# Energy Performance of LR-FHSS: Analysis and Evaluation
## 3 Overview of LoRaWAN and LR-FHSS
### LR-Fhss  
LR-FHSS is an extension of the LoRa physical radio modulation [28]. The purpose of this new PHY technique is to improve data transmission in congested networks wherein capacity is reduced by duty cycle restrictions, channel availability, and collision probability. LR-FHSS uses frequency hopping spread spectrum (FHSS), which also improves the link range and allows numerous devices to communicate on the same operating channel simultaneously while their signals can still be appropriately received and demodulated by the GW. LR-FHSS is the LoRa Alliance's implementation of FHSS, which is a technique used in other wireless technologies like Bluetooth or early Wi-Fi amendments. FHSS involves rapidly switching a signal's carrier frequency across a predetermined set of channels, making it more robust against interference and unauthorized access. These features are especially helpful in satellite networks, where EDs and GWs are far away from each other and there is high node density. LR-FHSS is only used to perform uplink transmission; downlink transmission continues to employ LoRa PHY. There are four LR-FHSS DRs: DR8 to DR11, and all of them are included. With LR-FHSS, the ED splits the payload into pieces and sends each piece over a separate physical channel, which is explained later. To provide redundancy, PHY headers are sent three times for DR8/DR10 and twice for DR9/DR11. Moreover, there are differences in the coding rates: DR8/DR10 use a CR of 1/3, whilst DR9/DR11 use a CR of 2/3. This means that DR8/DR10 are more robust than DR9/DR11, but at the expense of a lower bit rate. A more robust coding scheme might be helpful in low-signal-quality conditions (i.e., low SINR), but the longer transmission time could also increase the chance of collisions. This could lead to worse performance with respect to DR9/DR11, especially in scenarios with a large number of EDs [8]. The LR-FHSS bitrates are 162 bps (for DR8/DR10) and 325 bps (for DR9/DR11). The LR-FHSS PHY frame structure is composed of the header and the payload (referred to as PHYpayload), as shown in Figure 4. The header information gives the GW the tools it needs to reassemble the payload from the ED. It contains the channel hopping sequence, payload length, DR, number of header replicas, and coding rate. As we previously mentioned, the header is communicated more than once for redundancy; one header is transmitted at a fixed rate for a duration of 233.472 ms. The variable-sized payload, which is divided into segments with a duration of 102.4 ms each, comes after the header. After a 233.472 ms header segment and after a 102.4 ms payload segment, there is a frequency channel hop. A two-byte payload CRC is the last component of the PHY frame structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**DR Index** & **Modulation** & **Configuration** & **Physical Bit Rate [bps]** \\ \hline
0 & LoRa & SF12/125 kHz & 250 \\
1 & LoRa & SF11/125 kHz & 440 \\
2 & LoRa & SF10/125 kHz & 980 \\
3 & LoRa & SF9/125 kHz & 1760 \\
4 & LoRa & SF8/125 kHz & 3125 \\
5 & LoRa & SF7/125 kHz & 5470 \\
6 & LoRa & SF7/250 kHz & 11,000 \\
7 & FSK & 50 kbps & 50,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: LoRa EU863-870 DR characteristics. The operating channel width (OCW) for DR8/DR9 and DR10/DR11 is 137 kHz and 336 kHz, respectively. Each OCW is divided into several occupied bandwidths (OBWs) of 488 Hz. The minimum separation between physical channels, or the grid, is 3.9 kHz, which implies a separation of eight OBWs. Up to 688 OBW physical channels can be present in a 336 kHz OCW, but due to the 3.9 kHz separation constraint, only 86 physical channels can be used for each uplink frame transmission (336 kHz/3.9 kHz \(\simeq\) 86). This results in eight grids or groupings of physical channels (8 \(\times\) 86 = 688). On the other hand, for an OCW of 137 kHz, there are up to 280 OBW physical channels, but only 35 can be used due to the grid restrictions. The ED first selects the OCW and physical channel at random before the start of an uplink transmission.