## 5 Simulation Results
### Performance Evaluation  
Figure 2 presents the probability of erroneous estimation of the proposed IFO estimation scheme in the AWGN channel, considering the presence of residual FFO. A good match between analytical curves (lines) and simulated curves (symbols) is observed, regardless of the ISDB-T mode and residual FFO. In the case of the 2k mode, there is a slight gap between the theoretical and simulated curves for the high SNR region due to inaccuracy of the approximation used in (16), which tends to be more accurate as \(N_{t}\) increases. As expected, the performance of the IFO estimation scheme improves as the FFT size \(N\) increases, because the number of TMCC subcarriers is exactly proportional to the ISDB-T mode, as shown in Table 1. In particular, to cope with a limited number of TMCC subcarriers in 2k mode, the averaging strategy can be an appealing solution at the sacrifice of the processing delay, since the TMCC signal is continuously transmitted. In addition, the increase of uncertainty region for the IFO leads to the loss of detection accuracy, which becomes more prominent for a smaller number of TMCC subcarriers. Figure 3 shows the probability of an erroneous estimation of the proposed and conventional IFO estimators in the flat fading channel with the IFO range being fixed to \(M=5\), taking into consideration \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **2k Mode** & **4k Mode** & **8k Mode** \\ \hline Bandwidth & 5.575 MHz & 5.573 MHz & 5.572 MHz \\ \# of carriers per segments & 108 & 216 & 432 \\ \# of used carriers & 1405 & 2809 & 5617 \\ \# of GI samples & 256 & 512 & 1024 \\ \# of common TMCC carriers & 13 & 26 & 52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main system parameters. different transmission modes. It can be seen that the performance of the pilot-aided IFO detection scheme (10) can be better than that of the proposed detection scheme (14) in the absence of residual FFO \(\epsilon_{f}\) if the same number of pilot symbols as the TMCC is used in (10). The performance gap between both IFO estimators (10) and (14) is reduced to less than 1 dB as the number of pilots increases. When the residual FFO is present, however, it follows that this gap between both methods is further diminished, and eventually, the performance trend becomes reversed as the SNR increases. This is mainly because the performance of (14) is affected by the ICI only, whereas the performance of (10) is dependent on both the ICI and phase rotation caused by \(\epsilon_{f}\). When \(\epsilon_{f}=0\), the probability of erroneous detection of the blind estimation schemes (6) and (9) approaches zero when the SNR tends to infinity, whereas the probability of erroneous detection of the other schemes suffers from error floors. Due to the limited number of TMCC subcarriers in 2k mode, the blind estimation scheme (9) outperforms the proposed estimation scheme, whereas this phenomenon is reversed as \(N_{t}\) grows in 4k mode. This can be explained by recalling that the performance of the blind detection is constant to the ISDB-T mode. Figure 4 depicts the probability of erroneous estimation of the proposed and conventional IFO estimators in the TU channel, under the same simulation scenarios of Figure 3. Immediately, one can see that the trend of the curves is similar to that in Figure 3. Regardless of the ISDB-T mode, it is observed that the detection capability of the conventional IFO estimation methods (6) and (9) do not change. The reason for this is that its performance depends on the ratio of the number of data and  
Figure 3: Performance of the conventional and proposed IFO estimation schemes for the flat fading channel: (**a**) 2k mode, (**b**) 4k mode. Figure 2: Performance of the proposed IFO estimation scheme for the AWGN channel: (**a**) \(\epsilon_{f}=0\), (**b**) \(\epsilon_{f}=0.08\). null subcarriers. It is evident from Table 1 that this ratio is almost the same for all ISDB-T modes.