# Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources
## 6 Simulation Results  
In this section, we validate the effectiveness of the proposed simultaneous CI technique and compare it with both the conventional CI method and the classical subspace-based MUSIC method. In addition, as described above, we show that the multi-sample diversity of the proposed simultaneous CI technique improves the direction-finding performance even in the low-SNR regime. For computer simulations, we set the carrier frequency of signals to 1542 MHz, which is equal to the carrier frequency of the Global Positioning System (GPS) over L1 band. A UCA with \(M\) antenna elements is considered, and the radius of the UCA is assumed to be \(\lambda/2\), where \(\lambda\) represents the wavelength of the carrier frequency. Both UCA and ULA with M antenna elements are considered. In the UCA structure, the radius is assumed to be spaced at one degree for both the azimuth \(\hat{\phi}\in(0^{\circ},360^{\circ}]\) and elevation angle \(\hat{\theta}\in[0^{\circ},90^{\circ}]\). The detailed simulation parameters are summarized in Table 1.  
As a performance metric, the Root Mean Squared Error (RMSE) is considered to evaluate the direction-finding performance through Monte Carlo simulations. Specifically, when the azimuth and elevation angle estimates for the \(k\)-th source in the \(n\in\{1,\cdots,N\}\) iteration are \(\hat{\phi}_{k,n}^{*}\) and \(\hat{\phi}_{k,n}^{*}\), respectively, the RMSE is defined as [30]  
\[\text{RMSE}=\sqrt{\frac{1}{NK}\sum_{n=1}^{N}\sum_{k=1}^{K}\bigg{[}\big{(}\hat {\phi}_{k,n}^{*}-\phi_{k,n}\big{)}^{2}+\big{(}\hat{\theta}_{k,n}^{*}-\theta_{ k,n}\big{)}^{2}\bigg{]}}, \tag{10}\]  
where \(\phi_{k,n}\) and \(\theta_{k,n}\) denote true azimuth and elevation angle of the \(k\)-th source in the \(n\)-th iteration, respectively. Figures 4-10 show the RMSE of DOA estimation performance of the proposed simultaneous CI-based DOA estimation technique with UCA structure at the receiver. Figure 4 shows the RMSE performance of the simultaneous CI technique with UCA receiver according to SNR while considering a single source over multiple time-domain samples. In this simulation, Figure 4 considered DOA of signal sources \(\phi=40^{\circ}\) and \(\theta=10^{\circ}\), respectively. For the conventional CI method, the mean value of the received signal over all samples is used for DOA estimation. The RMSE of all DOA estimation techniques tends to decrease as the number of time-domain samples increases. In addition, it is observed that, for a single source, not only our proposed simultaneous CI but also the conventional CI outperforms the classical MUSIC at all SNR regions. This implies that for detecting a single \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Center frequency & 1542 MHz \\ Wavelength & 0.1944 m \\ Array structure & UCA, ULA \\ The number of antennas & 5, 10, 20 \\ Radius of UCA antenna structure & 0.0972 m \\ Antenna spacing between of ULA structure & 0.0972 m \\ Resolution for DOA estimation & \(1^{\circ}\) \\ Signal-to-Noise ratio & [\(-10\):10] dB \\ The number of samples & [10:200] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. source, the performance of the conventional CI method is sufficiently improved through simply averaging the received signals using multiple time-domain samples. Figure 5 shows the RMSE performance considering two signal sources in which the azimuth and elevation angles of these two sources are set to \(\phi=\{40^{\circ},180^{\circ}\}\) and \(\theta=\{10^{\circ},5^{\circ}\}\), respectively. In such an environment, when estimating one DOA, the directional component of the other signal source may interfere and it makes the accurate direction finding hard. Nevertheless, it is confirmed that the proposed simultaneous CI technique yields better RMSE performance than the conventional CI technique and MUSIC method by jointly combining spatial features of signal components for each sample. In other words, it is verified that the multi-sample diversity effect efficiently works in all SNR regions.