# Transmission Power Control in Wireless Sensor Networks Using Fuzzy Adaptive Data Rate
## 3 Adaptive Fuzzy Control Algorithm and Analysis of Power Consumption
### Relationship between PER and SNR  
Because RSSI is sensitive to environmental interference, it is an unreliable parameter, therefore, it will be difficult to evaluate the communication quality. Therefore, SNR is adopted for evaluating communication quality. According to [33], minimum detectable signal (MDS), also known as receive sensitivity, can be calculated by Formula (3). This paper takes the average SNR at PER 1% as receiver sensitivity.  
\[Sensitivity(dBm)=SNR+Noise \tag{3}\]  
The demodulator of CC1310 is a non-coherent demodulator of 2 FSK. From [34] we can learn the method to calculate the relation between Bit Error Rate (BER) and SNR, and the result can be extended to the relation of PER and SNR by importing the relation between BER and PER. We can obtain  
\[PER=1-\left(1-\frac{1}{2}e^{-\frac{E_{b}}{N_{0}}}\right)^{n} \tag{4}\]  
where \(\frac{E_{b}}{N_{0}}\) can be obtained by  
\[\frac{E_{b}}{N_{0}}=10^{(SNR+offset)/10} \tag{5}\]  
where \(n\) denotes data length.  
Each data rate has a different offset expressed in Equation (4). Figure 4 is illustrated to measure the relationship between PER and SNR. In this architecture, two CC1310 devices  
Figure 3: Relationship between power consumption, data rate, and transmission power.  
are utilized as the transmitter and receiver. The transmitter connects with a programmable attenuator. The programmable attenuator has an attenuation range from 0 to 120 dB and can be fine-tuned in 0.5 dB. After the transmitter had transmitted 1000 packets, the receiver recorded average SNR and PER for each attenuation. Owing to uncertain interferences around the environment, the experiment was made in an anechoic chamber.  
The offsets of each data rate are presented in Table 3. Substitute the offsets into Equation (4) to obtain the receiver sensitivity under PER 1%. Table 4 presents the values of SNR for each data rate under PER 1%, and the fixed value indicated in Table 4 is substituted into Equation (3) to obtain a sensitivity. The sensitivity is a dynamic value determined by time-varying noise. When the RSSI which is obtained from the received packet is higher than sensitivity, it means that the PER will be below 1% in theory. The lower the sensitivity, the better the receiving ability is. When the noise is fixed, the higher data rate results in a higher sensitivity and worse receiving ability; however, it reduces the power consumption by reducing the transmission time.  
Figure 5 illustrates the relation curves of four different data rates. To save more power, it can be achieved by adjusting the data rate and transmission power. There is an example given below to explain the algorithm concept proposed in this study. The transmission power of a sensor node is 10 dBm, its data rate is 50 kbps, and its SNR locates at 5.22 dB. In these conditions, the power consumption can be reduced further without changing the communication quality by simultaneously altering data rate and transmission power. The original and possible combinations which comprise data rate and transmission power are presented in Table 5. The combination of most power saving is 200 kbps and 13 dBm, and it can save power approximately 78% off the original set. However, 300 kbps is not a suitable data rate for this condition because its transmission power requires 16 dBm; this  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Data Rate (kbps)** & **12.5** & **50** & **100** & **200** & **300** & **400** & **450** & **500** \\ \hline \(SNR_{PER\,1\%}\) (dB) & 2.75 & 5.22 & 7.10 & 7.60 & 10.50 & 11.45 & 12.93 & 16.13 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Offsets of each data rate.  
Figure 4: Experimental architecture for relation of PER and SNR.  
is explained by the transmission power beyond the adjustment range to the device. In this case, the power consumption can be reduced by increasing data rate and transmission power simultaneously but not changing the communication quality.