# Channel Characterization and SC-FDM Modulation for PLC in High-Voltage Power Lines
## 5 Performance Analysis  
The performance of the proposed PLC system with the OFDM and SC-FDM modulation schemes was evaluated through bit-transmission speed, achieved by the _m-th_ constellation and bandwidth utilized, i.e., for an ideal OFDM system without guard intervals and pilots with a spectral efficiency equal to:  
\[E_{ideal}=\frac{N\alpha/T}{N/T}=\alpha\qquad(bits/s/\mathrm{Hz}) \tag{23}\]  
where \(2^{\alpha}\) corresponds to the data constellation size. Therefore, \(N\alpha/T\) represents the system throughput, and \(N/T\) corresponds to the system bandwidth. However, the annexation of guards and pilots in practical OFDM systems gives:  
\[E_{real}=E_{ideal}\bigg{(}\frac{N-N_{p}}{M+N}\bigg{)}\qquad(bits/s/\mathrm{Hz}) \tag{24}\]  
where \(N\) indicates the size of the OFDM symbol, \(N_{p}\) the number of pilots used and \(M\) the size of the CP. The system was tested and compared under the PLC-channel simulation environment for each coupling scheme in Table 1. The configuration parameters are shown in Table 3. For data transmission, the 64 QAM and 32 QAM constellations were used. The impulse response of the different channels in the discrete baseband representation is modeled as a FIR filter whose taps come from the inverse discrete Fourier transform of the sampled  
Figure 10: Models of the PLC-OFDM and PLC SC-FDM receivers in the baseband processing stages. Figure 9: Model of the PLC channel. transference functions. The maximum longitude was truncated to an interval that contained practically all of the signal energy, approximating this with \(L=50\) taps. In order to obtain raw data regarding the performance of the proposed system, channel-coding stages have been omitted. Consequently, the bit error rate (BER) is calculated directly after quantizing the equalizer output (bit detection). Two testing schemes were carried out for the system evaluation, the first consisting of the system operation with the abovementioned parameters using the conventional OFDM and the second consisting of precoding the data with the aid of the SC-FDM. Figure 11 shows the BER obtained for each coupling mentioned in Section 2, utilizing the OFDM modulation. For an SNR equal to 12 dB or lower, it can be observed that all couplings maintain a similar performance. However, for high SNR levels, the differences between the BER for each coupling become higher. For example, the difference between coupling \(A_{\text{c}_{1}}\) and \(A_{\text{c}_{4}}\) is of an order of magnitude for an \(SNR=20\) dB, while the other couplings that do not present fading as severe as in \(A_{\text{c}_{4}}\) maintain a similar behavior. Figure 12 shows the BER obtained using the SC-FDM scheme and the same testing configuration as before. A significant improvement can be observed for each coupling, maintaining a similar behavior under 20 dB in the SNR and a five-fold improvement in coupling \(A_{\text{c}_{4}}\) with respect to tests carried out with the conventional OFDM modulation. These results corroborate that the use of the SC-FDM significantly increases the raw performance of the PLC without a loss of spectral efficiency. Figure 11: BER vs. SNR comparison of the proposed conventional OFDM communication system among each of the couplings with \(N_{p}=16\), \(FFT=256\), 64 QAM and \(BW=200\) kHz. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline FFT size & \(N=256\) \\ CP & \(N_{g}=(1/16)N\) \\ Sampling frequency & \(F_{s}=200\) kHz \\ Carrier frequency & \(F_{c}=150\) kHz \\ Data carriers & \(N_{D}=220\) \\ Pilot carriers & \(N_{P}=16\) \\ Guard carriers & \(N_{G}=20\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: OFDM System Parameters. Figure 13 shows the BER results obtained with respect to energy per bit to noise power spectral density ratio (Eb/N0). This experiment reveals the impact of the average attenuation of each PLC coupling when the transmitter energy per bit is fixed. As in the previous test, the SC-FDM scheme is used.