## 4 Simulation Results  
The major system parameters adopted in our simulation are summarized in Table 1. The modulation scheme was DBPSK. The FEC encoder comprised outer as well as inner channel encoders. The outer channel encoder was Reed-Solomon (255, 239), which means that Reed-Solomon (RS) encoder required 239 data bytes, to which were added parity bytes to make a 255-byte codeword.  
The corresponding RS\((255,239)\) decoder at the receiver side was able to correct up to 8 bytes in the codeword. The inner channel encoder was a convolutional encoder with code rate \(r=1/2\) and constraint length \(K=7\). The generator sequences were \(171_{\mbox{octal}}\) and \(133_{\mbox{octal}}\).The frequency range used to transmit data was within the CENELEC A band and the sampling rate of the received signal was \(f_{\mathrm{s}}=400\) kHz. The length of the FFT was \(N_{\mbox{FFT}}=256\), of which 36 points were used for data carriers and 36 points were used for its conjugate parts. The remaining 184 carriers were null carriers. The first and last data carriers were placed at 35.9375 kHz and 90.625 kHz, respectively. The length of the CP was 30 points.  
In accordance with (2), we used a 50-path (\(N_{\mbox{path}}=50\)) powerline model with attenuation parameters \(a_{0}=10^{-3}\), \(a_{1}=2.5\times 10^{-9}\), and \(a_{2}=1\). The resulting impulse response of the powerline channel \(h[n]\) and its magnitude response \(|H(f)|\) are presented in Figure 5.  
The PGCSM model (see (3)) was used to produce additive CSIN according to the parameters stipulated in IEEE 1901.2 ([13], Annex D.3.1.2, LV14). The parameters provided in the Annex D.3.1.2 for modeling the CSIN were obtained by conducting field measurements in the low voltage substation and then fitting these measured data into models. Thus, even we did not collect the CSIN data by conducting real measurements, the simulation results could still reflect the situations in the real low voltage NB-PLC networks. The corresponding time-domain trace, spectrogram, and CSD plots are shown in Figure 6a-c, respectively. Note that the color bars in Figure 6b,c are used to indicate the strength of the resulting spectrogram and CSD function associated the additive CSIN at \(E_{b}/N_{0}=0\) dB. In general, the resulting values of CSD function are represented in linear scale as shown in Figure 6c, which clearly reveals the fundamental cyclic frequency is about 120 Hz. The value of GINR \(\Gamma\) is 0.01. Figure 7 illustrates the signal-to-interference-plus-noise ratio (SINR) at each subcarrier of the received signal when \(E_{b}/N_{0}=0\) dB. Note that our data subcarriers are mainly distributed between about \(0.36\times 10^{5}\) to \(0.9\times 10^{5}\) Hz.  
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Modulation & Differential binary phase shift keying (DBPSK) \\ Forward error correction (FEC) outer encoder & Reed-Solomon coding (RS(255,239)) \\ FEC inner encoder & Convolutional coding (\(r=1/2\), \(K=7\), \(g=(171_{octal},133_{octal})\)) \\ Frequency range & 35.9–90.6 kHz (CENELEC A) \\ Sampling rate (\(f_{\mathrm{s}}\)) & 400 kHz \\ Fast Fourier transform (FFT) length (\(N_{\mbox{FFT}}\)) & 256 \\ Data subcarriers & 36 \\ Null subcarriers & 184 \\ Cyclic prefix (CP) length & 30 \\ \hline \end{tabular}
\end{table}
Table 1: Simulation parameters for the NB-PLC systems.  
Figure 5: (**a**) Impulse response \(h[n]\) and (**b**) magnitude response \(|H(f)|\) of the powerline channel used in the computer simulation.  
Figure 6: (**a**) time-domain trace, (**b**) spectrogram, and (**c**) CSD plots for the generated CSIN data.