# Parent and PHY Selection in Slot Bonding IEEE 802.15.4e TSCH Networks
## 4 Slot Bonding Implementation
### Timing Values  
TSCH slot bonding bonds multiple _regular_ time slots into a bonded slot that is long enough to transmit or receive a frame of 128 bytes (125 data bytes, 2 CRC bytes and 1 byte frame length), given the data rate of the selected PHY [7]. As such, each bonded slot is tailored to the requirements of the specific PHY and thus has the advantage of limiting the waste of airtime resources.  
As described in Section 4.2, the two available CC1200 PHYs with data rates of 50 kbps and 1000 kbps are used. The differences between the two PHYs and their data rates are reflected in the total time slot lengths and the timing values for the different states within a time slot, as defined in the radio configurations of these PHYs. [PERSON] et al. list these different timing values and how they can be determined [3]. The largest difference between the two PHYs is reflected in the transmission length of the data frame due to the difference in data rate (i.e., in kbps), as the transmission length equals \(\frac{128\times 8}{datasar}\) milliseconds. Using the timings as defined in their original radio configurations, the total time slot lengths are 31.46 ms and 5.808 ms for 50 kbps and for 1000 kbps, respectively. However, the extra time at the start of the slot to reconfigure the radio for the appropriate PHY also has to be included. Similar to [PERSON] et al., 3 ms for this reconfiguration per time slot was added, bringing the total time slot lengths to 34.46 ms and 8.808 ms. As slot bonding requires bonding multiple slots together to form a longer time slot for PHYs with slower data rates, the total time slot length of the fastest PHY should be a common divisor of the time slot lengths of the slower PHY(s). Therefore, the slack time at the end of both time slots  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Modulation** & **Bandwidth (kHz)** & **Data Rate (kbps)** & **Time Slot Length (\(\mu\)s)** & **Bonded nr. of Slots** \\ \hline
2-GFSK & 200 & 50 & 36,000 & 4 \\
4-GFSK & 1667 & 1000 & 9000 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The used PHYs configurations, together with their configured time slot length and number of bonded regular slots.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Start Freq.** & **End Freq.** & **Bandwidth** & **200 kHz** & **1667 kHz** \\ \hline
863 MHz & 868 MHz & 5000 kHz & 25 & 3 \\
868 MHz & 868.6 MHz & 600 kHz & 3 & 0 \\
868.7 MHz & 869.2 MHz & 500 kHz & 2 & 0 \\
869.4 MHz & 869.65 MHz & 250 kHz & 1 & 0 \\
869.7 MHz & 870 MHz & 300 kHz & 1 & 0 \\
874 MHz & 874.4 MHz & 400 kHz & 2 & 0 \\
917.4 MHz & 919.4 MHz & 2000 kHz & 10 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Possible channel allocations for 200 kHz and 1000 kHz channels in the European sub-GHz frequency band, as listed by [PERSON] et al. [4].  
was extended to end up with total lengths of 9 ms and 36 ms, as shown in Table 1. This means that the _regular_ time slots in the TSCH schedule have a length of 9 ms (meaning that the TSCH ASN is incremented every 9 ms) and are used by the 1000 kbps PHY. When allocating a slot for the 50 kbps PHY, four regular slots of 9 ms will be bonded together. Figure 4 illustrates the differences between the time slots of the two chosen PHYs.