**1. Introduction**

High-frequency (HF) radar has been successfully deployed to detect ocean surface moving target and remote sensing of ocean surface dynamics such as wind direction and speed, current and wave parameters in many countries for decades [1–13] because it can provide real-time, all-weather surveillance beyond the horizon. Based on the geometry, HF radar can be generally divided into monostatic (transmitter and receiver are collocated) and bistatic (transmitter and receiver are separated) types. Bistatic HF radar possesses some inherent advantages over the monostatic case: (1) bistatic HF radar can improve the detection capability of stealth targets; (2) bistatic HF radar can address the ambiguous problem of sea state information extraction; (3) bistatic HF radar can suppress mutual interference between the transmitting and receiving antennas. Therefore, bistatic HF radar has attracted increasing attention internationally. For example, based on the ocean surface electromagnetic scattering theory presented by Walsh [14], Gill et al. [15] developed the first- and second-order ocean surface scattering cross sections for bistatic HF radar, which provides an important theoretical basis for the applications of bistatic HF radar. Subsequently, they investigated the effect of bistatic angle on radar cross sections (RCSs) in detail [16], which is helpful to determine a suitable geometry for the deployment

of bistatic HF radar. Based on the characteristics of sea clutter for bistatic HF radar, Lipa et al. [17] extracted ocean surface current. Trizna [18] successfully implemented an experiment to map ocean surface current and track the ship target using bistatic HF radar. Grosdidier et al. [19] validated the simulated bistatic HF radar Doppler spectra with the experimental data. Based on the RCS model developed by Gill et al. [15], Huang et al. [20] successfully obtained the unambiguous wind direction on the Southern China coast and the directional ocean wave spectra are respectively extracted from simulated noisy bistatic HF radar data [21] and synthetic bistatic HF radar data [22]. As the application of onshore bistatic HF radar matures, the floating platform based bistatic HF radar (the transmitter is deployed on a floating ocean platform and the receiver is installed on shore) gradually becomes a deployment trend. However, the platform motion may have an important effect on the application of bistatic HF radars.

In the floating platform based monostatic HF radar experiment, some researchers have observed that the platform motion can be viewed as phase modulation of radar Doppler spectra [23–26]. Theoretically, Walsh et al. [27,28] developed the first- and second-order ocean surface scattering cross section models for the case of a transmitter being installed on a floating platform with sway. They pointed out sway can induce additional peaks in radar Doppler spectra. Subsequently, Sun et al. [29] and Ma et al. [30,31] derived corresponding RCSs for shipborne and bistatic cases, respectively. However, based on the seakeeping theory [32,33], the deep-water floating platform generally has six degree-of-freedom (DOF) oscillation motion with multi-frequency due to the interaction between the complex ocean environment and floating platform. More recently, Ma et al. [34] extended the floating platform based bistatic RCSs to a dual-frequency platform motion case incorporating sway and surge. They presented that more additional peaks caused by the combined motion will symmetrically appear in radar Doppler spectra. Yao et al. [35,36] extended the first-order shipborne and bistatic RCSs to a horizontal oscillation motion case with a single-frequency and pointed out yaw may have a more important effect on radar Doppler spectra. Therefore, only considering two-dimensional platform motion with a dual-frequency model for the floating platform based bistatic HF radar is not realistic in practice. In this paper, on the basis of previous works [30,31,34,36], the first- and second-order ocean surface scattering cross sections for the floating platform based bistatic HF radar incorporating a more realistic multi-frequency six DOF oscillation motion model are presented. The results may have significant implications in future investigations for the application of floating-based bistatic HF radars.

The rest of this paper is organized as follows. In Section 2, a multi-frequency six DOF oscillation motion physical model is first developed. Subsequently, the first- and second-order ocean surface scattering cross sections for the floating platform based bistatic HF radar incorporating a single-frequency six DOF oscillation motion model are derived and, then, the results are extended to the multi-frequency case. Section 3 presents the simulation results and comparative analyses with different oscillation motion models and bistatic angles. Section 4 discusses the effect of six DOF oscillation motion and bistatic angle on the application of the floating-based bistatic HF radar in moving target detection and ocean surface dynamics parameter estimation. Conclusions are provided in Section 5.

## **2. Derivation**
