# A Low-Power WLAN Communication Scheme for IoT WLAN Devices Using Wake-Up Receivers
## 5 Delay and Power Analysis  
### Delay Analysis  
In the delay analysis, there are \(N\) nodes that request and receive the sensed data. We analyzed the average delay of the entire transmission: from when the AP requests to gather the sensed data from each sensor to when the AP collects the data from all of sensors. When the average delay is calculated, the average contention delay \(E[T_{\textit{contention}}]\) depends on the background traffic of other  
Figure 11: Multiuser format of wake-up frame. Figure 12: Collision case in multiuser wake-up procedure. MU = multi-user; AIFS = arbitration inter-frame spacing. IEEE 802.11 devices' transmissions. In this paper, the _contention_ delay is assumed to be calculated as in [25], when the number of STA in the background traffic and inter-arrival time are applied. When the average contention delay of wake-up packet transmission \(E[T_{\textit{contention-wupkt}}]\) is derived, the wake-up delay \(T_{\textit{wudelay}}\) and the subsequent triggering frame transmission delay are included in the collision delay, because AP detects the collision after it receives no response for the triggering frame, which is a single-user trigger or TF. Similarly, in the case of deriving the contention delay of single-user trigger \(E[T_{\textit{contention-SUtrig}}]\) or multi-user trigger \(E[T_{\textit{contention-MUltrig}}]\) frames, the transmission delay of the wake-up packet and \(T_{\textit{wudelay}}\) are included in the collision delay, because the retransmission of the wake-up packet is needed. On the other hand, \(T_{\textit{wudelay}}\) is not included in the collision delay of the data frame \(E[T_{\textit{contention-Duta}}]\) in the conventional transmission method, because AP knows that STA is in the awake state by receiving the acknowledgement frame of the single-user trigger. In the _conventional_ method, the average transmission delay is \(N\) times the transmission delay for each STA. In the average contention delay, the collision delay includes the wake-up delay caused by the retransmission of the wake-up frame in the contention for the wake-up packet and single user frame when it is excluded in the contention for data transmission. This is because no wake-up frame retransmission is required for the data frame transmission failure. The collision probability of the wake-up packet transmission and triggering frame transmission is also different, because if the packet arrives at the STA during the wake-up delay, the STA may transmit the packet at the same time as the AP's transmission for idle channels. Therefore, the average transmission delay in conventional method is:  
\[ \begin{split} E[T_{\textit{conventional}}]&=N(E[T_{ \textit{contention-supkt}}]+E[T_{\textit{contention-SUtrig}}]+E[T_{\textit{ contention-Data}}]+T_{\textit{wudelay}}+\\ T_{\textit{SUWUpkt}}+T_{\textit{SUtrigger}}+T_{\textit{SUData }}+2T_{\textit{ack}}+2 SIFS)\end{split}  \tag{1}\]  
where \(T_{\textit{SUWUpkt}}\), \(T_{\textit{SUtrigger}}\), and \(T_{\textit{SUData}}\) denote the transmission delay of the single-user wake-up packet, the single-user trigger, and the data frame respectively. In the unicast-MAC method, the acknowledgment frame for the triggering frame and the data frame are aggregated, and the contention for the data frame is not processed. Therefore, the average transmission delay is:  
\[ \begin{split} E[T_{\textit{SU\_MAC}}]&=N(E[T_{ \textit{contention-supkt}}]+E[T_{\textit{contention-SUtrig}}]+T_{\textit{ wudelay}}+T_{\textit{SUWUpkt}}+T_{\textit{SUtrigger}}+\\ T_{\textit{Ack+SUData}}+2T_{\textit{ack}}+2 SIFS)\end{split}  \tag{2}\]  
where \(T_{\textit{Ack+SUData}}\) denotes the transmission delay of the acknowledgement of single user trigger aggregated with the data frame. In the multicast-MAC procedure, we assume nine user transmissions in a group because the uplink MU OFDMA procedures in IEEE 802.11 ax enables up to nine user transmissions in the 20-MHz band.