## 5 Performance Evaluation  
Extensive simulations are carried out to compare the performance of the conventional and the proposed methods in the presence of the NBI under different channel conditions. In this work, we conducted simulation tests that are consistent with the theoretical models and methods provided to evaluate the performance. As claimed in Section 2, note that all the methods are simulated with the same preamble length for fair comparison. The simulation setup is configured in a typical PLC transmission system, with the parameters listed in Table 1. A multipath PLC channel model defined in [26] is applied to evaluate the detection  
Figure 5: Frequency–domain correlation results with signaling and different integer CFOs. algorithm in multi-path and power line transmission environments, with the profile of parameters listed in Table 2. The length of the frequency-domain TS for the OFDM preamble is set as \(L=192\), so at least the 7-bit signaling information can be conveyed. The simulations consider introducing an NBI with the power of \(-12\) dB with respect to the average signal power, in order to evaluate the capability of different methods against the NBI. The false probability for the SAC peak detection is simulated to evaluate the detection performance of the proposed and conventional preambles. As shown in Figure 6, at the target missed probability of \(10^{-3}\), the false probability of the proposed method is compared with that of [PERSON]'s method. It can be observed from Figure 6 that the false probability of the proposed method has a 4 dB gain over [PERSON]'s method under AWGN and PLC channels in the absence of the NBI. When the NBI is present, which is marked by dashed lines in Figure 6, it is shown that the proposed method is hardly affected by the NBI, whereas [PERSON]'s method suffers from a degradation of more than 1 dB under AWGN channel and more than 4 dB under the PLC channel. In order to investigate the SAC peak performance of different preambles in the presence of the NBI, as depicted in Figure 7, the SAC peaks of [PERSON]'s and the proposed methods \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline NBI power & \(-12\) dB \\ Symbol Rate & \(7.56\) MSymbol/s \\ Bandwidth & \(8\) MHz \\ Carrier Frequency & \(6\) MHz \\ CFO & \(30\) kHz \\ Symbol Duration & \(270.9\)\(\upmu\)s \\ Length of TS & \(192\) \\ FFT Size & \(1024\) \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter. \begin{table}
\begin{tabular}{c c c c c} \hline
**Path Index** & \(d_{i}\) **(m)** & \(g_{i}\) & & \\ \hline
1 & 200 & 0.64 & \(k\) & \(1.0\) \\
2 & 222.4 & 0.38 & \(a_{0}\) (s/m) & \(0\) \\
3 & 244.8 & \(-0.15\) & \(a_{1}\) (s/m) & \(7.8\times 10^{-10}\) \\
4 & 267.5 & 0.05 & & \\ \hline \end{tabular}
\end{table} 
Table 2: PLC channel parameter profile. Figure 6: False probability of preamble detection in AWGN and PLC channels when the missed probability is around \(10^{-3}\). in the presence of the \(-12\) dB NBI are simulated, which is compared with the case without NBI in Figure 4. It can be noted from Figure 7 that the SAC peak of [PERSON]'s method in the presence of NBI is significantly smaller than that without NBI in Figure 4. Moreover, the sub-peaks of [PERSON]'s method become stronger and the main peak becomes less sharper with respect to that without NBI, making the false timing detection probability increase. On the other hand, the SAC peak of the proposed method is almost not affected by the \(-12\) dB NBI, so the timing performance in the presence of the NBI is guaranteed. Finally, to investigate the performance of the integer CFO estimation and signaling detection, their false probabilities are simulated and presented in Figure 8. It is observed from Figures 5 and 8 that, if the preamble is correctly detected, it is feasible to accurately estimate both the integer CFO and the signaling information. One should note that, the signaling can be decoded correctly if and only if both pairs of peaks shown in Figure 5 are detected correctly.