# Analysis of AMI Communication Methods in Various Field Environments
## 2 Power Line Communication for AMI
### Measurement Methods for Power Line Communication
The y-axis (horizontal axis on the right) represents the frequency in the range of 2.13 MHz to 23.156 MHz. The z-axis (vertical axis) shows the magnitude response of the channel \(|H(f)|\) in dB. From the results, it is clear that the attenuation increases as the distance or frequency increases. An interesting observation from Figure 5 is that the loss of the underground power line is larger than that of the overhead power line at the same distance. The power of the PLC signal at a receiving end can be measured by the spectrum analyzer. When measuring the received power, a measurement using the PLC modem signal can be inappropriate due to the large background noise compared to limited PLC modem powers. In other words, when the received power is not high enough, the measured value cannot accurately present the signal power due to the relatively high background noise. Thus, we indirectly observe the received power by using an RF signal generator instead of the PLC modem as follows. First, we measure the magnitude response of the channel with an RF signal generator which can output high-power sine waves. Using this method, the magnitude response of the channel \(|H(f)|\) can be measured from (2). However, obtaining a magnitude response \(|H_{c}(f)|:=|H_{p}(f)|+|H_{2}(f)|\) is further necessary instead of \(|H(f)|\) because the employed PLC modem provides signals after a coupler, i.e., \(y(t)\). This response can be obtained from a relationship of  
\[|H_{c}(f)|=|H(f)|-|H_{1}(f)|\ \ \ \text{(dB)}. \tag{3}\]  
Figure 6 shows an example of \(|H_{c}(f)|\), the magnitude spectrum of the power line combined with a coupler at the receiver side (MP 1 at Site 1-2, which will be described in Section 4). For the received signal \(z(t)\), the measured power \(P_{z}(f_{k})\) can be given as  
\[P_{z}(f_{k})\approx|H_{c}(f_{k})|+P_{y}(f_{k})\ \ \ \text{(dBm)}, \tag{4}\]  
where \(P_{y}(f)\) is the measured power of \(y(t)\), the transmitted signal after the coupler as shown in Figure 4a. An example of the calculated power spectrum of the received signal (MP 1 at Site 1-2) is shown in Figure 7a. Let \(P_{S}\) denote the total received power of signal \(z(t)\). Then the received power \(P_{S}\) can be calculated from the power spectrum as  
\[P_{S}\approx 10\log\left(\sum_{k=N_{1}}^{N_{2}}10^{P_{z}(f_{k})/10}\right)+10 \log(\Delta f)-10\log(B_{R})\ \ \ \text{(dBm)}. \tag{5}\]  
Figure 5: Magnitude response \(|H(f_{k})|\) of the PLC channel at various distances from (2). (**a**) Overhead power line. (**b**) Underground power line. Here, \(N_{1}\) and \(N_{2}\) respectively are the beginning and ending points of a significant PLC signal spectrum at the spectrum analyzer (note that \(1\leq N_{1}<N_{2}\leq N\)). After removing the signal source from the power line, the background noise spectrum at the MP can then be obtained. Let \(P_{n}(f_{k})\) denote the measured noise power at frequency \(f_{k}\) with a RBW of 10 kHz. Figure 7b shows an example of a background noise spectrum obtained at MP 1 of Site 1-2. The total noise power, which is denoted as \(P_{N}\), can be calculated in a similar way of (5) as  
Figure 4.0  
Then, from (5) and (6), the SNR at an MP can be obtained as \(SNR=P_{S}-P_{N}\).