## 4 The Proposed Selective Retransmission Mechanism
### Energy Consumption
For the fully-reliable approach, the average consumed energy in each hop is 94.60 mJ for a mean PER of 5% and 115.12 mJ for a mean PER of 15%. In both graphics in Figure 7, the 1-level 2D DWT approach always consumes more energy since only packets with DR = 255 are not retransmitted. For the retransmission mechanism based on 2-level 2D DWT, packets with DR = 2, DR = 5 and DR = 8 are also not retransmitted if lost in hops before the hop DR. Another interesting observation is that nodes closer to the sink always consume less energy, and such a difference is more evident for a higher mean PER. As intermediate nodes closer to the sink tend to consume more energy due to the fact that they receive more combined upstream traffic, the proposed retransmission approach may considerably preserve such nodes, potentially prolonging the network lifetime. Finally, note the energy consumption for different values of DR. For low mean packet error rates, the additional energy consumption for ACK transmissions and packet retransmissions is significant, as can be seen in hops 3, 6 and 9 in Figure 7(a) when DR is equal to 2, 5 and 8, respectively. For higher mean PER, the energy saving avoiding reception and relaying of packets that are lost and not retransmitted in previous hops is more significant than additional transmission of ACK messages and packet retransmissions, as can be seen in Figure 7(b). Besides the relation between energy consumption and number of hops, we can also relate energy with the mean packet error rate, as presented in Figure 8. In that graphic, the active used path is composed of 10 intermediate hops and DR = 5 for the 2-level 2D DWT. Moreover, the considered PER is for packets sizing \(s\) bits, where \(g\) and \(b\) assume different values, resulting in mean PER from 2% to 20%, although we also computed the PER for smaller packets when necessary. As one can see in Figure 8, the fully-reliable transmission mechanism is severely affected by higher packet error rate, directly impacting the expected network lifetime. For the proposed selective retransmission mechanism, the impact in the expected average energy consumption is considerably lower than traditional fully-reliable transmission approaches, where all packets have the same  
Figure 7: Energy consumption in each intermediate node. treatment by intermediate nodes. Once again, it is worth noting that, while energy consumption rises when packets have to cross links with higher PER for the fully-reliable transmission approach, the average energy consumption decreases for the proposed selective retransmission mechanism, considering the same network conditions. Also as expected, the image transmission after a 2-level 2D DWT consumes less energy than the retransmission mechanism based on 1-level 2D DWT, for DR = 5 and \(H_{p}\) = 10, and this difference increases for higher mean PER. We can also analyze the effect of the value of DR for a 2-level 2D DWT. In Figure 9, we show the total energy consumption for a path composed of 20 hops when an image is transmitted employing the proposed retransmission mechanism based on 2-level 2D DWT, considering different values of DR for the \(\mathrm{HL_{(2)}}\), \(\mathrm{LH_{(2)}}\) and \(\mathrm{HH_{(2)}}\) subbands. Lower DR implies in more energy consumption, since packets will be transmitted with reliability guarantees over a bigger part of the path. Figure 8: Energy consumption for a path composed of 10 intermediate nodes. Figure 9: Energy consumption for different values of Data Relevance (DR). At last, we estimated the effect of a higher packet error rate in some links of the path. Considering a path composed of 20 intermediate nodes, we established a very low 2% PER for all links except in the middle of the path, where higher mean PER were simulated. As the links between hops 9 and 11 experienced a higher packet error rate, it was also verified the effect of the proposed retransmission mechanism for 2-level 2D DWT, considering DR before (DR = 5) an after (DR = 15) the region with increased PER.