## 4 Measurement Results and Analysis  
### Measurement Results and Modeling  
The relation between transmitted power and received power can be expressed as  
\[P_{r}\ =\ P_{t}-PL(d) \tag{6}\]  
In the actual experiment, the transmitted power \(P_{t}\) was fixed at +20 dBm. Since the received power \(P_{r}\) can be derived by extracting RSSI values from the received packets, the path loss \(PL(d)\) at distance \(d\) can be calculated by Equation (6). After completing the data collection, the least square fitting was used to estimate the path loss exponent \(n\) and correction parameters \(X_{\sigma}\), thus the path loss model could be obtained from Equation (3) or Equation (4). The received power in flat concrete road scenario and flat grass scenario are shown in Figure 2a,b, respectively. In general, the received power decayed with the increase of distance. The signal strength decreased more quickly closer to the transmitter, and much more slowly when far away from the transmitter. We also observed that, when the height of the transmitting antenna \(H_{t}\) = 5 cm and the height of the receiving antenna \(H_{r}\) = 5 cm, the received power was significantly less than that when \(H_{t}\) = 1 m and \(H_{r}\) = 1 m. In flat concrete road scenario, the received power decayed fairly quickly when \(H_{t}\) = \(H_{r}\) = 5 cm, with the received power dropping to under \(-\)80 dBm at a distance of 12 m from the TX node. However, when \(H_{t}\) = \(H_{r}\) = 1 m, the received power still reaches \(-\)80 dBm at a distance 50 m  
Figure 1: Measurement scenarios: (**a**) flat concrete road; (**b**) flat grass; (**c**) undulating grass; and (**d**) flat grass with obstacles. away from the TX node. A similar trend was observed in the flat grass scenario. Although the values of received power may fluctuate within a certain distance, the overall trend was rather obvious. With the received power data, the path loss can be calculated by Equation (6). Since a log-normal attenuation pattern of the received power can be observed in Figure 2, both the one-slope and two-slope log-normal models were adopted to fit the path loss data. The breakpoint was calculated by Equation (5). The results of least square fitting are shown in Figure 3. When \(H_{t}=H_{r}=5\) cm, the position of breakpoint was less than 1 m from the transmitter. In that case, the least squares fitting results of one-slope and two-slope models overlap, hence only one line can be seen in Figure 3a,b. According to the fitting results, the path loss exponent \(n\) and the random variable \(X_{\sigma}\) can be determined, thus we obtained the log-normal shadowing path loss models. Figure 4 shows the path loss models under the flat concrete road scenario. The received power decay  
Figure 3: Least squares fitting of measurement results: (**a**) flat concrete road, \(H_{t}=H_{r}=5\) cm; (**b**) flat concrete road, \(H_{t}=H_{r}=50\) cm; (**c**) flat concrete road, \(H_{t}=H_{r}=1\) m; (**d**) flat grass, \(H_{t}=H_{r}=5\) cm; (**e**) flat grass, \(H_{t}=H_{r}=50\) cm; and (**f**) flat grass, \(H_{t}=H_{r}=1\) m.  
Figure 2: Received power with different antenna heights: (**a**) flat concrete road; and (**b**) flat grass. 20 m, and then declined gradually. In general, the higher was the antenna height, the lower was the propagation loss of the link. This feature was especially noticeable when we compared the path losses with 5 cm and 1 m antenna heights. Figure 5 shows the similar characteristics in the flat grass scenario. We also tried to fix \(H_{\text{f}}\) to 5 cm, and vary \(H_{\text{r}}\) from 5 cm to 1 m. The pattern described above could still be clearly observed, i.e., higher receiving antenna led to higher received power. The antenna height is a key factor affecting the wireless link quality and the signal transmission distance. Therefore, when a WSN is deployed, increasing the antenna height is an effective method to obtain higher received power and gain better coverage.