## 5 Simulation Results and Discussions  
The simulations have been conducted to verify the usefulness of the proposed estimation scheme, considering the standard ROBO and high-speed ROBO modes. In our simulations, the HomePlug GP system is operated at 1.8\(\sim\)30 MHz frequency band. We use the main system parameters such as \(N=3072\), \(N_{g}=417\), \(N_{b}=1155\), and \(N_{c}=916\) carriers distributed in the frequency from approximately 1.8 MHz to 30 MHz. Table 2 summarizes the simulation parameters used in the experiment. To show the performance, the PLC channel model specified in the standard [29] is considered. Especially, Class 1 channel model is used, which represents scenarios with strong signal attenuation. To estimate the channel, a simple least square (LS) channel estimation followed by a one-tap FEQ is used for the conventional DD schemes. To make a fair comparison, the conventional estimation scheme C considers \(N_{o}=D+1=4\) so that it uses four consecutive OFDM blocks. To fully implement Equation (23), we have to know the subset configuration consisting of \(F_{m}\) and \(N_{m}\), which is determined depending on the system parameters and tone mask. Taking into account the North American carrier mask and the OFDM parameters specified in the ROBO modes [11], one can obtain that \(N_{s}=11\) for standard ROBO mode and \(N_{s}=10\) for high-speed ROBO mode. It is interesting to note that there are two or more subset configurations because the data symbol is repeated four times in standard ROBO mode. In this case, the subset configuration having the optimal MSE is selected. Table 3 lists the basic design parameters of the subset searched for each ROBO mode. In Figure 1, we compare the proposed scheme with three conventional DD schemes presented in Equations (6), (7), and (10) when \(\Delta_{s}=15\) ppm. For the sake of fairness, LS channel estimation scheme is adopted to compute (4) and the same channel estimate is used for Equations (6), (7), and (10). It is evident that there is a good match between theoretical analysis and simulated results. From the figure, one can find that the conventional schemes A and B have a non-negligible bias for high SNR condition, which is attributed to the reason that the frequency selectivity of the channel considerably affects the estimation performance as former work [23]. Unlike the conventional methods A and B, the effect of the frequency selectivity on the performance of the proposed scheme and the conventional scheme C is marginal. Since the conventional scheme C spends more OFDM blocks for estimation, its performance is slightly better than that of the proposed estimation scheme. Regardless of the ROBO mode, the performance of existing schemes is almost the same because they perform on carrier-by-carrier basis. On the other hand, the performance of the proposed scheme depends on the ROBO mode, which is mainly because of the different subset configurations as given in Table 2. In this example, the performance of the standard ROBO mode is about 2 dB better than that of the high-speed ROBO mode. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Sampling rate & \(f_{s}=75\) MHz \\ FFT size & \(N=3072\) \\ CP size & \(N_{g}=417\) \\ Number of subcarriers & \(N_{b}=1155\) \\ Number of non-masked subcarriers & \(N_{c}=916\) \\ Modulation & QPSK \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 2 illustrates the MSE curves between the existing and proposed estimation schemes versus SFO values. It is found that the performance of the conventional schemes A and B strongly relies on the amount of SFO. The performance of the conventional method C keeps stable about up to \(\Delta_{s}=15\) ppm, whereas the proposed estimation algorithm shows a substantial robustness against the amount of SFO regardless of ROBO modes and SNR values. This phenomenon means that the existing estimation schemes will experience an error floor due to SFO as SNR grows.