## 4 Simulation Results and Discussions
Figure 4 compares the minimum number of detection repetitions, \(L_{\min}\), obtained by utilizing the proposed algorithm with that of the conventional exhaustive search algorithm for \(M=64\). It is clear that our proposed algorithm can significantly reduce the required number of detection repetitions in the low SNR regime, which verifies the effectiveness of our proposed algorithm. In Figure 5, the strongest AoA estimation performance of our proposed algorithm is compared with that of the exhaustive search algorithm using RMSE as the performance metric for different scenarios in the scattering environment, e.g., \(\theta_{1}=\frac{\pi}{3}\) and \(\theta_{2}=\frac{103\pi}{180}\). It is interesting to see that our proposed algorithm works well for multi-path scenarios. The numbers of detection repetitions required for these two algorithms are presented in Figure 4. It can be observed that our proposed algorithm can have a slightly higher performance in terms of strongest AoA estimation while consuming a much smaller number of detection repetitions in low SNR regimes. In addition, the strongest AoA estimation performance of these two algorithms converge in medium-to-high SNR regimes. As expected, the performance of these two different algorithms approach to 1-bit CRLB with an increasing SNR, which is appropriated by using AQNM. Meanwhile, in Figures 6 and 7, we calculate the performance of strongest AoA estimation with different conventional schemes for the single-path scenario for different numbers of antennas \(M\), e.g., 1-bit CRLB appropriated by using AQNM and 1-bit FFT. Figure 4: Comparison of the minimum number of detection repetitions between our proposed method and the exhaustive search algorithm, \(M=64\). Figure 5: RMSE [rad] performance versus different SNRs [dB] for different scenarios. Figure 6: **(a)** The number of detection repetitions required for different algorithms versus different SNR for \(M=10\); **(b)** RMSE [rad] versus different SNRs for \(M=10\) with our proposed beamforming direction search algorithm, the exhaustive search algorithm and 1-bit FFT. Figures 6b and 7b compare the strongest AoA estimation performance of our proposed algorithm with that of the exhaustive search algorithm and research results from work ([PERSON] et al. 2017) ([PERSON] et al. 2017) ([PERSON] et al. 2017). The numbers of detection repetitions, \(L_{\min}\), required for the strongest AoA  
Figure 7: **(a)** The number of direction repetitions required for different algorithms versus different SNRs for \(M=30\); **(b)** RMSE [rad] versus different SNRs for \(M=30\) with our proposed beamforming direction search algorithm, the exhaustive search algorithm and 1-bit FFT. estimation of these three algorithms are presented in Figures (b)b and (a)a (In work [30], \(\tilde{L}_{\text{min}}\) required by utilizing 1-bit FFT is fixed to 10.). It can be observed in Figures (b)b and (b)b that our proposed algorithm can effectively reduce the estimation overhead while maintaining a reasonable estimation performance when the number of antennas is small. It can also be observed that our proposed algorithm can have a slightly higher performance in terms of strongest AoA estimation compared to 1-bit FFT algorithm in low SNRs. In the medium-to-high SNR regime, although our proposed algorithm is inferior with the 1-bit FFT in terms of RMSE performance, the detection repetitions required of our proposed algorithm is significantly smaller.