*3.3. E*ff*ect of Dual-Frequency Model on RCS*

In an actual marine environment, the frequency of the oscillation motion of a floating platform varies from low frequency (LF) to WF [40]. The WF response at the WF is 0.2–2 rad/s and the LF response at the in-plane resonances is around 0.02 rad/s. Therefore, in order to interpret the characteristics of the sea echo signals more realistically, a multi-frequency six DOF oscillation motion model incorporating LF and WF should be considered. In this study, in order to simply the simulation, a dual-frequency six DOF oscillation motion model incorporating both LF and WF was used. The LF six DOF oscillation motion parameters corresponding to the maximum spectral density of each one-dimensional oscillation motion were selected to simulate RCSs, which are listed in Table 2.

**Table 2.** Six DOF oscillation motion parameters for low frequency (LF).


Similar to the WF case, six DOF oscillation motion with LF will also result in some additional peaks. The frequency locations of these motion-induced peaks are extremely close to the Bragg peaks because of a low oscillation motion frequency. When a dual-frequency six DOF oscillation motion model incorporating a LF model and a WF model is considered, the frequency locations of the motion-induced peaks in the first- and second-order RCS curves are, respectively,

$$
\omega\_d = \omega\_{\rm bB} + \sum\_{i=1}^{2} \left[ \sum\_{j=1}^{N\_i} n\_{i,j} \omega\_{i,j} \right] + \sum\_{i=3}^{5} \left[ \sum\_{j=1}^{N\_i} \left( 2n\_{i1,j} + n\_{i2,j} \right) \omega\_{i,j} \right], \tag{62}
$$

$$
\omega\_d = \omega\_{hd} + \sum\_{i=1}^{2} \left[ \sum\_{j=1}^{N\_i} n\_{i,j} \omega\_{i,j} \right] + \sum\_{i=3}^{5} \left[ \sum\_{j=1}^{N\_i} \left( 2n\_{i1,j} + n\_{i2,j} \right) \omega\_{i,j} \right],
\tag{63}
$$

and

$$
\omega\_d = \omega\_{al} + \sum\_{i=1}^{2} \left[ \sum\_{j=1}^{N\_i} n\_{i,j} \omega\_{i,j} \right] + \sum\_{i=3}^{5} \left[ \sum\_{j=1}^{N\_i} \left( 2n\_{i1,j} + n\_{i2,j} \right) \omega\_{i,j} \right] \tag{64}
$$

where *Ni* = 2 represents two frequency components. Figure 10 displays the simulated first- and second-order RCSs for bistatic HF radar incorporating a dual-frequency six DOF oscillation motion model. From Figure 10a, the LF motion-induced peaks appear not only near the Bragg peaks but also near the WF motion-induced peaks, which agrees well with Equation (62). Furthermore, the amplitudes of the Bragg peaks and the WF motion-induced peaks are lower than those of the LF motion-induced peaks due to the modulation effect, which may 'break' Bragg scatter mechanism. A comparison of Figures 8f and 10b shows that the WF motion is the dominant factor affecting the second-order RCS. Figure 10c shows the total RCS containing the first- and second-order RCSs. From Figure 10c, it can be seen that a dual-frequency six DOF oscillation motion may have a more significant effect than a single-frequency case in Figure 9. In addition, the effects of different wind directions, wind speeds, and radar parameters on RCS for bistatic HF radar incorporating a dual-frequency six DOF oscillation motion model are similar to the sway case [30,31] and are not further discussed here.
