# Energy Performance of LR-FHSS: Analysis and Evaluation
## 5 Evaluation
### Battery Lifetime  
The battery lifetime of an LR-FHSS ED is a crucial performance parameter in IoT networks as it directly impacts the operational efficiency and maintenance requirements of devices that may have to be deployed in hard-to-reach locations. We evaluate ED battery lifetime by using Equations (12) and (15). We assume a battery capacity of 230 mAh, which is typical for button cell batteries [36]. It is essential to remind the reader that our study solely accounts for the radio module's current usage. Consequently, the increased current  
Figure 11: ED average current consumption as a function of \(T_{Period}\) for DR8/DR10, DR9/DR11, DR0, and DR5 comparing confirmed and unconfirmed transmission for a 1-byte FRM Payload size. Figure 10: ED average current consumption as a function of \(T_{Period}\) for DR8/DR10, DR9/DR11, DR0, and DR5 with the maximum FRM Payload size permitted for each DR for both confirmed and unconfirmed modes. consumption caused by other ED tasks, such as internal communications, CPU activity, data processing, etc., will result in a decreased actual battery lifespan. Figures 12-14 illustrate the theoretical ED battery lifetime as a function of \(T_{Period}\) for the maximum payload size allowed for each DR and for a 1-byte payload, respectively. Consistent with the average current consumption study, the ED battery lifetime increases asymptotically with \(T_{Period}\). The impact of using confirmed and unconfirmed transmission are shown in Figure 12. For \(T_{Period}\) = 500 min, the battery lifetime for DR8/DR10 reaches around 6.5 years, while DR9/DR11 provide a slight enhancement of up to 6.9 years. If we extend the measurement out of the scope of the figure, for a one-day notification interval, the theoretical battery lifetime for DR9/DR11 reaches around 16 years, while it slightly decreases to ~15 years for DR8/DR10. Except for DR5, battery lifetime differences between confirmed and unconfirmed transmission for any of the DRs considered in Figure 12 are low. However, when \(T_{Period}\) increases, these differences tend to slightly increase, yielding longer battery lifespans for unconfirmed transmission. Quantitatively, the differences between confirmed and unconfirmed transmission for LR-FHSS DRs and DR0 are minor, with the former showing differences of around 0.23 years. Nonetheless, for DR5, the difference is notorious, reaching a peak of 2.2 years, which translates into an 8% lifetime increase for unconfirmed transmission. Additionally, the results show greater differences in the lifetimes between confirmed and unconfirmed transmission for the DR0 and DR5 cases compared to the LR-FHSS ones. This is due to the varying contributions that different DRs set in the receive windows make to energy consumption, especially when measured relative to the \(T_{Tx}\) values. For example, for a similar ToA in the uplink when comparing DR8/10, DR9/11, and DR0, the difference is more pronounced in the latter case, as it uses a DR in the downlink that is the same one used in the uplink, which is the slowest one. DR5 lifetime results are significantly greater than those of the other DRs studied by a considerable margin due to its increased data rate (and lower ToA), which is in line with the findings in the average current consumption study. However, its reliability and communication range is also the worst among the considered DRs [25]. We also investigate the effect on battery lifetime of transmitting a modest 1-byte FRM Payload size (see Figure 13). In particular, DR0 and the LR-FHSS DRs share similar results, as the data rates are similar. DR8/DR10 are the most energy-consuming DRs in that group,  
Figure 12: Theoretical ED battery lifetime as a function of \(T_{Period}\) for DR8/DR10, DR9/DR11, DR0, and DR5 for the maximum FRM Payload size permitted for each DR and comparing unconfirmed with confirmed uplink transmission. while DR9/DR11 are the least consuming ones, with theoretical battery lifetime results of up to around 20 years for a 500 min period.