# Performance of Narrow Band Wide Area Networks with Gateway Diversity
## 4 Numerical Results  
This section presents numerical results derived from a simulation study on a Network Simulator-3 (NS-3) with the ns-3.33 version [16; 17; 18]. The simulator is modified to match the system model presented in Section 3. The PSR and PER are related as follows: PSR = 1-PER. The end-nodes and gateways are randomly positioned within the simulated area per iteration and the average PSR, along with its distribution, is calculated across all the iterations. Each node generates on average one packet per two minutes. In order to illustrate the link budget with the LoRa modulation, the average PER versus distance between one GW and one end-node is presented in Figure 10. A link-level range of 524 m can be achieved with an average PSR, (i.e., 1-PER) of at least 85% for 99 percent of the iterations with SF-11. Such PSR is referred to as the Top Percentile 99 (TP-99) PSR, which is derived from the empirical cumulative distribution function (eCDF) of the PSR across iterations. Such TP-99 PER versus distance obtained from the field measurements are also added to the plot to illustrate that the developed model predicts the coverage area well. The TP-99 results from the field are obtained over the worst-case interference levels across several sites at the same distance to the GW. Results are measured with static locations in the Westchester, CA suburban area with 1000 packets per site, where multiple sites are tested per the distance to the GW. Such an impact from interference derived from the field measurements is added to the link budget in the NS-3 simulator as well. The field measurements are obtained with an EVK to EVK link with an SX-1262 chipset. Figure 9: Path loss measurement versus log distance from the GW in a suburban neighborhood in Mountain View, CA, USA. When there are two gateways serving a single node, the EN packets can be forwarded by either of the two GWs. Figure 11 illustrates the average UL PER of an EN with respect to its distance to each of the GWs. We observe that an EN with a 524 m distance to either GW has a PSR > 97%, which is significantly better than a single GW. Similarly, the ENs that are more than 524 m away from one of the GWs can still achieve a PSR > 85%. This phenomenon is called GW diversity, which helps GWs together cover regions that are beyond their individual coverage area. Even though GW diversity is effective against path loss, it is susceptible to interference and is expected to lead to reduced returns in high-interference deployments. Its impact on the coverage area with an increase in the number of end-nodes in the network is illustrated using the results obtained from the NS-3 simulation, and are presented in Table 3. It is observed that as the end-nodes in the network increase, the interference in the network increase in turn, negatively impacting PER. The devices that are towards the edge of the network range become susceptible to interference from end-nodes that are closer to the gateway. Furthermore, as the simulation region is expanded, the nodes suffer from increased path loss. We see that with fifty ENs and one GW distributed over a 1.44 km\({}^{2}\) region, the TP-99 PSR drops to as low as 39%. In a similar scenario, in order for the TP-99 PSR to reach 85%, the number of GWs needs to be increased to five. The improvement in PSR is achieved due to GW diversity and thanks to the improved link margin for the devices, which were earlier at the edge of the network and now get a chance to be closer to another GW (Figure 12). The improvement in the coverage area is observed to increase to 1.44 km\({}^{2}\) with SF-11 with a TP-99 PSR of 86%. Similar results are observed with SF-8, where an area of 0.42 km\({}^{2}\) can be covered with a TP-99 PSR of 87%. The DL TP-99 PSR is slightly worse than UL PSR in a large area when GW diversity is used. That is because the best GW is decided during the UL transmissions, and that same GW is used for DL transmissions, where the shadow fading might change.