**4. Discussion**

On the basis of the preceding simulation results, it may be clearly concluded that a dual-frequency six DOF oscillation motion has a critical effect on ocean surface scattering cross section of bistatic HF

radar, which may seriously affect the applications of the bistatic HF radar installed on a floating platform in ocean surface moving target detection and remote sensing of ocean surface dynamics parameters such as wind direction, wind speed, current, and ocean wave parameters. The characteristics (the energy distributions of the Bragg peaks and motion-induced peaks) of radar Doppler spectra depend on the oscillation motion parameters. Wind speed is also one of the factors affecting the oscillation motion parameters. Although the oscillation motion parameters of a large floating platform under a hurricane condition were selected for examples in this study, a small floating platform may yield similar phenomena under a moderate or low sea state. The reliability still needs to be further verified using field data with different floating platforms (shape and size) and different wind speeds in future work.

The motion-induced peaks may mask the moving target echoes and it may be extremely difficult to separate the target echoes from the motion-induced peaks if the target echoes appear near the Bragg peaks. This is because the amplitudes of the motion-induced peaks may be larger than those of the Bragg peaks, which may cause false alarm.

Furthermore, ocean surface wind direction is generally extracted according to the intensity ratio of the positive and negative Bragg peaks. Considering that the energies of the Bragg peaks are modulated by six DOF oscillation motion, the wind direction measurement results may be inaccurate if the modulation effect is ignored. Ocean surface current is generally measured based on the position difference between the theoretical Bragg peaks without ocean surface current and the measured Bragg peaks with ocean surface current. Generally, for the field data, the positions of the Bragg peaks are identified by searching for the strongest peaks in the positive and negative Doppler spectrum. However, due to the modulation effect of six DOF oscillation motion, the energies of the Bragg peaks may be lower than those of the motion-induced peaks, which may severely influence the measurement of ocean surface current. As we all know, the information of ocean surface wind speed and wave parameters is contained in the second-order radar Doppler spectrum. Although the modulation effect of six DOF oscillation motion on the second-order RCS is small, the motion-induced peaks in the first-order RCS may overlap with the second-order RCS, which would severely contaminate the second-order RCS and may have an unfavorable effect on the measurement of wind speed and ocean wave parameters.

Moreover, for six DOF oscillation motion, yaw is a dominant factor affecting RCS. Considering that, the oscillation motion can be regarded as frequency modulation on RCS and the modulation effect depends on the amplitude and frequency of the oscillation motion. Therefore, in order to reduce the effect of yaw on RCS and considering the influence of the floating platform superstructure on electromagnetic scattering, the installation location of the antenna should be at the edge of the floating platform but near the rotation center.

In addition, the modulation effect of six DOF oscillation motion on RCS is reduced with increased bistatic angle. That is, the amplitudes of the motion-induced peaks and the second-order RCS decrease for a large bistatic angle, which may be beneficial for ocean surface moving target detection. However, this case may be adverse for the extraction of ocean surface wind speed and wave parameters from the second-order RCS due to the disappearance of the second-order electromagnetic peaks for a large bistatic angle. Therefore, it is very important to choose a reasonable bistatic angle for different application purposes using a floating platform based bistatic HF radar.

Therefore, in order to improve the performance of moving target detection and the accuracies of ocean surface dynamics parameter measurements, a motion compensation method should be investigated to remove the motion-induced peaks in RCS and to recover the amplitudes of the firstand second-order RCSs in the future.

## **5. Conclusions**

In this paper, the first- and second-order ocean surface cross sections for bistatic HF radar incorporating a multi-frequency six DOF oscillation motion model were theoretically derived. When the bistatic angle is zero, the derived results can be reduced to the monostatic case, and when there is no six DOF oscillation motion, the derived results can be simplified to the onshore bistatic case. Simulations were conducted under different oscillation motion models and different bistatic angles.

Results show that each one-dimensional oscillation motion may induce additional peaks symmetrically appearing the first- and second-order radar Doppler spectra and the combined six DOF oscillation motion may result in more additional peaks. The amplitudes and frequencies of these motion-induced peaks depend on the amplitude and frequency of six DOF oscillation motion. The platform oscillation motion can be viewed as frequency modulation for radar echoes and the modulation effect of six DOF oscillation motion on the first-order radar Doppler spectra is more obvious than that on the second-order radar Doppler spectra. However, the motion-induced peaks appearing in the first-order radar spectra may overlap with the second-order radar spectra, which may raise the second-order radar spectra. It should be noted that yaw is the dominant factor affecting radar Doppler spectra, especially for the second-order spectra. Furthermore, the amplitudes of the Bragg peaks may be lower than those of the motion-induced peaks if a LF six DOF oscillation motion model is considered. This is a very important phenomenon for the application of bistatic HF radar. In addition, the modulation effect of six DOF oscillation motion and amplitudes of the second-order radar Doppler spectra decrease with increasing bistatic angle. For a large bistatic angle, the second-order electromagnetic peaks may be far away from the Bragg peaks or even diminished from radar Doppler spectra. Therefore, if the influences of the platform oscillation motion and bistatic angle on radar Doppler spectra are ignored, it will severely affect the applications of bistatic HF radar in moving target detection and ocean surface dynamics parameter measurements.

Here, the derived results were investigated only with simulated data, the rationality of the derived results should be further validated with field data. Nonetheless, this work provides an important theoretical foundation to determine suitable geometries for the deployment of a platform-based bistatic HF radar.

**Author Contributions:** Conceptualization, G.Y., J.X.; Methodology, G.Y., J.X., W.H.; Writing—original draft preparation, G.Y.; Writing—review and editing, J.X., W.H.; Software, G.Y.

**Funding:** This research was funded by National Natural Science Foundation of China key project (61132005), Special Research Foundation for Harbin Science and Technology Innovation Talents (RC2014XK009022), Natural Sciences and Engineering Research Council of Canada Discovery Grants under Grant NSERC RGPIN-2017-04508 and Grant RGPAS-2017-507962.

**Acknowledgments:** The authors would like to thank anonymous reviewers for their valuable comments in improving the quality of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
