## 5 Performance Evaluation
### Simulation Results
The usage of subspace clusters in the HSFZ and relays with success probabilities above the threshold in the LSFZ to transfer packets from far LDs to the GW mitigated the near-far fairness issue. The other schemes, on the other hand, demonstrated a negative decrease in success probability as the distance between the LDs and the GW increased due to poor link quality, noise, collision among the nodes, and other interference from obstacles such as buildings and vegetation encountered by nodes located far from the GW [55]. Figure 8 illustrates the variation in the number of nodes as a function of the energy consumption for the SFPCR scheme and the three other schemes under consideration. In contrast to the SFPCR scheme, the results for all three comparative schemes demonstrated a slightly direct correlation between energy use and number of nodes. The FSRC scheme utilized the most energy, exceeding 29 \(\upmu\)J, as a result of using more LDs with a higher SF  
Figure 6: Plots variation in Success Probability according to the Payload Size (B) with a comparison between the SFPCR scheme and other protocols. Figure 7: Plots variation in Success Probability according to the Distance of LoRa devices from the GW with a comparison between the SFPCR scheme and other protocols. and broadcasting packets sent throughout the network, which introduced considerable routing overhead and used a great deal of energy. Similar to the cluster-based scheme, which had huge cluster sizes, the cluster member nodes had to connect with other nodes located at great distances, resulting in increased energy consumption owing to intracluster distance communication. In addition, the mesh scheme consumed 22.2% more energy than the SFPCR scheme because of the unnecessary multihops to send a signal strong enough to reach the GW. However, the SFPCR scheme consumed approximately 67.4% less energy than the comparative schemes because it primarily utilized short hops with a lower SF, controlled redundant transmission by data fusion from CHs in the HSFZ and also managed the number of transmissions and retransmissions to the GW by employing slotted ALOHA [45]. Consequently, the network's lifespan was increased. Figure 9 shows a direct proportionality between payload sizes and energy consumption for all schemes. As packet size increases, so does energy consumption, limiting the lifespan of an IoT network that is energy constrained. This is due to the broadcast storm problem caused by source nodes and relay nodes deployed in the network; in comparison, the cluster-based, mesh, and proposed SFPCR schemes consumed relatively little energy, limiting the use of distant nodes with higher SF to transmit directly to the GW, which consumes a great deal of energy. In addition, the SFPCR scheme transmitted small packets with short hops and a lower spreading factor in order to save transmission power. This implied that the source node in the HSFZ transmitted to the closest CH and relay node, thereby reducing the amount of time spent in the air. Consequently, the amount of energy lost was restricted. In Figure 10, all schemes demonstrated a low quantity of energy consumption between the GW and approximately 3000 m, where direct transmission occurred; nevertheless, the FSRC scheme lost significantly more energy than the other schemes because of broadcasts made by relays and source nodes. The results demonstrated that the proposed SFPCR scheme consumed the least amount of energy as the distance increased, and the number of transmissions was regulated because all distant nodes in the HSFZ coordinated their transmission through the CHs rather than a direct transmission of data packets to the GW and because of the use of relay nodes in the LSFZ with a low SF to transmit packets of nodes with a success probability below the threshold. Figure 8: Plots variation of energy consumption (uJ) as a function of number of nodes with a comparison between the proposed SFPCR scheme and other protocols.