## 4 Problem Statement  
From the moment a ContikiMAC node is turned on, the radio check is repeatedly adapted to send and receive data types, such as routing packets, medium control packets, or packets containing environment sensor information. Each node performs a large number of WakeUp Rx modes depending on the environment. Two conditions can be considered: (1) the node is ideally positioned over minimum interference with other unrelated radio or noise signal; (2) the node is in a state of coexistence with unrelated radios, noise, or interference. In the state 1, between each data reception (positive WakeUp) the node will have a large number of idle listening that plays a significant role in the activity of a radio. In the state 2, in addition to idle listening, the node also has many false WakeUp. Figure 2 shows samples of positive, false, and idle listening WakeUp on the Radio Timeline in Cooja simulator  
Figure 1: Simulation scenario and network graph based on the RPL routing protocol. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Protocol** & **Standard** \\ \hline Application & Collect view & - \\ Transport & UDP & IETF RFC 768 \\ Network & RPL/IPv6 & IETF RFC 6550 \\ Adaptation & 6 lowpan & IETF RFC 6282 \\ Data link & IEEE 802.15.4 MAC (CSMA) & IEEE 802.15.4 \\ Radio Duty Cycling & ContikiMAC & - \\ Physical & IEEE 802.15.4 PHY & IEEE 802.15.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Network layers structure used on the nodes [36]. The \(x\)- and \(y\)-axes represent to node numbers and their activity of radio, respectively. In this simulated example, the power configuration and the network layers of the nodes are according to Tables 2 and 3, respectively. The red, blue, and green colors in the activity of radio line show interference, sending packet, and receiving packet respectively [41]. The ContikiMAC considers CCA_CHECK_TIME that is the time it takes to perform a CCA check. In fact, CCA_CHECK_TIME is a balancing time for other timing parameters in ContikiMAC, and it has no direct effect on CCA duration. The time spent on each false WakeUp is depending on MAX_NONAACTIVITY_PERIODS. It is the maximum number of periods we allow the radio to be turned on without any packet being received. Each period counts as a sum of CCA_CHECK_TIME and CCA_SLEEP_TIME. The CCA_SLEEP_TIME is the time between two successive CCA checks. The time variables in ContikiMAC that affect both idle listening and false WakeUp times are shown in Table 4. The fast-sleep mechanism is responsible for the diagnosis of false WakeUps in ContikiMAC. Therefore, if the node fails to receive data after \(11\) periods (\(21.1\) ms), it quickly returns to sleep mode. Table 5 shows the number of idle listenings and false WakeUps during the 10-min simulation in the 5, 7, 12 nodes according to Sections 3.3 and 3.4. For example, the time spent in idle listening and false WakeUp in Node7 is calculated as Equation (2). In fact, almost \(1.6\%\) of the network time is wasted in idle listening and false WakeUp in Node 7. This is, of course, a mere indication of the effect of the wake-up time loss on idle listenings and WakeUps, and it is not a definite value. Thus except for the positive WakeUps, the node tolerates inefficient energy consumption in idle listening and false WakeUps. Because this value varies depending on the application and location of the nodes. \[T_{node\,7}=\ T_{idle}+\ T_{false}T_{node\,7}=(13895\times 0.4)+(220\, \times\,21)=5558+4620=10178\ \mathrm{ms} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **CPU Ticks** & **Unit (ms)** \\ \hline CCA\_CHECK\_TIME & 32768/8192 & 0.4 \\ CCA\_SLEEP\_TIME & (32768/2000) + 1 & 1.7 \\ MAX\_NONAACTIVITY\_PERIODS & \(10\times(\)CCA\_CHECK\_TIME + CCA\_SLEEP\_TIME\()\) & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Amount of effect on idle listenings and false WakeUps according to ContikiMAC_c.