*3.1. Comparison of the Cross-Correlation Algorithm and Frequency Diversity Algorithm*

The cross-correlation method and cross-spectrum method have a similar performance under the same signal-to-noise ratio. Moreover, the conventional cross-spectral method is based on the discrete spectrum of the received signal to directly estimate the azimuth. In practical applications, the relative frequency deviation of signals and the leakage of spectrum will lead to an azimuth estimation error. Thus, here, we only compare the proposed algorithm with the cross-correlation method. Assuming that the two hydrophones are 128m apart, the signal is Gaussian white noise, with 100–200 Hz bandpass filtering. First, consider a single target with an incident angle of 40◦. The sampling frequency is 4 kHz, and the number of samples is 4096. According to the relevant algorithm processing time length, set Δ*f*= 1 Hz in the frequency diversity algorithm. The sampling bandwidth *M*Δ*f* is set to 100 Hz according to the signal bandwidth. When the in-band SNR of the received hydrophone signal is set to 0 dB, where the noise is Gaussian white noise, the simulation result is shown in Figure 4.

**Figure 4.** DOA of two hydrophones, SNR = 0 dB: (**a**) the cross-correlation method and (**b**) frequency diversity algorithm.

When the in-band SNR is set to −16 dB, the simulation results are shown in Figure 5:

**Figure 5.** DOA of two hydrophones, SNR = −16 dB: (**a**) The cross-correlation method and (**b**) frequency diversity algorithm.

It can be seen, from Figures 4 and 5, that the DOA estimation performance of the frequency diversity algorithm is superior to the cross-correlation method under different SNR. When the SNR is reduced to −16 dB, the cross-correlation method can no longer estimate the azimuth of the target, while using the frequency diversity algorithm, and a robust estimation of the target azimuth can still be achieved. Change the number of sound sources to two, and the bearing angles are 30◦ and 50◦. The in-band SNR is set to −10 dB. The simulation results are shown in Figure 6.

When the number of sound sources is changed to two, it can be seen from Figure 6, that when the in-band SNR is reduced to −10 dB, the cross-correlation method can no longer estimate the azimuth of the target. This is because the source signal has a wideband, and the two target signals are not completely independent. Therefore, there are many periodic pseudo peaks in the cross-correlation. Therefore, when the number of targets changes from 1 to 2, the SNR used to compare the performance of the two algorithms is increased from −16 dB to −10 dB. When frequency diversity techniques are used, the target azimuth can still be estimated robustly. The reason is that the frequency diversity technique uses the phase relationship in the signal frequency dimension, so the processing gain is improved, compared to the cross-correlation method, and the resolution is not affected by the correlation between signals. Since the simulated two target signals are band-limited white Gauss noise, whose spectrum is random, in the latter analysis, it can be found that the beamformed output amplitude obtained by the proposed algorithm, is related to the energy distribution in the frequency domain, so the amplitudes of the two sources are different.

**Figure 6.** DOA of two hydrophones, SNR = −10 dB, two targets: (**a**) the cross-correlation method and (**b**) frequency diversity algorithm.
