## 7 Numerical Study
### Joint Modulation and Coding Schemes Assignment and Transmission Power Control  
In this section, we are going to answer the main research question that is posed in this article. For the generated network instances, we analyze to what extent traffic throughput can be increased by joint MCSs assignment and TPC. Because the impact of the MCSs assignment is comprehensively discussed in [17], in this study we skip the analysis of all possible MCSs subsets combinations and focus on the following four cases differing in the number of MCSs available for each node and the type of TPC applied:  
* A--one MCS from the set of available MCSs \(\mathcal{M}\), namely BPSK 3/4, and no TPC; the transmission power of each node equals 90 mW,
* B--all three MCSs from the set of available MCSs \(\mathcal{M}\) and no TPC; the transmission power of each node equals 90 mW,
* C--all three MCSs from the set of available MCSs \(\mathcal{M}\) and discrete TPC; the transmission power of each node can take the value from set [50 mW, 90 mW, 130 mW],
* D--all three MCSs from the set of available MCSs \(\mathcal{M}\) and continuous TPC; the transmission power of each node can take the values from range [50 mW, 130 mW]. The results, i.e., the frame sizes, which were obtained for the considered cases are presented in Tables 2-4, respectively, for small, medium, and large networks. Each table contains results for ten randomly generated networks of a given size as well as the results that are averaged over all ten network instances. All of the frame sizes reported in this section are expressed in the number of time slots. The averaged results are then illustrated in Figure 4.  
The presented results show that the significant gain can be achieved by applying all three available MCSs. As far as the averaged results are concerned, the value of this gain is equal to 32.5%, 33.5%, and 19.9% for small, medium, and large networks, respectively. The frame size can be then significantly decreased by applying TPC; however, it is not the most essential whether it is discrete or continuous TPC. For small networks, the average frame size after applying discrete TPC is further decreased by 22.2%, and the difference between discrete TPC and continuous TPC only equals 1%. Note that, in nine out of ten small networks, it does not matter which type of TPC we choose--a difference only exists for Network 7. The difference is also not very significant when it comes to the medium networks. When compared to case B, the averaged frame size can be decreased by 19.2% by applying discrete TPC and by 21.3% applying continuous. However, contrary to the previous case, small differences between discrete TPC and continuous TPC exist for most networks. The similar, again not very significant, difference between discrete and continuous TPC is for large networks. In this case, the averaged frame size is decreased by 23.1% by applying discrete TPC and by 25.1% when continuous TPC is used. Note that these values applied to the averaged results; however, it should be noticed that the influence of the TPC strongly depends on the network topology (compare, for example, Network 8 and Network 9). Finally, we should highlight the substantial different between case A (no power control with single MCS) and case D (continuous power with multiple MCSs), which is equal to 48.1%, 47.7%, and 40.1% for small, medium, and large networks when it comes to the averaged results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **A** & **B** & **C** & **D** \\ \hline Network 1 & 162 & 133 & 118 & 116 \\ Network 2 & 242 & 194 & 122 & 121 \\ Network 3 & 149 & 107 & 108 & 107 \\ Network 4 & 188 & 141 & 124 & 119 \\ Network 5 & 215 & 194 & 125 & 121 \\ Network 6 & 202 & 126 & 114 & 111 \\ Network 7 & 190 & 137 & 125 & 121 \\ Network 8 & 254 & 218 & 144 & 144 \\ Network 9 & 175 & 239 & 105 & 101 \\ Network 10 & 281 & 258 & 177 & 173 \\ Avg & 205.8 & 164.7 & 126.2 & 123.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized frame sizes for large networks.