## Underlying Theories
### IEEE802.15.4e Tsch  
In 2008, IEEE created the 802.15 Task Group 4e [26] to redesign the MAC protocol in the existing 802.15.4 standard to overcome the deficiencies explained in the previous section. One of the results of the design is the use of a time synchronized channel hopping (TSCH) strategy that is useful for improving transmission reliability and energy efficiency. With these energy-saving and reliable characteristics, the IEE802.15.4e TSCH standard is suitable to be part of the Internet of things protocol stack [27]. The 802.15.4e TSCH technology provides a reliable and energy-efficient transmission because it uses the timeslot (TS) and channel-hopping (CH) methods simultaneously. The timeslot access method will eliminate collisions between active nodes to provide deterministic latency and increase throughput on the application that uses it. In the absence of collisions, it will also save on energy use at each node. The channel hopping mechanism will make each node use different frequencies on each transmission. Channel hopping can reduce the influence of interference and multipath fading to improve communication reliability. Thus, TSCH will increase network capacity, increase transmission reliability, and improve latency, while maintaining duty cycles at a low level [24]. The TSCH standard uses a slotframe structure in its timeslot arrangement. Figure 3 shows an example of a slotframe (S) with 12 timeslot times, with a duty cycle of 50%. Thus, in each slotframe there will be six timeslots (\(\lambda\)) that can be used by nodes to stay active and six timeslots for idle/sleep mode. The smaller the value of the duty cycle, the more efficient the use of energy on the network. Figure 2: Superframe structure of IEEE802.15.4. CAP, contention access period; CFP, contention free period; and GTS, guaranteed timeslot. The number of timeslots in a slotframe (slotframe size) will determine the repetition frequency of the timeslot and the timing for the nodes to carry out the communication process. The smaller the size of the slotframe, the more chance for nodes to actively send/receive data, with the consequence that the duty cycle will increase. The standard does not specify the size of the slotframe, but depends on its application, the size of the slotframe ranges from 10 to 1000 ts [28]. Within each individual timeslot duration, network nodes have the opportunity to send or receive data, receive or send acknowledgments (ACKs), or sleep. By default, the duration of one timeslot according to the 802.15.4e standard is 10 ms [27]. As previously stated, channel hopping can improve communication reliability, because at each transmission opportunity, the nodes will use different frequencies. The frequencies used are related to the channel offset parameter, ChOff. ChOff is translated into a frequency using Equation (1); by using this equation, channel hopping will occur:  
\[\mathrm{f}=\mathrm{F}(\mathrm{ASN}+\mathrm{ChOff})\bmod\mathrm{n}_{\mathrm{ ch}}\mathrm{l}. \tag{1}\]  
ASN is the absolute slot number, and the ASN value shows the number of timeslots used since the network started operating or since a certain time determined by the PAN coordinator. The ASN value will increase along with the passing of the timeslot used for the process of transmitting and receiving in the network. F is a function realized with a lookup table, containing a set of frequencies that are ready to use. ChOff is the channel offset and \(\mathrm{n}_{\mathrm{ch}}\) is the number of frequencies available, where \(0\leq\mathrm{ChOff}\leq(\mathrm{n}_{\mathrm{ch}}-1)\). In the IEEE802.15.4e standard, the value of \(\mathrm{n}_{\mathrm{ch}}\) is 16 [27]. The relationship between ASN, S, and slotframe cycle (R) is \(\mathrm{ASN}=(\mathrm{R}\times\mathrm{S}+\mathrm{T})\), where T is the timeslot number (\(0\leq\mathrm{T}\leq\mathrm{S}-1\)). To be more clear, we can see the illustration in Figure 4.  
Figure 4 shows an example of the timeslot and channel hopping (TSCH) concept with two cycles of slotframes.