# Link Investigation of IEEE 802.15.4 Wireless Sensor Networks in Forests
## 3 Performance of Single Link
### Propagation Analysis  
We first examine the PRR against the RSSI and the LQI. In experiments, two nodes \(A\) and \(B\) form the link with two directions, \(A\)-\(B\) and \(B\)-\(A\), for a given link distance and a given transmit power. Figures 10 and 11 give the correlation of the PRR and the RSSI and LQI, respectively. Figure 8: The asymmetry (\(D_{n\mathrm{s}i}\)) of RSSI under two different forest environments. (**a**) Bajia; (**b**) Campus. Figure 10: The PRR versus RSSI under two different forest environments. (**a**) Bajia; (**b**) Campus. Figure 9: The asymmetry (\(D_{l\mathrm{i}ij}\)) of LQI under two different forest environments. (**a**) Bajia; (**b**) Campus. It is clear in Figure 10 that the correlation between PRR and RSSI varies with an obvious transition in the two forest environments. When the RSSI is greater than \(-87\) dBm, the PRR is always beyond 90%, indicating a desirable link; when the RSSI is less than \(-92\) dBm, the PRR is close to zero; however, when the RSSI ranges from \(-92\) dBm to \(-87\) dBm, the PRR is hard to predict. Note here that the sensitivity of the CC2420 radio chip used in experiments is \(-90\) dBm. In the vicinity of such a threshold of sensitivity, the background noise might dominate so often that the PRR not only keeps lower, but also varies irregularly in a large range. In Figure 11, the PRR variation against the LQI also experiences a transition, which is not sharper than that in Figure 10. Comparing the two sub-figures in Figure 11, it can be found that most points in Figure 11b are located on the top right, where the PRR and the LQI are both larger. Recall that in Figure 3, the link in the Campus forest (especially in the direction _A-B_) produces higher LQI measurements than that in the Bajia forest. According to the PRR vs. LQI distribution, we have that an LQI larger than 96 can lead to a link with PRR beyond 90%, but when the LQI is less than 96, the PRR varies greatly within 90% and zero. For instance, in the Bajia forest, for the LQI of 75, the corresponding PRR may be equal to 5% or 85%, and for the PRR of 60%, the LQI may be equal to 70 or 90. Though the link is very dynamic in forest environments, studying the propagation of low-power wireless radios in forests are still helpful to configure relatively reliable parameters in simulation experiments. The radio signal suffers from attenuation during propagation, i.e., the signal strength generally decays, according to Equation (1), as the distance between sender and receiver increases. In Equation (1), \(d\) is the physical link distance, \(P_{0}\) is the received signal power of the receiver one meter away from the sender and \(n\) is the parameter that weighs the signal attenuation on communication distance. The key job of modeling the propagation attenuation is to determine \(n\). In this paper, we consider the RSSI measurement as the received signal strength and transform Equation (1) into Equation (2). \[P=P_{0}\,d^{-n} \tag{1}\]  
\[P(\mathrm{dBm})=P_{0}(\mathrm{dBm})-10\times n\times\log_{10}\,d \tag{2}\]  
We treat the \"\(10\log_{10}\,d^{\prime}\)\" to be a factor and deduce a linear regression model ( i.e., the linear least square) to fit parameter \(n\); the results for the Bajia forest are shown in Figure 12. We find that the attenuations are different from transmit power to transmit power. We here give results with the highest and the lowest transmit powers (31 and 11, respectively). In Figure 12, the small dots represent the RSSI distribution and the triangles the mean of RSSI measurements. We give two types of linear fits: the solid line is obtained according to the RSSI in all Bajia experiments and the dashed line according to the RSSI in Bajia experiments with a link distance not greater than 28 m. Such a choice is determined  
Figure 11: The PRR versus LQI under two different forest environments. (**a**) Bajia; (**b**) Campus.