# IEEE 802.11 ax OFDMA Resource Allocation with Frequency-Selective Fading
## 7 Numerical Results  
The general model of the system is described in Section 4. We consider a \(40\,\mathrm{MHz}\) channel in the \(5\,\mathrm{GHz}\) band. The RU structure is shown in Figure 1. The flow sizes are taken from a truncated lognormal distribution with minimal, average, and maximal values of \(100\) KB, \(3\) MB, and \(100\) MB, respectively. The arrival time of the new flow is taken from the truncated exponential distribution with minimal, average, and maximal values of \(1\,\mathrm{s}\), \(3\,\mathrm{s}\), and \(6\,\mathrm{s}\), respectively. For simplicity, the maximum power difference for all experiments is \(10\) dB and equal for all MCSs. To calculate \(PL(s_{dist})\) from (10), we use the following signal attenuation model [32]:  
\[ \begin{split} PL(s_{dist})&=40.05+20\log_{10}(f_{c} /2.4)+20\log_{10}(min(s_{dist},5))+\\ &+\mathbb{I}(s_{dist}>5)\times 35\log_{10}(s_{dist}/5)\end{split}  \tag{11}\]  
where \(f_{c}\) is the center frequency in GHz, \(\mathbb{I}\) is the indicator function, and \(s_{dist}\) is the distance from STA to the AP. This formula shows the dependency of the path loss (expressed in dB) on the distance. As we consider a \(40\,\mathrm{MHz}\) channel, we take into account the RU sizes as follows:  
\[P(r_{size})=10\log_{10}(r_{size}/18) \tag{12}\]  
where \(r_{size}\) is the number of \(26\)-tone RUs, from which \(r\) consists of according to Figure 1. For example, the \(52\)-tone RU consists of two \(26\)-tone RUs, \(242\)-tone RU consists of \(9\) and the maximal value is \(18\) (\(484\)-tone RU). The \(Fading(s,r)\) values are calculated using the TGac D NLOS [33] model recommended for \(11\)ax simulation [32]. In our simulation, we place three APs at the vertices of an equilateral triangle with a side \(R_{AP}=50\) m. The maximum distance between STA and AP is \(R=30\) m.  
The greedy algorithm has been implemented for the experiments for the MR, PF, and SRPT utility functions described in Section 5. We also consider schedulers from [8] that do not divide the channel by frequency for the comparison. In the first series of experiments, we examine the performance of  
* the proposed schedulers (denoted as greedy),
* the schedulers that perform an exhaustive search over all STA-RU allocations and thus obtain an optimal solution of the optimization task (2) (denoted as exhaustive), and
* the schedulers that do not divide the channel by frequency (denoted as legacy). The results are shown in Figure 4 in case \(T_{fd}=0\,\mathrm{s}\), i.e., when the APs always know the relevant channel conditions. The average upload time is the average time to transmit a flow, and goodput is the overall throughput of the system. The total number of STAs equals \(N\). Note that all APs work simultaneously, so there may be several parallel OFDMA transmissions (in the case when TFs are transmitted at the same time or when an AP cannot receive TF from the other AP successfully). The results show that the developed OFDMA schedulers significantly outperform the legacy ones: the average upload time is almost two times lower, and the throughput is approximately \(20\%\) higher. At the same time, the proposed greedy scheduler, although it is a heuristic approach, does not degrade performance much with respect to the optimal solution. The loss in the average upload time is approximately 10%, and the loss in throughput is approximately 5%, but the computation time is much lower. In Figure 4, we show results only for small numbers of STAs, up to \(N=21\), because it takes too much time to obtain results for the exhaustive search schedulers. In Figure 5, we show results for bigger numbers of STAs for the greedy schedulers and the legacy schedulers. The results show that even for big numbers of STAs, the proposed greedy schedulers have a significant gain in goodput and the average upload time. An important result is that the gain in average upload time is more significant for small numbers of STAs, and the gain in throughput becomes more significant for bigger numbers of STAs.