*3.2. E*ff*ect of Six DOF Motion on RCS*

Figure 7 shows the simulated first-order RCSs for different platform motion models. It can be seen that each one-dimensional oscillation motion will induce additional peaks. The locations and amplitudes of these additional motion-induced peaks are different from each other, which are decided by the frequency and amplitude of corresponding oscillation motion, respectively. From Equation (47), the initial phase of each one-dimensional oscillation motion has no effect on RCSs. Therefore, the oscillation motion of the floating platform can be regarded as frequency modulation of RCS of the onshore bistatic HF radar. From Figure 7d,e, pitch and roll have a smaller effect on RCSs compared to other oscillation motions. This is because the oscillation amplitudes of pitch and roll are relatively small. However, yaw results in more additional peaks appearing in the first-order RCS curve with a small oscillation amplitude and the amplitudes of these yaw-induced peaks are higher with respect to other cases. This is because the radar antenna is generally installed at the edge of the platform (especially a ship) to reduce the electromagnetic effect of platform superstructures on radar Doppler spectra. In this study, the antenna is assumed to be deployed far from the center of rotation. Thus, a small oscillation amplitude of yaw may cause a large horizontal antenna displacement.

When a six DOF oscillation motion model is considered, more additional motion-induced peaks will appear in the first-order RCS curve, which are not only caused by each one-dimensional oscillation motion but also by the combined motion. For such a case, the frequency locations of these motion-induced peaks can be expressed as

$$
\omega\_d = \omega\_{b\mathcal{B}} + \sum\_{i=1}^{2} n\_i \omega\_i + \sum\_{i=3}^{5} (2n\_{i1} + n\_{i2}) \omega\_i. \tag{59}
$$

Therefore, the modulation effect on the first-order RCS of six DOF oscillation motion is significantly greater than that of each one-dimensional oscillation motion.

**Figure 7.** Simulated first-order RCSs for different motions. (**a**) Sway case; (**b**) surge case; (**c**) yaw case; (**d**) pitch case; (**e**) roll case; (**f**) six DOF case.

Figure 8 shows the simulated second-order RCSs for different platform motion models. The additional motion-induced peaks appearing in the second-order RCS curve are not obvious. Similar to the sway case, the effect of surge on the second-order RCS is also small, as shown in Figure 8b. From Figure 8d,e, the effect of pitch and roll on the second-order RCSs may be ignored. However, yaw has an important effect on the second-order RCS due to a larger displacement of the antenna, as shown in Figure 8c. When a six DOF oscillation motion model is considered, more additional peaks caused by each one-dimensional oscillation motion and the combined motion may appear in the second-order RCS curve and the corresponding frequency locations are

$$
\omega\_d = \omega\_{hd} + \sum\_{i=1}^{2} n\_i \omega\_i + \sum\_{i=3}^{5} (2n\_{i1} + n\_{i2}) \omega\_{i\prime} \tag{60}
$$

and

$$
\omega\_d = \omega\_{cd} + \sum\_{i=1}^{2} n\_i \omega\_i + \sum\_{i=3}^{5} (2n\_{i1} + n\_{i2}) \omega\_i. \tag{61}
$$

**Figure 8.** Simulated second-order RCSs for different motions. (**a**) Sway case; (**b**) surge case; (**c**) yaw case; (**d**) pitch case; (**e**) roll case; (**f**) six DOF case.

However, by comparing Figure 8c,f, the RCS curves are basically similar. That is, the modulation effect of yaw on the second-order RCS is dominant.

Figure 9 displays the simulated total RCS containing the first- and second-order RCSs for the bistatic HF radar incorporating a single-frequency six DOF oscillation motion model. From Figure 9, it is seen that the motion-induced peaks appearing in the first-order RCS curve will overlap with the second-order RCS curve and, then, the amplitude of the second-order RCS may be raised. For such a case, the amplitudes of the Bragg peaks are still larger than those of the motion-induced peaks. Compared to the sway case in Figure 6b, more motion-induced peaks with larger amplitude appear in the total RCS curve. Therefore, in practice, just considering one- or two-dimensional oscillation motion is not realistic.

**Figure 9.** Simulated total RCSs containing first- and second-order RCSs.
