in U\) from BS \(b\in\mathbf{B}\) & \(\sigma_{ll}\) & WBH required number of time slots \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(\mathcal{S}_{ab}^{\text{tr}}\) & & & \\ \(\mathcal{S}_{ab}^{\text{tr}}\) & Reserved rate for \(u\in\delta\), \(b\in\mathbf{B}\) & \(\mu_{r}\)\({}^{\text{WBH}}\) & WBH Transmission success probability of one packet in a single transmission \\ \(\Gamma_{\text{lu}}^{\text{trtr}}\) & Received SINR for UE \(u\in U\) from BS \(b\in\mathbf{B}\) & \(\sigma\) & Pathloss exponent of WBH link \\ \(\alpha_{l}^{\text{min}}\) & Bandwidth of PRB in \(N_{l}^{\text{s}}\) per \(m\in\mathcal{M}\) & \(T_{ll}^{\text{tr}}\) & RAN transmission time \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(r_{\text{lu}}^{\text{min}}\) & Data rate for UE \(u\in U\) from BS \(b\in\mathbf{B}\) on \(n\in N_{b}^{\text{s}}\), per & Number of paired mini slots for \(l\in\mathcal{L}\) with \(e\in\mathbb{E}\) \\ \(m\in\mathscr{M}\) & & & \\ \(R_{\text{lu}}\) & Overall DL received rate for \(u\in U\) from BS \(b\in\mathbf{B}\) & \(D_{l}\) & maximum threshold RAN’s packet delay \\ \(\Omega_{\text{lu}}^{\text{min}}\) & PRBs allocation decision variable, for & & \\ \(u\in U\), \(b\in\mathbf{B},m\in\mathscr{M}\) & \(T_{ll}^{\text{RTT}}\) & HARQ retransmission delay \(l\in\mathcal{L}\), \(b\in\mathbf{B}\) \\ \(\gamma_{\text{lu}}^{\text{min}}\) & Number of allocated PRBs for \(u\in U\), \(b\in\mathbf{B},m\in\mathscr{M}\) & \(T_{ll}^{\text{WT}}\) \\ \(f_{\text{lu}}^{\text{min}}\) & Number of minimum required PRBs for & & \\ \(u\in U\), \(b\in\mathbf{B},m\in\mathscr{M}\) & \(T_{ll}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation List.