# Modeling the Energy Performance of LoRaWAN
## 5 Evaluation
### Energy Cost of Data Delivery  
In this subsection, we evaluate the last considered performance parameter, i.e., the energy cost of data delivery for both unacknowledged and acknowledged transmission. We next apply Equations (13), (14), (30) and (31) to determine \(EC_{delivery\_unACK}\) and \(EC_{delivery\_ACK}\), respectively. We assume a battery voltage of 3.6 V.  
Figure 18 provides the energy cost of data delivery for the unacknowledged approach, as a function of \(T_{Notif}\) and the DR used, for BER = 0. For a given DR, and for BER = 0, the relative difference in energy cost of data delivery between acknowledged and unacknowledged transmission is the same as the difference in terms of current consumption analyzed in Section 5.1.2. However, such difference is only significant for low notification periods, and therefore it is not graphically visible in Figure 16, therefore the figure serves for both unacknowledged and acknowledged approaches. As shown in Figure 18, for BER = 0, the energy cost of data delivery follows a linear trend as a function of \(T_{Notif}\). As it has been previously shown in Figures 8 and 9, average current consumption, and therefore energy consumption becomes asymptotically constant as a function of \(T_{Notif}\). Therefore, as \(T_{Notif}\) increases, the energy consumed by the end-device increases linearly with time, while the number of delivered bits remains constant. Because we are considering the maximum frame payload size allowed by each DR, note that the slope of the curves for DR0-DR2 is the same, since these three DRs allow the same maximum frame payload size (i.e., 51 bytes), the slope for DR3 is lower, since the maximum frame payload size is greater (i.e., 115 bytes), and finally the slope for DR4, DR5 and DR6 is the the lowest, since for these DRs the maximum frame payload size is the largest supported by LoRaWAN (242 bytes). DR0 exhibits slightly greater energy cost of data delivery than DR1, due to the lower bit rate of DR0, which leads to a greater data message and acknowledgment transmit time, as well as receive window duration. The same reasoning applies to the comparison of the energy cost of data delivery of DR1 and DR2. The energy cost of data delivery for DR4 is \(\sim\)19% and \(\sim\)40% greater than the one for DR5 and for DR6, respectively, for the lowest notification period, and decreases down to \(\sim\)1% for both DR5 and DR6 for the highest notification period considered (note that these differences are not visible in Figure 18). We next evaluate the upper bound on the energy cost of data delivery by considering a frame payload size of 1 byte. Results are shown in Figure 19, along with the ones obtained for a maximum-sized frame payload. As it can be seen, for a given notification period and DR, the energy  
Figure 17: Impact of \(p_{call}\) on end-device lifetime in acknowledged transmission, as a function of \(T_{Notif}\) for different DR settings, and for BER = 0.  
cost per delivered payload bit for a 1-byte frame payload is roughly two orders of magnitude greater than the one obtained for a maximum-sized frame payload. We then study the impact of non-zero BER on the energy cost of data delivery, assuming a maximum-sized payload for DR0, and the same payload size for DR5, and considering also unacknowledged and acknowledged data message transmission (see Figure 20). Acknowledged transmission leads to a greater energy cost, by at least one order of magnitude, due to the additional energy consumption of retransmissions, in comparison with the unacknowledged approach. On the other hand, BER has a greater impact on DR5 than on DR0, since the former transmits (and may retransmit) data messages at a higher bit rate, leading to lower energy consumption, which makes retransmissions, and their related overhead, energy-expensive. We next focus on how collisions influence the energy cost of data delivery (see Figure 21). As expected, collisions increase the energy required per delivered payload bit.