## 4 Simulation Verification
channel acoustic signal time delays. The target echo simulation was performed, using the BELLHOP ray tracing program, to obtain the time delay and amplitude attenuation of the target echo signals of different channels. We superimpose them to obtain the multipath echo signals. The target scattering was simplified to specular scattering in the simulation because the target scattering angle was difficult to simulate. Figure 12 shows the acoustic signal propagation trajectory obtained by simulation using the BELLHOP program. The depth of the ocean is set at 600 m. The depth of the sound source and the receiving point is 200 m, and the distance between them is 500 m. The angle range of the sound source signal emission is \(-15^{\circ}\)-\(15^{\circ}\), and the sound source emits 20 signals at equal intervals. The receiving point receives signals in the depth range of its depth \(-10\) m-\(10\) m, and the receiving angle range is also \(-15^{\circ}\)-\(15^{\circ}\). Our simulation of the acoustic signal propagation path can make the echo signal more realistic, which in turn makes the verification of the effect of the proposed target recognition method more reliable. Among them, Figure 13a-d are the estimation process of the target distance, the orientation, the apparent angle, and the echo broadening information, respectively [31]. Then, the apparent angle and echo broadening of each cycle are converted into the apparent scale to analyze the correlation between echo broadening and apparent angle of the submarine, mobile acoustic decoy, and suspended type acoustic decoy. Figure 14 shows the apparent scale of the target converted according to the apparent angle and echo broadening of each cycle. The echo broadening and apparent angle cannot distinguish the scale difference between the real-scale target and the virtual-scale target. Under substantial interference, the target scale cannot be accurately recognized only by the echo broadening and apparent angle alone. Therefore, we recognized the target by correlating the echo broadening and the apparent angle. We also analyzed the difference between the equivalent scales obtained from the target echo broadening and the apparent angle in the following. Figure 11: The sound speed profile. Figure 12: The underwater acoustic signal propagation. \[\varphi_{s}=\frac{-\mathrm{i}k_{0}\mathrm{A}}{2\pi}\int_{S_{0}}\frac{\mathrm{ e}^{\mathrm{i}2k_{0}r}}{r^{2}}V(\theta)\cos\theta ds \tag{17}\]0 Cont. The apparent scale difference of each target is obtained from the apparent angle and the echo broadening; as shown in Figure 15, it can be observed that the apparent scale difference of each cycle of the submarine target is within the range of [0.2 m, 4.0 m], which is obviously smaller than the apparent scale difference of the mobile acoustic decoy and the suspended acoustic decoy. Figure 16 shows the apparent scale difference of different ship angles. The target porthole angle is set to be 0\({}^{\circ}\)-180\({}^{\circ}\) in steps of 15\({}^{\circ}\). It can be seen that when the target angle is in the range of 0\({}^{\circ}\)-75\({}^{\circ}\) and 105\({}^{\circ}\)-180\({}^{\circ}\), the apparent scale difference of the submarine target is in the range of [0.5 m, 2.2 m], which is much smaller than the apparent scale difference of the mobile acoustic decoys and suspended acoustic decoys. When the target angle is in the range of 75\({}^{\circ}\)-105\({}^{\circ}\), the apparent scale difference of submarine, mobile acoustic decoys and suspended acoustic decoys is about 12 m, so it is impossible to distinguish between the targets. Therefore, the torpedoes in this chord angle range cannot recognize the real and fake targets based on the echo broadening and apparent angle. This is due to the fact that the time delay difference between the echoes at the two ends of the target is very small near the positive transverse chord angle, which corresponds to the small equivalent distance between them.