# A Novel Method to Determine the Optimal Location for a Cellular Tower by Using LiDAR Data
## 4 Results and Discussions
### Determination of the Strength of the Signal
#### 4.1.4 Validation
Five random points are generated in each block of the L-shaped area. Centroids c1, c2 \(\ldots\) cn will be considered as cell phone tower locations one by one and the average signal strength of each block of L-shaped area will be checked. A threshold is set for each block, checking signal strength; if the signal strength lies between \(-\)50 and \(-\)70 dB m, then the count will increase by 1, while the rest remains the same. The centroid tower location is c1, c2, c3 \(\ldots\) cn, and whichever gets the maximum count will be the perfect location for the cell phone tower. Next, we check the distance between the centroid \"C\" and the new tower location out from the c1, c2, c3 \(\ldots\) cn. Then, from Figure S10 shown below, the new centroid location is determined as C'. L-shaped area (50 m \(\times\) 75 m)--Repeat the above procedure and find out the distance between the centroid \"C\" and the new tower location. The distance is 8.5 m, as shown in Figure S11a. U-shaped area (one tail short, one long)--Similarly, the above procedure is repeated for the case again, and the distance is 7 m, as shown in Figure S11b. After analyzing different shaped cases and calculated distances, it is clear that the dimension of the square created at centroid \"C\" should be taken as half of the distance of the centroid to the outlines of the area. The length is mentioned as \"L\". Step 5: Determination of average phone signal strength (each grid consists of five random points) at every 5 m \(\times\) 5 m grid location from every potential tower location (xl, yl). Where I ranges between 1 and m, m being the total number of grid cells in step 4, and n is the total number of grid cells in step 2. Step 6: Signal strength map for cell tower located at the finest tower location. From the tower location to five random points in each block after dividing the project area into blocks (5 m \(\times\) 5 m). The signal strength map is shown in Figure S12. A 3D map for the RGIPT campus when a cell tower is at the original position is shown in Figure S13a. Similarly, the new proposed location of one cell tower on campus is shown in Figure S13b. Step 7: For deploying P = 3, p is number of cell phone towers in an area. Inscribed the given Rectangle \"R\" in circle \"O\", the diameter of the circle is equal to the diagonal of \"R\". The Center of \"R\" is denoted by \"C\", which is now divided into three equal angles of (\(360^{\circ}/3\)) = \(120^{\circ}\) each. The angle will be divided into different combinations. Take the inscribed area of the rectangle and delete the other circle area. The following combinations are possible, shown in Figure S14a-c.  
1. Taking one case out of different combinations and isolating the three equal areas as shown in Figure S14, the isolated area is shown in Figure S15a. 2. Taking one isolated area out of three mentioned as (Area 1) and fitting the area in the rectangle \"LMNO\" is shown in Figure S15b. Step 8: Divide the whole isolated area into blocks of area (5 m \(\times\) 5 m) within the segment divided in step 7. Step 9: Calculate the centroid of the rectangle in which Area 1 is inscribed within the segment. The centroid is mentioned as \"CAreal\", as shown in Figure S16(1). Step 10: Now, again a square is taken as in step 4 (Point 1) of dimension based on half of the distance from \"C\" to the centroid \"CAreal\". Dimension is (m \(\times\) m). (* whole area will always be divided into blocks of dimension (5 m \(\times\) 5 m), the only square which is taken for cell tower location correction is divided into cells of 2 m \(\times\) 2 m). Similarly, as in step 5 (Point1), the square is now divided into blocks of 2 m \(\times\) 2 m and repeats the same process to find the new centroid location (CAreal'), as shown in Figure S16(2). Step 11: Determination of the average phone signal strength (each grid consists of five random points) at every 5 m \(\times\) 5 m grid location from every potential tower location (xl, yl) within a segment.