# Broadband DOA Estimation by Exploiting DFT Extrapolation
## 3 Simulation Results
### Results  
Figure 1a,b represent the DOA RMSEs measured at 10 dB and 20 dB SNR, and the number of peaks in the spectral domain, respectively, when the three randomly chosen DOAs were \(-31\), \(10\), and \(38^{\circ}\). In Figure 1a, at 10 dB SNR, the RMSEs of the 36-element real array are all within \(5^{\circ}\). At relatively high frequencies, the RMSE of the 12-element real array was similar to that of the extrapolated array. However, at lower frequencies, a difference was observed in this regard. The RMSE of the 12-element real array exceeded \(5^{\circ}\) below 1.6 GHz, with a significant increase in the lower frequencies. When the real array was extrapolated, the RMSE exceeded \(5^{\circ}\) at 1.2 GHz but did not increase rapidly, unlike that of the 12-element real array. The reason for the rapid increase in the RMSE, as in the 12-element real arrays, was found to be highly related to the number of peaks. If the number of peaks was three or less, the DOA could not be estimated, and the RMSE will increase rapidly to \(45^{\circ}\), as described in Section 3.1. Figure 1a shows a drastic change in the RMSE values at frequencies where the estimated number of peaks is less than three. This also occurred at an SNR of 20 dB. In Figure 1b, the RMSE of the 36-element real array remains below \(5^{\circ}\) above 600 MHz, sharp changes in the RMSE are observed at 1.5 GHz for the 12-element real array, and at 0.9 GHz for the extrapolated array. This is also related to the number of peaks. This indicates that expanding the virtual array through DFT extrapolation expands the measurable frequency band.  
Figure 2a,b represent the DOA RMSEs measured at 10 dB and 20 dB SNR and the number of peaks in the spectral domain, respectively, when the four randomly chosen DOA are \(-36\), \(-8\), \(23\), and \(49^{\circ}\). These results are similar to those shown in Figure 1. In Figure 2a, the RMSE of the 36-element real array remains below \(5\) degrees above 700 MHz, and sharp changes in the RMSE are seen at 2.1 GHz for the 12-element real array, and at 1.1 GHz for the extrapolated array. In Figure 2b, the RMSE of the 36-element real array remains below 5 degrees above 500 MHz, and drastic changes in the RMSE are observed at 2.1 GHz for the 12-element real array, and at 1.0 GHz for the extrapolated array. It can be observed that the changes are related to the number of peaks. Figure 2 also indicates that measurable frequency band for the four DOAs was expanded by DFT extrapolation.  
Figure 3a,b represent the DOA RMSEs measured at 10 dB and 20 dB SNR and the number of peaks in the spectral domain, respectively, when the five randomly chosen DOA are \(-68\), \(-40\), \(-14\), \(27\), and \(53^{\circ}\). In Figure 3a, the RMSE of the 36-element real array remains below 5 degrees above 1 GHz, DOAs are able to detected only at 3 GHz for the 12-element real array, and above 2.4 GHz for the extrapolated array. In Figure 3b, the RMSE of the 36-element real array remains below 5 degrees above 1 GHz, DOAs are able to be estimated only at 3 GHz for the 12-element real array, and above 1.8 GHz for the extrapolated array. Measurable frequency band for the five DOAs was expanded by DFT extrapolation as well.  
The number of peaks fluctuated throughout the frequency range, even at higher frequencies. This is because the noise affects the beam patterns in the spectral domain, and peaks at an angle that is not the DOA.  
Figure 1: RMSEs obtained from the DOA estimation and the number of peaks when the DOA was \(-31\), \(10\), and \(38^{\circ}\) under (**a**) 10 dB SNR and (**b**) 20 dB SNR.  
Figure 2: RMSEs from the DOA estimation and the number of peaks when the DOA was \(-36\), \(-8\), \(23\), and \(38^{\circ}\) under (**a**) 10 dB SNR and (**b**) 20 dB SNR.