# Enhanced Beacons Dynamic Transmission over TSCH
## 2 Time Slotted Channel Hopping Background and Related Work  
### TSCH Background  
In the TSCH mode, the time slotting process reduces the nodes' radio duty cycle (RDC) and saves power. Meanwhile, frequency hopping allows frequency diversity to mitigate the effect of channel fading and increases network reliability. Indeed, if a transmission that fails the retransmission is conducted on a different frequency, it generally has a higher chance of success if the cause of the problem was multipath fading or external interference. Furthermore, due to the availability of multiple orthogonal channels, more nodes can communicate at the same time (i.e., the same slot) using different channels (identified by different channel offsets). TSCH proposes a slotted multichannel MAC protocol for low-range wireless personal area networks (LR-WPAN), where the time is divided into slots whose duration is sufficient to send a data packet of maximum length and receive the corresponding acknowledgment. The slots can be shared or dedicated, and three actions can be performed as follows: transmit, receive, or sleep in each slot [9]. Dedicated slots are contention-free, i.e., only a single sender-receiver pair is supported. On the other hand, shared slots can be contention prone, allowing multiple sender nodes to reach the same receiver, for a sender node to reach many receivers (link layer multicast), or for having a common slot for organizing broadcasting at MAC level [10]. In a given time slot, multiple packets cannot be exchanged simultaneously on the same channel (if the receiver is in the interference range of non-intended transmitters); the operation of each node must be organized to avoid collisions and achieve high reliability and efficiency. For this purpose, TSCH uses a two-dimensional scheduling table called a slotframe. A slotframe is defined in [11] as a sequence of time slots that repeat periodically. Duty cycling is achieved by introducing sleeping slots in each slotframe. In TSCH, channel offset allows two nodes to communicate while another pair of nodes communicate simultaneously in the same time interval, but using a different frequency. The frequency on which a pair of nodes meets depends on the channel hopping pattern stored. Each slot of a slotframe is identified by a combination of a slot offset (\(slotOffset\)), a channel offset (\(chOffset\)), and the Absolute Slot Number (\(ASN\)) which is the total number of slots that have elapsed since the start of the network. The channel offset is an integer constant that is used to determine the channel hopping pattern in the following way:  
\[CH=\mathcal{F}\big{(}(ASN+chOffset)\text{mod}(m)\big{)}, \tag{1}\]  
where \(m\) is the total number of available channels and function \(\mathcal{F}(\cdot)\) is a lookup table containing the available channels. An example is illustrated in Figure 1, where each slotframe has 7 slots and \(m=16\) channels available in the channel hopping sequence. Nodes \(A\) and \(B\) have channel offset 1 and slot offset 3. The \(slotOffset=3\) indicates that the active slot is programmed in the fourth slot of each slotframe, then following (1) and assuming an arbitrary vector \(\mathcal{F}=[21,14,17,23,12,11,19,25,13,26,16,24,15,18,20,22]\) where \(|\mathcal{F}|=m=16\), the physical frequency used for said link during the cycle of slotframe \(k\) in the fourth slot (\(slotOffset=3\)) would be \(\mathcal{F}((4+1)mod\ 16)=\mathcal{F}(5)\), which represents the sixth frequency within the channel hopping sequence, corresponding to channel 11. At the slotframe \(k+1\) also in the fourth slot, the corresponding channel would be \(\mathcal{F}((11+1)mod\ 16)=\mathcal{F}(12)=15\). Nodes \(C\) and \(D\) are also configured with \(slotOffset=3\) but its channel offset is 15. So, they can communicate at the same time as nodes \(A\) and \(B\) but using different frequencies, i.e., \(\mathcal{F}(3)=23\) and \(\mathcal{F}(10)=16\) at slotframe \(k\) and \(k+1\), respectively.