# Characterization of Narrowband Noise and Channel Capacity for Powerline Communication in France
## 3 Main Experimental Results and Discussion
### Transfer Function Analysis and Signal-to-Noise Ratio  
Figure 16 gives the results of the transfer function analysis for each site. Regarding the urban and urban dense sites, the attenuation is less than the rural and the sub rural site one. The strong attenuation in the rural site is mainly caused by the line attenuation of the overhead cables.  
Figure 16: Results of transfer function analysis for each site.  
Figure 15: Noise at the urban dense 1 site.  
The signal-to-noise ratio (SNR) is an indicator of the quality of the PLC transmission. From a literature review, the reliability of NB-PLC technologies such as the G1-PLC and G3-PLC can be summed up in Figure 17. It represents the bit error rate (BER) for each kind of modulation depending on the quality of the transmission in terms of SNR-values.  
As can be seen in Figure 17, the G3 Alliance fixed the minimum accepted BER level (i.e., \(10^{-4}\)). So, it enables to evaluate the performances of the G3-PLC technology. Table 1 gives the SNR threshold that allows communication with a maximum BER equal to \(10^{-4}\).  
As can be seen in Equation (4), in this study, is the SNR-parameter corresponds to the ratio between the power of the received signal in the receiver side and the power of the noise measured at the same point of the electrical network [36; 37]. In this study, the received signal and the noise are measured simultaneously at noon.  
\[SNR_{dB}=10\cdot\log\left(\frac{Pe\cdot\left|H(f)^{2}\right|}{Pn}\right) \tag{4}\]  
* _Pe_: emitted power of the signal. This parameter is set to 120 dB\(\mu\)V.
* _f_: frequency.
* \(\left|\left.H(f)\right|\right.\): transfer function modulus.
* _Pn_: noise power measured at 10 a.m.  
As can be seen in Figure 18, the evolution of the SNR shows negative values in the low frequencies for all sites and especially, in the sub rural site. When the SNR tends to zero, the white noise and the PLC signal have an equivalent power. When the SNR is lower than zero, the noise has a higher power than the PLC signal. When the SNR is higher than zero, the noise has a lower value than the PLC signal.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Modulations** & **G1 (S-FSK)** & **G3 (D8 PSK)** & **G3 (DQPSQ)** & **G3 (DBPSK)** & **G3 (Robo)** \\ \hline SNR (TEB: \(10^{-4}\)) & 12 dB & 9.6 dB & 5.6 dB & 2.5 dB & \(-1.2\) dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: SNR maximum value for the G1-PLC and G3-PLC technologies.  
Figure 17: Reliability of the G1-PLC and the G3-PLC technologies: source G3-PLCTM Alliance [38].  
The quality of the network in the urban dense 1 and urban dense 2 sites enables to use less complex transmission techniques. Moreover, it offers higher transmission rates. Many technologies, such as the PRIME and G3-PLC communication protocols, are based on the OFDM modulation. It can operate in two modes of transmission: a normal mode and a robust mode. The G3-PLC communication protocol uses either the differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK) or differential 8-Phase Shift Keying (D8 PSK) modulation for each of its 36 subcarriers. It incorporates error correction by convolutional coding and Reed Solomon coding. The robust mode works identically except that it also applies a repetition of the bit to be transmitted which must be equal to four times. The aim is to increase the transmission reliability, but it strongly limits the useful rate.