## 5 Simulation and Analysis
### DOA Estimation Performance  
Figure 2 illustrates the spatial spectrum generated by the Cyclic-MUSIC algorithm at both zero cyclic frequency and base cyclic frequency, with an SNR of \(-5\) dB. It can be seen from the figure that, when \(\alpha=0\), the Cyclic-MUSIC algorithm estimates three peaks, corresponding to the directions of one OFDM signal and two DME signals, while it cannot distinguish the desired from the interfering signals. When \(\alpha=1/T_{s}\), the algorithm estimates the only peak, which is the DOA of the OFDM signal.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Theoretical Complexity** \\ \hline Proposed & \(\mathcal{O}(LPQM^{2})\) \\ INCM-volume & \(\mathcal{O}\big{(}\max(SM^{2},M^{3.5})\big{)}\) \\ INCM-linear & \(\mathcal{O}\big{(}M^{3.5}\big{)}\) \\ INCM-projection1 & \(\mathcal{O}\big{(}\max(SM^{2},JM^{2})\big{)}\) \\ INCM-projection2 & \(\mathcal{O}\big{(}\max(TM^{2},LM^{3.5},SM^{2},JM^{2})\big{)}\) \\ INCM-subspace & \(\mathcal{O}(LM^{3})\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of algorithm complexity.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Transmission Bandwidth & 498.05 kHz \\ FFT Length & 64 \\ Subcarrier Spacing & 9.765625 kHz \\ Cyclic Prefix Time & 17.6 μs \\ Effective Symbol Time & 102.4 μs \\ OFDM Symbol Period & 120 μs \\ Number of Effective Subcarriers & 50 \\ Channel Coding & RS + Convolutional Coding \\ Modulation Method & QPSK \\ DME Carrier Offset & 500 kHz \\ Array Type & Uniform Linear Array \\ Number of Array Elements & 10 \\ Element Spacing & Half-wavelength \\ Channel Type & AWGN Channel \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 3 presents the spatial spectrum produced by the Cyclic-MUSIC algorithm at an SNR of 20 dB. By analyzing and comparing the simulation results in Figures 2 and 3, it can be observed that the Cyclic-MUSIC algorithm can accurately estimate the direction of OFDM signals at both high and low SNRs. Moreover, the DOA estimation performance is better when SNR = 20 dB, with a more distinct normalized spectral peak.  
To further investigate the relationship between DOA estimation performance with SNR, root mean square error (RMSE) is introduced with the equation  
\[\text{RMSE}=\sqrt{\frac{1}{\text{MC}}\sum_{k=1}^{\text{MC}}\left(\hat{\theta}_ {mk}-\theta_{mk}\right)^{2}} \tag{33}\]  
where _MC_ represents the number of Monte Carlo experiments, \(\hat{\theta}_{mk}\) represents the estimated angle of the \(m\)th signal in the \(k\)th Monte Carlo simulation, and \(\theta_{mk}\) represents the actual angle of the \(m\)th signal.  
Figure 4 depicts the simulation of the RMSE variation curve relative to the SNR for OFDM signal estimation using the Cyclic-MUSIC algorithm. It can be clearly seen that the RMSE of DOA estimation is small at both high and low SNRs, proving that the algorithm can accurately estimate the direction of the OFDM signal in both scenarios. Additionally, the RMSE decreases as the SNR increases, indicating that the performance of the Cyclic-MUSIC algorithm improves with increasing SNR.  
Figure 3: Power spectrum of Cyclic-MUSIC algorithm at SNR = 20 dB.  
Figure 2: Power spectrum of Cyclic-MUSIC algorithm at SNR = \(-5\) dB.