# A Low-Power WLAN Communication Scheme for IoT WLAN Devices Using Wake-Up Receivers
## 5 Delay and Power Analysis
### Power Analysis  
We calculated the power consumption for each STA only for triggering the uplink data and transmission procedure. In the analysis, \(E[C_{\textit{pkt\_type}}]\) indicates the average number of collisions for each packet type, which is the reciprocal number of the collision probability. The analysis ignores the power consumption during the wake-up receiver operation because it is negligible compared to the power consumption in the main transceiver.  
The average power consumption in the STA for the conventional method is based on:  
\[E^{\textit{conv.}}_{STA}=E^{\textit{conv.}}_{\textit{WUI}}+E^{\textit{conv.} }_{\textit{iidle}}+2P^{\textit{trxx}}_{\textit{sw}}T^{\textit{trxx}}_{\textit{ sw}}+E^{\textit{conv.}}_{\textit{tx}}+E^{\textit{conv.}}_{\textit{rx}} \tag{6}\]  
where  
\[E^{\textit{conv.}}_{\textit{WUI}}=(1+E[C_{\textit{WULpkt}}])P_{\textit{st}}T_{ \textit{WULdelay}} \tag{7}\]  
\[E^{\textit{conv.}}_{\textit{iidle}}=(E[T^{\textit{SULIrig}}_{\textit{contention }}]+E[T^{\textit{Wu-pt}}_{\textit{contention}}]-E[C_{\textit{WUpkt}}]T_{ \textit{WULdelay}}+E[T^{\textit{Data}}_{\textit{cont}}])P_{\textit{listen}} \tag{8}\]  
\[E^{\textit{conv.}}_{\textit{tx}}=(1+E[C_{\textit{SU\_data}}])P_{\textit{tx}}T_ {\textit{SU\_data}}+P_{\textit{tx}}T_{\textit{ack}} \tag{9}\]  
\[E^{\textit{conv.}}_{\textit{rx}}=(1+E[C_{\textit{SULIrig}}])P_{\textit{rx}}T_ {\textit{SULIrig}}+P_{\textit{rx}}T_{\textit{ack}} \tag{10}\]  
where \(P_{\textit{st}}\) denotes the setup power, \(P^{\textit{trxx}}_{\textit{sw}}\) denotes the transition power of transmission state and receiving state, \(P_{\textit{tx}}\) is the transmission power, and \(P_{\textit{rx}}\) is the receiving power.  
In the unicast-MAC method, there is no contention procedure for the data frame transmission, and the power consumed for this contention is reduced. Therefore, the power consumption of STA for the uplink transmission procedure in the unicast-MAC method is:  
\[E^{\textit{SUMAC}}_{\textit{STA}}=E^{\textit{SUIMAGE}}_{\textit{WUI}}+E^{ \textit{SUIMAGE}}_{\textit{slide}}+2P^{\textit{trxx}}_{\textit{sw}}T^{\textit{ trxx}}_{\textit{sw}}+E^{\textit{SUIMAGE}}_{\textit{tx}}+E^{\textit{SUIMAGE}}_{\textit{rx}} \tag{11}\]  
where  
\[E^{\textit{SUIMAGE}}_{\textit{WUI}}=(1+E[C_{\textit{WUpkt}}])P_{\textit{st}}T_ {\textit{WULdelay}} \tag{12}\]  
\[E^{\textit{SUIMAGE}}_{\textit{iidle}}=(E[T_{\textit{contention-SUtrig}}]+E[ T_{\textit{contention-wupkt}}]-E[C_{\textit{WUpkt}}]T_{\textit{WULdelay}})P_{\textit{listen}} \tag{13}\]  
\[E^{\textit{SUIMAGE}}_{\textit{tx}}=P_{\textit{tx}}T_{\textit{ack}+\textit{ SU\_data}} \tag{14}\]  
\[E^{\textit{SUIMAGE}}_{\textit{rx}}=(1+E[C_{\textit{SULIrig}}])P_{\textit{rx}}T_ {\textit{SULIrig}}+P_{\textit{rx}}T_{\textit{ack}} \tag{15}\]  
In the multicast-MAC and multicast-scheduled procedure, the frame length of the MU transmission is longer than that for single-user frames. In addition, the contention delay and average number of contentions for MU TF are different from those of single-user transmissions, as described in the delay analysis. The transmission power of the STA in MU transmission is different because it uses a smaller bandwidth than single user transmission. Therefore, the average power consumption in each STA is:  
\[E_{STA}^{MUI}=E_{WUI}^{MUI}+E_{idle}^{MUI}+2P_{sw}^{tyrx}T_{sw}^{tyrx}+E_{tx}^{ MUI}+E_{rx}^{MUI} \tag{16}\]  
where  
\[E_{WUI}^{MUI}=(1+E[C_{WUIpkl}])P_{st}T_{WULdelay} \tag{17}\]  
\[E_{idle}^{MUI}=(E[T_{contention-MUtrig}]+E[T_{contention-uwpkt}]-E[C_{WUIpkt}] T_{WULdelay})P_{listen} \tag{18}\]  
\[E_{tx}^{MUI}=P_{tx\_MU}T_{MU\_data+ack} \tag{19}\]  
\[E_{rx}^{MUI}=(1+E[C_{MUI\_trig}])P_{rx}T_{MUL\_trig}+P_{rx}T_{M-STA-BA} \tag{20}\]