# PROFEE: A Probabilistic-Feedback Based Speed Rate Adaption for IEEE 802.11 bc
## 5 Experiments
### Performance of the Three Estimators  
The first part of the experiments is to analyze the performance of each of the three estimators for positive feedback (one ACK, ACK collision, and ACK silence) and negative feedback (one NACK, NACK collision, and NACK silence). As mentioned before in Section 3. Ideally, the three estimators should provide a similar estimation of either \(n_{ACK}\) or \(n_{NACK}\), provided the AP transmits a vast number of messages (in theory is an infinite number). However, the AP is interested in obtaining an accurate estimation as soon as possible using a few messages. As we will see, for a small finite number of messages, each estimator will show a different accuracy and convergence time depending on the particular scenario and the probabilities being used (\(p_{ACK}\) and \(p_{NACK}\)). Figure 7 shows the results of the experiments. The AP computes the number of STAs receiving messages correctly/incorrectly using the three estimators and for three different probabilities (0.1, 0.01, and 0.001). There are 1000 STAs distributed in a disk of 100 m radius. Receiving STAs used even-numbered messages to transmit ACKs and odd-numbered messages for transmitting NACK messages to the AP. The highest MCS (MCS(5)) was used  
Figure 6: Scenario for the experiments. Randomly distributed STAs at 100 m, 200 m, and 300 m. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of APs & One AP only located in the center of a disk \\ Number of STAs (n) & 10, 100, and 1000 STAs random uniformly \\  & distributed within a disk \\ Disk Radius & 100, 200 and 300 m \\ Propagation model & 2.4 GHz frequency, Friis propagation model, \\ Initial transmit power: & Nist error model \\ Final transmit power: & 1 dBm \\ Spectrum Channel: & Standard: 802.11 ax, Width 20 MHz \\ Mobility: & Both the AP and the STAs remain static \\ Network layer & Only a broadcast address is required. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. in all these figures. The green horizontal line shows the real number of STAs receiving messages correctly/incorrectly in each experiment. As can be observed, each estimator has a different accuracy and convergence time depending on the used probability. However, each estimator presents some general behavior. The ACK/NACK estimator (see Figure 7a,b) presents significant errors and takes longer to converge to a steady state. The collision estimator (see Figure 7c,d) presents even more significant error variations, and it takes even longer to reach a steady state. Finally, the silence estimator (see Figure 7e,f) has good accuracy and reaches a steady state after a few hundred messages. Figure 7: Performance of three estimators for 1000 STAs randomly positioned at 100 m. In this scenario, 841 STAs receive messages correctly, and 159 STAs receive them incorrectly. Table 4 shows the absolute estimation error (measured in the number of STAs) in the steady state for 10, 100, and 1000 STAs distributed in the same 100 m radius disk. The table shows results after 2000 and 5000 messages. The estimation that presents the smaller error in each cell for a given number of messages is highlighted for each probability. As verified in the table, the _silence_ estimator offers the most accurate estimation in 14 out of the 18 cells shown for 2000 messages and in 15 out of 18 cells for 5000 messages, the ACK/NACK correct feedback estimator in 4 out of 18 cells for 2000 messages and in 3 out of 18 cells for 5000 messages, and the collision estimator in 4 out of 18 cells for 2000 messages and in 5 out of 18 cells for 5000 messages. Cells where the silence estimator did not achieve the lowest error occurred when \(p_{ACK}\) or \(p_{NACK}\) were far from their optimal value. Figure 7 shows that the silence estimator also reaches the steady state faster than the other two.