# Channel Characterization and SC-FDM Modulation for PLC in High-Voltage Power Lines
## 5 Performance Analysis
It can be seen that in comparison to Figure 12, there are significant differences in the performance. The best results are achieved using the \(A_{c_{5}}\) coupling, in contrast with the \(A_{c_{4}}\) coupling, which has a significant loss of performance. The \(A_{c_{1}}\) and \(A_{c_{2}}\) couplings showed similar performance due to their closeness in frequency response and attenuation levels. Figure 12: BER vs. SNR comparison of the proposed SC-FDM communication system among each of the couplings with \(N_{p}=16\), \(FFT=256\), 64 QAM and \(BW=200\) kHz. Figure 13: BER vs. Eb/N0 comparison of the proposed SC-FDM communication system among each of the couplings with \(N_{p}=16\), \(FFT=256\), 64 QAM and \(BW=200\) kHz. Figure 14 illustrates the comparison of the two modulation schemes over coupling \(A_{c_{5}}\). [PERSON]'s HV-PLC model [6], which does not include reflection and coupling equipment effects, is compared there against the one being proposed here. The 3 dB performance difference (see Table 4) in Figure 14 shows the relevance of including the previously mentioned effects. The spectral efficiency achieved in the system is 5.2941 bit/s/Hz using the 64 QAM constellation with a transmission capacity of 1.058 Mbits/s for the selected bandwidth, representing a better throughput than conventional PLC systems, unable to counteract the frequency selectivity of the channel to the BW above 100 kHz, which sustain transmission capacities between 28 kbit/s and 100 kbit/s. The superiority of the SC-FDM modulation scheme can be seen in Figure 15. For an SNR = 18 dB, we obtain a BER lower than \(10^{-4}\) with a spectral efficiency of 5.2941 bit/s/Hz. In order to achieve the same performance with the conventional OFDM scheme, the constellation must be reduced to 32 QAM, obtaining an inferior spectral efficiency of 4.4118 bit/s/Hz, or the constellation can be kept at 64 QAM with a cost of 3 dB in the SNR to sustain the same spectral efficiency. It is also important to highlight that a better performance can be obtained in all cases utilizing channel-coding schemes and forward-error correction (FEC) at the cost of throughput reductions. Finally, Figure 16 shows the comparison in the performance between the conventional PLC-systems, the modulation scheme 8-QAM of a single carrier (SC) and the linear equalization least mean squares (LMS) on the data reception, in contrast to the system proposed in this paper, both in 64 kHz bandwidth. The operating superiority of the SC-FDM scheme is shown as above 12 dB SNR, exhibiting a difference above 4 dB in performance for the couplings \(A_{c_{1}}\), \(A_{c_{2}}\), \(A_{c_{3}}\), \(A_{c_{5}}\) and above 8 dB with respect to \(A_{c_{4}}\). Figure 14: BER vs. SNR comparison of the proposed OFDM and SC-FDM communication systems for the \(A_{c_{5}}\) with \(N_{p}=16\), \(FFT=256\), 64 QAM and \(BW=200\) kHz. Solid lines represent the results using the proposed channel model and dashed lines represent the results obtained with [PERSON]’s channel model. Figure 16: BER vs. SNR comparison of the proposed SC-FDM and SC-LMS communication system for the \(A_{c_{5}}\) with \(N_{p}=16\), \(FFT=256\) and \(BW=64\) kHz, 8 QAM, \(F_{c}=150\) kHz. \begin{table}
\begin{tabular}{c c c} \hline \hline
**BER** & **OFDM Conventional** & **SC-FDM Proposed** \\ \hline \(10^{-3}\) & 16.5 dB (SRN) & 15 dB (SNR) \\ \(10^{-4}\) & 19 dB (SRN) & 17 dB (SNR) \\ \(10^{-5}\) & 22.5 dB (SRN) & 18 dB (SNR) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Raw bit error rate performance comparison. Figure 15: BER vs. SNR comparison of the proposed OFDM and SC-FDM communication system for the \(A_{c_{5}}\) with \(N_{p}=16\), \(FFT=256\) and \(BW=200\) kHz. Configurations cover 64 QAM SC-FDM, 64 and 32 QAM conventional OFDM.