# LESS: Link Estimation with Sparse Sampling in Intertidal WSNs
## 7 Performance Evaluation
### Large-Scale Trace-Driven Simulations
#### 7.3.2 Results  
We also evaluate the link quality reconstruction, routing path reconstruction and topology reconstruction in the coast and the uniform topology, and the results are shown in Figures 15 and 16.  
**Link quality reconstructions in the coast topology & the uniform topology:** Figure 15a shows the estimation accuracy of the coast topology and Figure 16a is the case of the uniform topology. We find that the coast topology demonstrates higher accuracy than the uniform topology at all sampling rates. In the coast topology, nodes are densely deployed in each deployment site while nodes are evenly distributed in the uniform topology (the deployment area is evenly divided into blocks and each block has only one node) as shown in Figure 14. The characteristics of the topology lead to different performance in link quality reconstructions, e.g., nodes in the same deployment site in the coast topology share similar link quality status with each other. As a result, the performance of LESS in the coast topology benefits from the redundancy of link quality.  
In addition, we find that parameter of altitude range slightly influences the link quality recovery accuracy with a low sampling rate. For a node, it is more likely to be under water with a lower altitude. When more nodes are under water, the derived matrix is getting sparse as the matrix contains more \"0\". The influence of altitude will be elaborated in detail below.  
**Routing path reconstruction in the coast topology & the uniform topology:** Unlike for link quality recovery, altitude range reveals significant different performance in routing path recovery in Figures 15b and 16b. Lower altitude range has better performance in both coast topology and uniform topology with similar link quality reconstruction accuracy. Specifically, when the sampling rate is 0.5, the routing path reconstruction accuracy is over 95% with the altitude range of \([2,3]\) while only 88.4% and 85.7% in \([2,4]\) and \([2,5]\) in Figure 15b. The reason is the redundancy in lower altitude range  
Figure 14: Nodes deployments in the large-scale simulations.  
Figure 15: Evaluation of performance in the coast topology: (**a**) link quality reconstruction accuracy in the coast topology; (**b**) routing path reconstruction accuracy in the coast topology; and (**c**) topology reconstruction accuracy in the coast topology.  
makes the estimation error much evenly distributed in link quality at each point. Thus, the result of the routing path estimation faces less impacts in shortest path routing schemes, i.e., elements in the link quality matrix have similar errors. We also notice the routing path recovery is not as good as in real trace in Figure 12b. The reason is the probable routing paths in real traces and large-scale simulations are in different magnitudes, which leads different performances in the routing path reconstruction. In real-trace experiments, nodes have limited choices of the next hop, and are more likely to select the right node as the next hop. In the large-scale simulation, a node may have over 20 neighbors and link quality reconstruction error may mislead the result of next-hop choices.  
**Topology reconstruction in the coast topology & the uniform topology:** As mentioned above, the topology reconstruction error focuses on false positive, i.e., mistaking a non-existent link as an existing one. We analyze topology reconstruction accuracy in Figures 15c and 16c. Like the real-trace evaluation, we set a threshold to eliminate invalid links whose link quality values are less than the threshold.  
Altitude range also plays an important role in the topology reconstruction, and lower altitude range has a better performance. The result also matches our deduction that data with redundancy is favorable in data reconstruction for compressive sensing. Besides, the coast topology has a high recovery rate at low sampling rates, e.g., the topology reconstruction accuracy is over 90% when the sampling rate is 0.2 at every altitude range.