## 6 Analysis of the eLPRT Protocol
### Contention-Free Retransmissions  
The results presented in this section concern the use of retransmissions, and consider two contention-free retransmission strategies. The first strategy (\"RP after CAP\"), adopted by the eLPRT protocol, places the Retransmission Period (RP) after the CAP and before the Normal Transmission Period (NTP). The second strategy (\"RP before CAP\") places the RP after the beacon and before the CAP. The delivery ratio results presented in Figure 7 use the same value of \(BER_{bad}\) for both the beacon and the data packet. As the results show, the effectiveness of the retransmission mechanism with small number of nodes is low for both cases. The explanation is based on the fact that the allocation of slots for transmission of data packets starts from the end of the superframe and goes towards its beginning, as the number of nodes increases, which means that the transmissions of the first nodes are closely followed by the beacon of the next superframe. In a scenario with burst errors, there is a high probability that the bad state observed during the transmission of the data packets from these nodes extends into the reception of the beacon. When a node misses the beacon, it is unable to retransmit, since it does not have the information about the position of slots allocated for retransmission in the superframe. Therefore, burst errors tend to reduce the effectiveness of the retransmission mechanism, affecting more intensely data packets that are allocated near the following beacon. As the number of nodes in the network increases, the average distance between the data packets and the next beacon also increases, decreasing the probability that the beacon is affected by the bad state observed during the transmission of previous data packets. When the BER that affects the beacon is high, it has a significant effect in the performance of both retransmission strategies. This effect is independent of the location of the retransmission period, since the retransmission information is not received for both strategies when the beacon is lost. Therefore, the delivery ratio for both strategies in this case is similar. The increase of the output power of the base station transmitter enables decreasing the BER for the beacon frames since the bit error rate tends to decrease with the increase of the signal-to-noise ratio (SNR) [14]. This increment in the output power is not problematic in terms of energy consumption since, unlike the sensor nodes, the base station is not energy constrained. The base station's output power can be raised, for example, through the use of a RF range extender such as the CC2591 [15], which provides a gain up to 22 dB. Simulation results using the same conditions of the previous simulations, except for the \(BER_{bad}\) relative to the reception of the beacon (was changed to \(10^{-4}\), to account for an increase in the base station output power) are shown in Figure 8. Under these conditions, the delivery ratio for the \"RP after CAP\" strategy increases significantly, with particular relevance for small number of nodes. Regarding the \"RP before CAP\" strategy, no significant delivery ratio increase is observed. Since the retransmission is placed close to the failed transmission, the probability that burst errors affect both packets is higher in this last strategy. Figure 8: Delivery ratio of eLPRT with \(BER_{bad}=10^{-2}\) (data) and \(10^{-4}\) (beacon). Figure 7: Delivery ratio of eLPRT, with \(BER_{bad}=10^{-2}\). For both cases, as the number of nodes approaches the capacity of the network, the space available for retransmissions in the superframe decreases and, consequently, the delivery ratio approaches the value without retransmissions. The larger separation between the original data packet and the scheduled retransmission in the \"RP after CAP\" strategy has the benefit of increased robustness against burst errors.