# Environmental Impacts on Hardware-Based Link Quality Estimators in Wireless Sensor Networks
## 5 Environmental Impacts on Hardware-Based LQEs
### Environmental Impacts on SNR Based LQEs  
#### 5.3.1 SNR and PRR in Different Environments  
Figure 12 shows the relationship between _SNR_ and _PRR_ in different environments, including the minimum, maximum, and mean value of _SNR_. Generally, _SNR_ is calculated as follows [12; 21; 22]:  
\[SNR=RSSI-N \tag{16}\]  
where _RSSI_ and \(N\) are the received signal power and background noise power in dBm. It can be seen that the trend of change between _SNR_ and _PRR_ is basically the same for the three different environments. In terms of \(\mu_{sur}\), _PRR_ increases as \(\mu_{sur}\) increases. When \(\mu_{sur}\) is lower than 4.5 dB, _PRR_ approaches 0; when \(\mu_{sur}\) is higher than 8 dB, _PRR_ approaches 100%; when \(\mu_{sur}\) is located between 4.5 dB and 8 dB, _PRR_ rapidly increases from 0 to 100%. In terms of the fluctuations of _SNR_, it is significantly greater in the corridor than that in the runway and artificial lawn.  
To describe the impact of environmental changes on the fluctuations of _SNR_ more intuitively, the fluctuation ranges of _SNR_ in different environments were statistically obtained, and their CDFs are shown in Figure 13. The fluctuation range of _SNR_ is calculated by subtracting the minimum _SNR_ from the maximum one. It can be seen that the fluctuation range of _SNR_ in the corridor is the largest, with more than 80% of the fluctuation range higher than 10 dB, and about 30% higher than 15 dB. In contrast, the fluctuation range in the artificial lawn is much smaller. There is less than 2% of the fluctuation range higher than 10 dB, while none is higher than 15 dB. The fluctuation range in the runway is between the corridor and artificial lawn, with about 20% of the fluctuation range higher than 10 dB and about 3% higher than 15 dB.  
Furthermore, the background noise in these different environments was also measured, and their CDFs in different environments are shown in Figure 14. It is clear that the fluctuation range of background noise in the corridor is the largest, and that in the lawn is the smallest. From Equation (16), it is obvious that _SNR_ is related to both _RSSI_ and background noise. Combined with Figures 9 and 13, it is reasonable to say that background noise is also contributed to the fluctuation range of _SNR_ in different environments.  
Figure 12: _SNR_ vs. _PRR_ in different environments.  
To observe the environmental impact on the relationship between _SNR_ and _PRR_ more clearly, the relationship between \(\mu_{sur}\) and _PRR_ is shown in Figure 15. There already exist some studies which utilize the relationship between _SNR_ and _PRR_ to estimate link quality [8; 21; 22; 23; 24; 26; 27]. It can be seen that there is no obvious difference between the relationships between \(\mu_{sur}\) and _PRR_ in different environments. This means that the relationship between \(\mu_{sur}\) and _PRR_ is almost unaffected when the environment changes.  
Figure 14: CDFs of the background noise in different environments.  
Figure 13: Cumulative distribution functions (CDFs) of the fluctuation range of _SNR_ in different environments.  
Figure 15: \(\mu_{sur}\) vs. _PRR_ in different environments.