# Energy Performance of LR-FHSS: Analysis and Evaluation
## 4 Current Consumption Model of an LR-FHSS ED
### Confirmed Transmission  
In contrast to unconfirmed uplink transmission, in confirmed uplink transmission, the NS informs the ED via a confirmation downlink frame that the uplink frame was successfully received. In this section, we model the current consumption of the ED when it performs a confirmed uplink transmission.  
In a confirmed transmission, the ACK can be sent in the first window (see Figure 8) or in the second one (Figure 9) with probabilities of \(p_{1}\) and \(p_{2}\), respectively. Equation (14) models the average current consumption of an ED performing confirmed transmissions periodically, \(I_{avg\_ACKTx}\), where \(I_{avg\_ACKTx1}\) and \(I_{avg\_ACKTx2}\) indicate the average current consumptions that correspond to receiving the downlink frame in the first and second receive windows, respectively. For the purpose of the model, we consider that the probability of receiving an ACK in the first or in the second receive window is \(p_{1}=p_{2}=0.5\).  
\[I_{avg\_ACKTx}=p_{1}\times I_{avg\_ACKTx1}+p_{2}\times I_{avg\_ACKTx2} \tag{14}\]  
Figure 8 illustrates the case where the ACK is received in the first receive window, eliminating the need for the second receive window. This reduction in the number of states consequently leads to lower energy consumption. Specifically, compared with unconfirmed transmission, states 4, 5a, 5, and 5b from Table 4 are removed, and \(T_{Rx1}\) is variable depending on the DR and payload length used. To calculate \(I_{avg\_ACKTx1}\), we use Equation (1), considering the states applicable to a confirmed transmission, the \(T_{Rx1}\) value that corresponds to the DR used for the uplink transmission, as shown in Table 7, and that an ACK has no FRM Payload.  
Figure 8: Current consumption of an ED during the process of transmitting a confirmed frame with DR9. In this case, the ACK is received in the first window (Rx1), so the second window is not opened.  
If the ACK is received in the second receive window, the duration of the latter is extended, as depicted in Figure 9. Therefore, \(T_{Rx2}\) will change to a value that depends on the DR used. Typically, the data rate used for this window is the most robust one (i.e., DR0). From our measurements, \(T_{Rx2}=1141\) ms. Therefore, \(I_{avg\_ACKTx2}\) is equal to \(I_{avg\_uintTx}\), obtained as in Equation (1) except for this specific \(T_{Rx2}\) value. Current consumption in the first receive window is higher when the ACK is received in it, but it is lower on average for the whole transmission process because the second receive window is eliminated, as opposed to unconfirmed uplink transmissions. Therefore, the current consumption increases when the ACK is received in the second receive window due to the contribution of both receive windows, including the first receive window and its already large duration (by default, it is configured to DR0).  
After determining \(I_{avg\_ACKTx}\), let \(T_{lifetime\_ACKTx}\) denote the lifetime of a battery-operated LR-FHSS ED performing confirmed transmissions periodically. \(T_{lifetime\_ACKTx}\) can be calculated as shown in Equation (15).  
\[T_{lifetime\_ACKTx}=\frac{C_{battery}}{I_{avg\_ACKTx}} \tag{15}\]  
Finally, the energy cost of transmitting each user data bit for confirmed uplink frames, \(EC_{ackTx}\), is modeled in Equation (16).  
\[EC_{ackTx}=\frac{I_{avg\_ACKTx}\times V\times T_{Period}}{L_{data}} \tag{16}\]  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**State** & & 3 \\ \hline
**Parameter** & & \(T_{Rx1}\) (ms) \\ \hline \multirow{3}{*}{**DR**} & 8/10 & 576.4 \\  & 9/11 & 286.6 \\  & 0 & 991.8 \\  & 5 & 41.20 \\ \hline \hline \end{tabular}
\end{table}
Table 7: States and parameters affected by a confirmed uplink transmission when the ACK occurs in the first receive window.  
Figure 9: Current consumption of an ED during the process of transmitting a confirmed frame with DR8. The ACK is received in the second window (Rx2).