## 5 Performance Validation
### Performance Results  
To validate our approach, we have deployed nodes in different configurations and within both M-SSP1 and M-SSP2. To fully test the proposed algorithm's capability, we generated within M-SSP1 and M-SSP2 more than 1600 rays and used the proposed ray classification technique to determine the ray type. When applying our approach, 96% of the rays are classified correctly while only 4% were misclassified. We have chosen four different configurations shown in Figure 12 as examples to fully comprehend the reasons behind the observed 4% error. The figure displays the Bellhop eigen rays generated for node #3 and the location of its neighbors. In the configuration shown in Figure 12b our approach manages to classify all rays correctly except for two rays. The first ray terminates at node #7, where the depth of the node is 1.4 m, i.e., is located very close to the sea surface. In this case the value of \(c_{LEP}\) is higher than the maximum SSP value; thus, a reflection was assumed and the value of \(x_{LEP}\) was obtained using a straight-line approximation. The location of the \(x_{LEP}\) was found to be 18.3 m before the location of node \(x_{R}\) in an actual horizontal range of 800 m, i.e., an error of 2.28% in calculating the location of the LEP. Thus, the algorithm assumes that the ray was received immediately after it was reflected from the sea surface and categorized the direct ray into a ray facing a single nondifferentiable LEP. Similar conclusion can be made for ray terminating at node #17 where the ray was classified falsely as having three LEPs while it experienced a single LEP. A closer look at the location of the second LEP reveals that it was estimated to be 5.5 m before the actual location of the node. Since the quadrants of transmission and reception mandates and odd number of LEPs, the nodes opted to choose a three LEP propagation path. Moreover, in both cases, the proximity of the node is extremely close to the location of the LEP and given the actual range value the error is classified as insignificant. Such errors can be filtered out by adding some error cushion to the actual LEP location where if a node is within a marginal proximity of the LEP, it ignores the last LEP. When classifying the rays using the configuration used in Figure 12c, the direct ray terminating at node #20 was erroneously categorized as having a single LEP. Since the calculated value of \(c_{LEP}\) was larger than the observed SS in the water column, the algorithm opted to use a straight-line approximation and found the first LEP point 78 m before the node location. Moreover, node #20 is located at a horizontal distance of 4938 m, i.e., at the extent of the simulation area. At such a large distance, the straight-line model managed to retain an absolute error of 78 m and hence is deemed appropriate for estimating reflected ray paths to an extent of 5 km. In part (e) and (f) of Figure 12, M-SSP2 is utilized to show different refraction patterns than those used in the previous examples. Since most of the transmission angles in part (e) are close to the horizontal axis and due to the fact that the SSP is not symmetrical, a new environment is introduced to validate the proposed algorithm. We observe that the ray classification algorithm produces error only in three cases and in the remaining 40 rays shown in parts (e) and (f) were classified correctly. For the 3 cases, similar findings are observed as those found in part (b) and (c). Thus, the four different configurations shown in Figure 12 demonstrate the capability of our ray classification technique in identifying the ray type for node located at ranges less than 5 km. Figure 13 shows the percentage of ray misclassification when selecting an erroneous angle (labeled \"Angle Error\"). Specifically, we inject an additive Gaussian error with zero mean and variable standard deviation \((\sigma)\) values to the selected angle and observe how many signals are misclassified.