# Cross-Layer Optimization for Heterogeneous MU-MIMO/OFDMA Networks
## 6 Conclusions  
In this paper, we propose a cross-layer optimization framework that considers both OFDMA and MU-MIMO for heterogeneous wireless networks. Our model not only assumes that nodes have different capabilities in terms of their bandwidth and numbers of antennas, but also supports practical use cases in which nodes can operate with either OFDMA or MU-MIMO, or with both at the same time. By taking into account the interactions between the key elements of the physical layer to the network layer for multi-hop networks, we formulate the proposed model as a MILP problem, and through MATLAB  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(i\) & \(S_{i}\) & \(B_{i}\) \\ \hline
3 & 1 & 40 \\
4 & 4 & 40 \\
6 & 2 & 40 \\
7 & 3 & 80 \\
9 & 3 & 160 \\
11 & 3 & 20 \\
12 & 1 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Node Configurations for Max–Min Fair Allocation.  
Figure 4: Resource allocation results for (**a**) the sum-rate maximization and (**b**) the max–min fair allocation. The max–min rate optimization achieves better fair resource allocation, at the expense of the sum-rate.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Link**} & \multicolumn{4}{c}{\(t=1\)} & \multicolumn{4}{c}{\(t=2\)} & \multicolumn{4}{c}{\(t=3\)} & \multirow{2}{*}{**Rate**} \\ \cline{2-2} \cline{7-11}  & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** \\ \hline \(12\to 3\) & 1 & 1 & 20(4) & OFDMA & - & - & - & - & 1 & 1 & 20(6) & OFDMA & [1 0 1] \\ \(12\to 6\) & - & - & - & - & 1 & 1 & 20(3) & MIMO & - & - & - & - & - & [0 1 0] \\ \(6\to 3\) & - & - & - & - & - & - & - & - & 1 & 1 & 20(6) & OFDMA & [0 0 1] \\ \(11\to 3\) & 3 & 1 & 20(5) & OFDMA & - & - & - & - & - & - & - & - & [0 1 0] \\ \(3\to 9\) & - & - & - & - & 3 & 1 & 20(7) & MIMO & - & - & - & - & [0 1 0] \\ \hline \hline \end{tabular}
\end{table}
Table 7: Resource Allocation Result for the Sum-rate Maximization.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Link**} & \multicolumn{4}{c}{\(t=1\)} & \multicolumn{4}{c}{\(t=2\)} & \multicolumn{4}{c}{\(t=3\)} & \multirow{2}{*}{**Rate**} \\ \cline{2-2} \cline{7-11}  & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** & \(f\) & \(s_{tf}\) & \(b_{tf}(k)\) & **Mode** \\ \hline \(12\to 6\) & - & - & - & - & - & - & - & - & 1 & 1 & 20(5) & OFDMA & [0 0 1] \\ \(6\to 3\) & 1 & 1 & 20(6) & MIMO & - & - & - & - & - & - & - & - & [1 0 0] \\ \(7\to 3\) & - & - & - & - & - & - & - & 2 & 1 & 20(4) & OFDMA & [0 1] \\ \(3\to 4\) & - & - & - & - & 2 & 1 & 20(6) & OFDMA & - & - & - & - & - & [0 1 0] \\ \(11\to 3\) & - & - & - & - & - & - & - & - & - & 3 & 1 & 20(3) & OFDMA & [0 0 1] \\ \(3\to 9\) & - & - & - & - & - & 3 & 1 & 20(7) & OFDMA & - & - & - & - & [0 1 0] \\ \hline \hline \end{tabular}
\end{table}
Table 8: Resource Allocation Result for the Max–Min Fair Allocation.  
numerical evaluations, we verify that it can take full advantage of each technology for a given set of network resources. In addition, from the optimization results, we can observe that when the two technologies are used jointly, more multi-user transmissions are enabled thanks to the flexibility of resource allocation, and thus higher use of the link capacity is achieved.  
Conceptualization, K.-h.L.; methodology, K.-h.L.; validation, K.-h.L.; investigation, K.-h.L.; writing, K.-h.L. and D.K.; All authors have read and agreed to the published version of the manuscript. This work was supported by the National Research Foundation of Korea (NRF) funded by the Korea Government (MSIT) under Grant NRF-2018R1C1B5086466.  
The authors declare no conflict of interest.