# First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Derivation of a First-Order RCS of Shipborne Bistatic HFSWR

**T**, propagates along a path ${\overrightarrow{\rho}}_{1}$ and then follows a path, ${\overrightarrow{\rho}}_{2}$, to the receiving station

**R**. ${\theta}_{1}$, ${\theta}_{2}$, ${\phi}_{1}$, and ${\phi}_{2}$ are the angles of the transmitting signal path (${\overrightarrow{\rho}}_{1}$), receiving signal path (${\overrightarrow{\rho}}_{2}$), transmitting antenna vector displacement ($\delta {\overrightarrow{\rho}}_{1}$), and receiving antenna vector displacement ($\delta {\overrightarrow{\rho}}_{2}$), respectively, measured anticlockwise with the baseline, $\overrightarrow{\rho}$, as the reference direction. As illustrated in Figure 1, when the ships that carry

**T**and

**R**, are moving, the new signal path lengths can be approximately estimated by:

#### 2.2. First-Order RCS with Different Motion Types

#### 2.2.1. First-Order RCS with Uniform Linear Motion

#### 2.2.2. First-Order RCS with Periodic Oscillation Motion

#### 2.2.3. First-Order RCS with Hybrid Motion

## 3. Simulation Results and Discussion

#### 3.1. Both Platforms Move in Uniform Linear Motion

#### 3.2. Both Platforms Move in Periodic Oscillation Motion

#### 3.3. Both Platforms Undertake Periodic Motion and Uniform Linear Motion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Simulated shipborne bistatic (red dotted line) and shipborne monostatic (blue solid line) first-order Doppler spectra for a detection range sum of 150 km. (

**a**) The platforms’ speed is 5 m/s. (

**b**) The platforms’ speed is 6.5 m/s.

**Figure 4.**Simulated shipborne bistatic (red dotted line) and shipborne monostatic (blue solid line) first-order Doppler spectra for a detection range sum of 50 km. (

**a**) The platforms’ speed is 5 m/s. (

**b**) The platforms’ speed is 6.5 m/s.

**Figure 5.**Simulated shipborne bistatic (red dotted line) and shore-based bistatic (blue solid line) first-order Doppler spectra for different motion velocities. (

**a**) The motion speed of the shipborne bistatic radar is 5 m/s. (

**b**) The motion speed of the shipborne bistatic radar is 10 m/s.

**Figure 6.**Simulated first-order Doppler spectra for which the transmitting and receiving platforms do not move along the baseline. (

**a**) Different transmitting platform moving speeds. (

**b**) Different transmitting platform moving directions.

**Figure 7.**Simulated first-order Doppler spectra for non-baseline motion (blue) and baseline motion (red). (

**a**) First-order Doppler spectra at a detection distance of 50 km. (

**b**) Variation of the first-order spectrum spread width over detection distance.

**Figure 8.**Simulated first-order Doppler spectra for oscillation motion (blue solid line) and motion-free (red dotted line). (

**a**) First-order Doppler spectra of two systems. (

**b**) Zoomed-in view of the positive Doppler spectra in (

**a**).

**Figure 9.**Simulated first-order Doppler spectra when the transmitting and receiving platforms undertake the same oscillation motions. (

**a**) First-order Doppler spectra of two oscillation directions. (

**b**) Zoomed-in view of the negative Bragg peak in (

**a**).

**Figure 10.**Simulated first-order RCS with periodic oscillation motion and uniform linear motion. (

**a**) First-order Doppler spectra of two oscillation directions. (

**b**) Zoomed-in view of the first-order Doppler spectra in (

**a**).

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**MDPI and ACS Style**

Ji, Y.; Liang, X.; Sun, W.; Huang, W.; Wang, Y.; Wang, X.; Li, Z.
First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation. *J. Mar. Sci. Eng.* **2022**, *10*, 649.
https://doi.org/10.3390/jmse10050649

**AMA Style**

Ji Y, Liang X, Sun W, Huang W, Wang Y, Wang X, Li Z.
First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation. *Journal of Marine Science and Engineering*. 2022; 10(5):649.
https://doi.org/10.3390/jmse10050649

**Chicago/Turabian Style**

Ji, Yonggang, Xu Liang, Weifeng Sun, Weimin Huang, Yiming Wang, Xinling Wang, and Zhihao Li.
2022. "First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation" *Journal of Marine Science and Engineering* 10, no. 5: 649.
https://doi.org/10.3390/jmse10050649