# Energy Performance of LR-FHSS: Analysis and Evaluation
## 4 Current Consumption Model of an LR-FHSS ED
### Unconfirmed Transmission  
Initially, we aim to model the average current consumption of an LR-FHSS ED in the unconfirmed mode, denoted \(I_{avg\_unTr}\). To this end, we first identify and characterize the different states the ED goes through to perform an unconfirmed transmission in terms of the duration and current consumption for each state. To create a realistic model of the ED's behavior, we carry out measurements using the experimental scenario presented in Section 4.1. The measurements are performed only on the radio module of the ED. This  
Figure 5: Experimental scenario for measuring the current consumption of the considered LR-FHSS ED. is because our ED hardware platform comprises components (e.g., LEDs, communication interfaces, etc.) that are useful for development but unnecessarily increase energy consumption compared with that of a production-environment ED. We assume that the LoRaWAN ED transmits data units periodically; therefore, we model its current consumption over one period. Each period includes the transmission of a frame (along with the necessary related LoRaWAN protocol procedures), with the device remaining in a sleep state otherwise. An unconfirmed transmission comprises one uplink frame transmission and two subsequent receive windows. Recall that LR-FHSS is only used in uplink transmission; therefore, downlink traffic employs LoRa PHY. Figure 6 shows a power analyzer capture of the complete procedure for the transmission of an unconfirmed data unit using DR8 with a PHYPayload size of 17 bytes (i.e., 4 bytes of FRM Payload size). We next identify and characterize each state involved in the transmission procedure (labeled with a tag composed of a number and a letter). Details for every state depicted in Figure 6 are shown in Table 4. These states correspond to different operations of the radio interface. We measured the duration and current consumption of each state for several individual transmission processes, and the differences we found were negligible. The actual frame transmission happens in state 1, whereas the first and the second receive windows correspond to states 3 and 5, respectively. States 1a, 3a, and 5a are the initial states whereby the radio module is preparing for the subsequent main state. States 1b, 3b, and 5b, on the other hand, correspond to the post-operational stages, during which the radio module transitions to the sleep state. The radio interface remains in sleep mode in states 2, 4, and 6. Moreover, taking a closer look at state 1, we observe the impact of the LR-FHSS frequency channel hops (i.e., physical carrier hops) on current consumption. Figure 7 shows an expanded view of one such frequency hop. Each hop implies a brief and smooth drop in current consumption. The average current consumption in the unconfirmed mode, \(I_{avg\_unTx}\), is modeled in Equation (1). \(T_{Period}\) denotes the period between two consecutive transmissions. \(T_{j}\) and \(I_{j}\) represent the duration and current consumption, respectively, of a specific state \(j\) in Table 4. Note that frequency channel hops are encompassed in state 1. \[I_{avg\_unTx}=\frac{1}{T_{Period}}\sum_{j}T_{j}\times I_{j} \tag{1}\]  
Figure 6: Current consumption profile of ED transmitting an unconfirmed uplink frame with DR8. The PHYPayload size is 17 bytes. Then, the duration of the sleep interval, \(T_{Sleep}\), which depends on several variables like \(T_{Period}\), is shown in Equation (2). \[T_{Sleep}=T_{Period}-T_{act\_unTx} \tag{2}\]  
where \(T_{act\_unTx}\) represents the sum of all non-sleep-state durations of the states involved in the transmission of a frame (see Equation (3)). \[ \begin{split}& T_{act\_unTx}=T_{preTx}+T_{Tx}+T_{postTx}+T_{RX1 unit }+T_{preRx1}+\\ &+T_{Rx1}+T_{postRx1}+T_{Rx2 unit}+T_{preRx2}+T_{Rx2}+T_{postRx2} \end{split}