Algorithm 1 Proposed MGF-NOMA and SGF-NOMA

1:Input:$\mathcal{R}$, $\mathrm{O}\in \left\{\mathrm{MS},\mathrm{MM}\right\}$, $\mathrm{D}\in \left\{\mathrm{UL},\mathrm{DL}\right\}$ 2:$\mathfrak{s}\leftarrow$Obtain SRS from UEs 3:$\mathcal{U}\leftarrow$Determine active set of UEs 4:$N\leftarrow ⌈\frac{U}{R}⌉$                          // Determine maximum cluster size 5:$C\leftarrow R$                             // Determine number of clusters 6:if D=UL then 7:    $\mathcal{I}\leftarrow$SortDescend(${\mathfrak{s}}_u,\forall u$)                        // UE ordering for UL 8:else 9:    $\mathcal{I}\leftarrow$SortAscend(${\mathfrak{s}}_u,\forall u$)                        // UE ordering for DL 10:end if 11:${\mathcal{U}}_n\leftarrow \mathcal{I}\{(n-1)R+1:nR\},n\in [1,N]$                  // Form UE partitions 12:${\mathcal{C}}_r\leftarrow {\mathcal{U}}_1\left\{r\right\},\forall r$                              // Initialize clusters 13:for n=1:N-1 do                          // Iterative UE admission starts 14:    ${\mathcal{A}}_n\leftarrow {\bigcup }_{i=n+1}^N{\mathcal{U}}_n$                      // Initialize admission awaiting UEs 15:    ${\mathit{Q}}_n\leftarrow$EvalCostMatrix($\mathfrak{p},{\mathcal{C}}_r,{\mathcal{A}}_n$) 16:    if O=MS then                         // Max–Sum Rate Assignment 17:        ${\mathfrak{f}}_r,\chi \leftarrow$Linear Sum Assignment(${\mathit{Q}}_n$) 18:    else if O=MM then                        // Max–Min Rate Assignment 19:        ${\mathfrak{f}}_r,\chi \leftarrow$Linear Bottleneck Assignment(${\mathit{Q}}_n$) 20:    end if 21:    ${\mathcal{C}}_r\leftarrow {\mathcal{C}}_r\bigcup {\mathcal{A}}_n\left\{j\right\},\chi [r,j]=1,\forall r,\forall j$                    // Update clusters 22:end for 23:${\mathcal{l}}_r\leftarrow \mathcal{L}(C_r+1),\forall r$                          // Update cluster levels 24:${\omega }_r\leftarrow \mathcal{W}(C_r+1),\forall r$                         // Update cluster weights 25:UE${}_j\leftarrow (r,{\mathcal{l}}_r\left[j\right]),{\mathrm{UE}}_j\in {\mathcal{C}}_r,\forall j,\forall r$                      // Send RARs out 26:return ${\mathfrak{f}}_r$, ${\mathcal{C}}_r$, ${\mathcal{l}}_r$, ${\omega }_r$ 27:procedure EvalCostMatrix($\mathfrak{p},{\mathcal{C}}_r,{\mathcal{A}}_n$) 28:    for i=1:R do 29:        for j=1:$A_n$ do 30:           ${\mathcal{T}}_r\leftarrow {\mathcal{C}}_r\bigcup {\mathcal{A}}_n\left\{j\right\}$                       // Admit $j^{th}$ UE of ${\mathcal{A}}_n$ to ${\mathcal{C}}_r$ 31:           if D=UL then 32:               $\mathcal{l}\leftarrow \mathcal{L}(n+1)$                        // power levels as per (7) 33:               if O=MS then 34:                   ${\mathit{Q}}_n[i,j]\leftarrow {\sum }_{k\in {\mathcal{T}}_r}B{log}_2(1+{\gamma }_r^k\left(\mathcal{l}\right))$ 35:               else if O=MM then 36:                   ${\mathit{Q}}_n[i,j]\leftarrow \underset{k\in {\mathcal{T}}_r}{min}\left\{B{log}_2(1+{\gamma }_r^k\left(\mathcal{l}\right))\right\}$ 37:               end if 38:           else if D=DL then 39:               $\omega \leftarrow \mathcal{W}(n+1)$                       // power weights as per (9) 40:               if O=MS then 41:                   ${\mathit{Q}}_n[i,j]\leftarrow {\sum }_{k\in {\mathcal{T}}_r}B{log}_2(1+{\gamma }_r^k\left(\omega \right))$ 42:               else if O=MM then 43:                   ${\mathit{Q}}_n[i,j]\leftarrow \underset{k\in {\mathcal{T}}_r}{min}\left\{B{log}_2(1+{\gamma }_r^k\left(\omega \right))\right\}$ 44:               end if 45:           end if 46:        end for 47:    end for 48:return ${\mathit{Q}}_n$ 49:end procedure 50:procedure Linear Sum Assignment(${\mathit{Q}}_n$) 51:    $\stackrel{}{\chi }\leftarrow \underset{\chi }{max}{\sum }_{\forall i,\forall j}{\mathit{Q}}_n[i,j]\chi [i,j]$ 52:           $\mathrm{s}.\mathrm{t}.{\sum }_i\chi [i,j]\le 1,{\sum }_j\chi [i,j]=1$ 53:return $\stackrel{}{\chi }$ 54:end procedure 55:procedureLinear Bottleneck Assignment(${\mathit{Q}}_n$) 56:    $\stackrel{}{\chi }\leftarrow \underset{\chi }{max}\left\{\underset{\forall i,\forall j}{min}\left\{{\mathit{Q}}_n[i,j]\chi [i,j]\right\}\right\}$ 57:           $\mathrm{s}.\mathrm{t}.{\sum }_i\chi [i,j]\le 1,{\sum }_j\chi [i,j]=1$ 58:return $\stackrel{}{\chi }$ 59:end procedure