# Real-Time Station Grouping under Dynamic Traffic for IEEE 802.11 ah
## 5 Optimal Input Parameter Derivation
### Optimal Number of Stations in One RAW Slot  
As the idea of RAW is to limit the number of station contending for the channel, an appropriate number of stations \(\sigma^{r}_{opt}\) that share a RAW slot should be determined in order to strike the proper balance between contention and channel utilization. Several researchers have proposed analytic models to calculate throughput of 802.11 ah networks with a variable number of stations [23; 26; 27; 28; 29; 30]. These models can be used to obtain a value for \(\sigma^{r}_{opt}\). However, they all assume an ideal channel, which does not take the capture effect into account. In real life, the capture effect allows the receiver to still decode certain packets in case of a collision, when the received power of the colliding packets differs significantly. This significantly increases throughput, resulting in pessimistic throughput estimations of existing analytical models. This is especially true for low data rates, where packets are more easily captured as lower signal-to-interference power ratio is required. Currently, our 802.11 ah ns-3 simulator implementation inherits the partially implemented capture effect feature from the standard 802.11 module in ns-3 version 3.23, which allows a packet to be captured when it arrives at the receiver before a colliding packet with lower receive power, while both packets will be dropped if the colliding packet has higher power. Therefore, in order to get more realistic results, we derive \(\sigma^{r}_{opt}\) through simulation rather than analytical models. We calculate \(\sigma^{r}_{opt}\) as the number of stations that achieve the highest throughput in saturated state. As 802.11 ah focuses on IoT and M2M scenarios, 1 and 2 MHz channel bandwidths are most commonly used, with the data rate ranging from 0.15 to 7.8 Mbps. Table 3 lists the optimal \(\sigma^{r}_{opt}\) for different data rates (0.15, 0.6, 2.6 and 7.8 Mbps) and packet sizes (16, 64, 256 and 1024 bytes), as derived using simulation results. The simulations were performed using the same PHY and MAC parameters as used in Section 6 (cf. Table 4). All the stations are in saturated state and there are no hidden nodes among them. The RAW slot duration used in the simulation equals the beacon interval (100 ms). As [PERSON] et al. [30] reveal that the amount of wasted channel time in a RAW slot supporting cross-slot boundary is bounded by the duration of the AIFS (316 \(\upmu\)s), the value of \(\sigma^{r}_{opt}\) obtained from these simulation results is suitable for RAW slots with different durations as well. The simulation results show that the optimal value of \(\sigma^{r}_{opt}\) is quite small for high data rates and large packet payload sizes, even becoming 1 station per slot for packets of 1024 bytes. As the data rate and packet payload size decrease, \(\sigma^{r}_{opt}\) becomes larger, reaching 180 stations for data rate 0.15 Mbps and packet payload size 16 bytes. The larger \(\sigma^{r}_{opt}\) for lower data rates is mainly caused by the capture effect, as low data rates need lower SIR (signal-to-interference power ratio) in order to capture the collided packets. Since only stations with sequential AID can be assigned to the same group (and therefore slot), we use \(\sigma^{r}_{opt}\) as the maximum number of stations that can be allocated in one RAW slot. As AID assignment may be suboptimal, this may bring about slight performance degradation as the actual number of stations that can be assigned to one RAW slot may be smaller than \(\sigma^{r}_{opt}\). This could be alleviated through AID reassignment. As mentioned above, we derive the optimal number of stations \(\sigma^{r}_{opt}\) in one RAW slot based on the saturated state. In an unsaturated state, which is the most common case in reality, contention decreases. In this unsaturated case, allowing \(l>\sigma^{r}_{opt}\) stations to contend in each RAW slot will achieve the same throughput, and at the same time achieve lower latency.