## 5 Simulation Results
### Results  
The interference cancellation performance evaluation is conducted in two environments with SIR = 5 dB and 0 dB. First, the estimation performance of the fine frequency is evaluated. Figures 8 and 9 present the root mean square errors (RMSEs) of the estimated fine frequency under SIR = 5 dB and 0 dB, respectively. Let \(f_{F}T\) and \(\hat{f}_{F}T\) denote the normalized fine frequency to be identified and the estimated fine frequency, respectively. The RMSE is defined as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tap** & **Delay (_usec_)** & **Gain (_dB_)** \\ \hline
1 & 0 & \(-1\) \\
2 & 50 & \(-1\) \\
3 & 120 & \(-1\) \\
4 & 200 & 0 \\
5 & 230 & 0 \\
6 & 500 & 0 \\
7 & 1600 & \(-3\) \\
8 & 2300 & \(-5\) \\
9 & 5000 & \(-7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ETU channel model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline FFT size, \(N\) & 256 \\ Pilot length, \(L_{p}\) & 48 \\ CP length, \(L_{c}\) & 12 \\ Sampling clock, \(1/T\) & 1706 kHz \\ Carrier frequency & 2 GHz \\ Oversampling, \(P\) & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation environments. \[\sigma_{e}=\sqrt{E\big{[}\Big{(}f_{F}T-\hat{f}_{F}T\big{)}^{2}\big{]}} \tag{17}\]  
In Figures 8 and 9, the left and right subplots represent RMSEs for AWGN and ETU channels, respectively. As the SIR increases, the interference power decreases, which improves the estimation accuracy for SIR = 0 dB compared to SIR = 5 dB, particularly in the low-SNR region. The results also demonstrate that RMSE decreases as the frequency oversampling factor \(P\) increases. For \(P\) = 16, the RMSE reaches its minimum around SNR = \(-\)5 dB and remains almost the same at higher SNRs. Interestingly, the RMSE performance shows negligible differences between the AWGN and ETU channels. This result shows that the proposed NBI cancellation technique is robust to different channel models. These findings indicate that increasing \(P\) is beneficial for more complete NBI cancellation. For example, when the interference is much stronger than the desired signal or the modulation order is higher, a larger \(P\) would be preferable. In our BER simulations, \(P\) = 16  
Figure 8: RMSE performance for fine frequency estimation under SIR = 5 dB (**left**): AWGN channel; (**right**): ETU channel. Figure 9: RMSE performance for fine frequency estimation under SIR = 0 dB (**left**): AWGN channel; (**right**): ETU channel. was chosen as it provides a balance between precision and computational complexity, offering suitable performance for QPSK modulation under SIR = 0 dB and 5 dB. The performance is measured by comparing the BER after interference cancellation. Specifically, three BER curves are compared: the ideal BER performance without interference, the conventional interference cancellation technique [22], and the proposed interference cancellation technique. Figures 10 and 11 show the BERs in the AWGN channel for SIR = 5 dB and 0 dB, respectively. The dotted lines represent the results with a repetition of 1, while the solid lines show the results with a repetition of 4. For comparison with ideal performance, the BER performance without interference is also shown. In the ideal BER curve, a repetition of 4 improves the BER performance by approximately 6 dB. In Figure 10, when interference is present and no cancellation is applied, the worst performance is observed. When the conventional interference cancellation method is applied, some improvement in performance is noted, but significant performance degradation is still observed compared to the ideal BER. In contrast, when the proposed fine frequency shift interference cancellation is applied, BER performance shows negligible loss compared to the ideal BER, regardless of the repetition count. Figure 11 shows the performance when SIR = 0 dB.