## 4 Performance evaluation
### Data Analysis  
First, Table 3 shows the basic statistics (i.e., total packets received, mean RSSI, mean CCA, and mean PDR) aggregated by node. As can be observed, a total of 10,710,868 packets were received out of 14,113,440 packets (i.e., 11 nodes, 99 days, 24 h, 60 min, 9 messages) transmitted by all the nodes during the deployment, representing an aggregate PDR (Packet Delivery Ratio) of 75.9%. However, nodes experienced different communication impairments (i.e., multi-path propagation and external interference), leading to a per-node PDR that ranged between 65.9% and 87.4% depending on the communication distance and the noise levels. In that regard, it is important to notice that even nodes that were close together experienced high RSSI and PDR variability. For example, nodes 55-99, 55-DD, 55-65, and 56-0B were deployed at the same distance from the gateway (i.e., 115.1 m), but have RSSI values ranging between 85.3 dBm and 96.2 dBm and average PDR ranging from 67.9% to 85.1%. Given these results, we decided to cluster the nodes according to the distance (\(d\)) to the gateway, allowing us to make comparisons within similar groups. In particular, we defined three groups of nodes: (1) nodes that are close to the gateway (i.e., \(d<80\) m: 56-53, 55-AD, and 55-E4), (2) nodes thatare at a medium distance from the gateway (i.e., \(80\leq d<150\) m: 55-99, 55-DD, 55-65, and 56-0B), and (3) nodes that are far from the gateway (i.e., \(d\geq 150\) m: 56-32, 55-B3, 55-63, and 63-0A). As an example, in Table 3, we can observe that nodes of the far group present an average CCA value (\(-119.0\) dBm) that is lower than those of the close group (\(-113.0\) dBm). This can be explained by the fact that the gateway is located near the warehouse entrance, where other wireless technologies are known to be deployed and operating in the same sub-GHz band (i.e., 868 MHz), creating interference. Moreover, we observe that nodes of the close group with a higher CCA average have lower PDR values at the physical layer. For example, node 55-E4 has a CCA of \(-111.2\) dBm and a PDR of 68.0%, whereas node 55-AD has a CCA of \(-115.5\) dBm and a PDR of 79.9%. This can be explained by the fact that nodes with higher CCA average values would refrain from transmitting more often due to the CCA threshold value defined in Table 2.  
Table 4 shows the per-node RSSI, CCA, and PDR values separated by modulation type. As can be observed, SUN-FSK provided the highest physical layer PDR (81.3%) compared to SUN-OQPSK (80.7%) and SUN-OFDM (65.7%). However, SUN-OQPSK provide the minimum standard deviation (6.6) compared to SUN-FSK (7.8) and SUN-OFDM (14.7). This can be explained because SUN-OQPSK has a higher sensitivity (\(-116\) dBm) compared to SUN-FSK (\(-114\) dBm) and SUN-OFDM (\(-109\) dBm), allowing it to successfully receive packets that were received with a lower RSSI with higher probability. In that regard, it is important to notice that the PDR at the physical layer is low despite the fact that the RSSI is well above the sensitivity limit for each modulation. For SUN-FSK, the average RSSI of \(-87.1\) dBm is only able to provide a PDR of 81.3% despite that the sensitivity limit is \(-114\) dBm. Similarly, for SUN-OQPSK, the average RSSI of \(-94.8\) dBm can only provide a physical layer PDR of \(80.7\%\) with a sensitivity limit of \(-116\) dBm. Finally, for SUN-OFDM, the average RSSI of \(-93.4\) dBm can only provide a physical layer PDR of \(65.7\%\) with a sensitivity limit of \(-111\) dBm.