# PROFEE: A Probabilistic-Feedback Based Speed Rate Adaption for IEEE 802.11 bc
## 5 Experiments
### Modulation Selection Algorithm  
Now that the probability selector algorithm has found the best probabilities for transmitting ACKs and NACKs that accurately estimate the number of STAs receiving messages correctly/incorrectly, we can proceed with the second algorithm that selects the best MCS. As Section 4 mentions, the AP seeks to choose the highest MCS possible while keeping the percentage of STAs that do not receive messages correctly within the desired range.  
Figures 9 (for 100 STAs) and 10 (for 1000 STAs) show the simultaneous operation of the probability selector algorithm (left column) and the modulation selector algorithm (right column) for a network area of radius 100 m (first row), 200 m (second row), and 300 m (third row). In each row, the left plot shows the behavior of the probability selector algorithm for transmitting ACKs and NACKs after every \(2f=2k\) messages (1000 odd-numbered messages used for NACK and 1000 even-numbered messages used for ACK). As mentioned in Section 3, the desired percentage of silence events that guarantees low error estimation is set between \([15,45]\%\). Once the percentage of silences of both \(n_{NACK}\) and \(n_{ACK}\) falls within this range, the AP moves to the second algorithm and decides to increase, decrease, or keep the current MCS depending on whether the percentage of STAs receiving messages incorrectly is below, above, or within the desired range (set to \([10,20]\%\) of STAs in all experiments), respectively. In all plots, the initial MCS is MCS(5). However, any other initial MCS strategy should work (i.e., the lowest or the middle MCS).  
As we can see in the figures, the probability selector algorithm takes about 4000-8000 messages to reliably estimate the number of STAs receiving messages correctly/incorrectly every time the second algorithm changes the MCS. Similarly, as the scenario increases the network radius, more MCS changes are needed as more STAs become further away from the AP, thus requiring a lower MCS to receive messages correctly. As for the number of STAs, we can see that it takes fewer messages for the probability selector algorithm to converge for 1000 STAs (see Figure 10) compared to 100 STAs (see Figure 9).  
While the 20,000-30,000 messages transmitted for the two combined algorithms to converge to the desired behavior could appear too many, in practice, it will take only a few  
Figure 8: Algorithm for obtaining the \(p_{NACK}\) that minimizes the error for \(n_{NACK}\) using the silence estimator.  
seconds, depending on the number of messages per second being transmitted by the AP. We consider the H.265 codec as an example of the AP sending video/audio content to STAs. Table 5 shows the number of seconds this particular codec takes to reach 24\(k\) messages for some of its resolution modes.  
Overall, Figures 9 and 10 show that the proposed method can find the best MCS that maintains the number of STAs receiving messages incorrectly within the desired limits independently of the number of STAs and the size of the scenario. Similarly, as Table 5 illustrates, the proposed method takes only a few seconds to find the best possible MCS.  
Figure 10: _Cont_.  
Figure 9: Rate Adaption for 100 STAs.