*3.1. Simulation 1: Simulated Space–Time Distribution for Di*ff*erent Headings of the Shipborne Platform*

Based on Equation (14), the distribution of the broadening of the first-order sea clutter for a coast–ship bistatic HFSWR when the shipborne platform was anchored is shown in Figure 2. Here, we set the elliptical eccentricity as e = 0.7, frequency as 4.7 MHz, navigation speed *vR* = 0 km/h, and wind direction as 90◦.

**Figure 2.** Distribution of the broadening of the first-order sea clutter of a coast–ship bistatic HFSWR when the shipborne platform was anchored.

It can be seen from Figure 2 that the broadening ranges of the right sea clutter spectrum and left sea clutter spectrum were symmetrical for a coast–ship bistatic HFSWR when the shipborne platform was anchored, i.e., the width of the right sea clutter spectrum was equal to that of the left sea clutter spectrum when the heading was given. Here, the right first-order spectrum was selected as an example. The right bound retained the value of *fRR* = *<sup>g</sup>* πλ , while the value of the left bound *fRL* was

$$f\_{RL} = \begin{cases} \sqrt{2gk\_0 \cos\left(\frac{\beta\_{\text{max}}}{2}\right)}, 0^\diamond < \varphi\_R < \theta\_{R1} \\ \sqrt{2gk\_0 \cos\left(\frac{\beta}{2}\right)}, \theta\_{R1} < \varphi\_R < 90^\circ \end{cases},\tag{16}$$

where β*max* is the largest bistatic angle for a given elliptical eccentricity e, i.e., β*max* = *arcsin*(*e*), and θ*R*<sup>1</sup> is its corresponding direction of arrival. Here, <sup>β</sup> <sup>=</sup> 2arctan *sin*ϕ*<sup>R</sup>* 1 *<sup>e</sup>* +*cos*ϕ*<sup>R</sup>* .

The space–time distribution of the Doppler frequency shift of the first-order sea clutter and the simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR at three different headings when the shipborne platform was anchored are shown in Figure 3. It can be seen that the simulated space–time distribution of the frequency shift of the sea clutter varied with the direction of arrival. The space–time distribution of the Doppler shift of the first-order sea clutter of a coast–ship bistatic HFSWR system is presented as two nonlinear curves with the cosmic value of the incoming direction, and the two curves are symmetrical along the y-axis.

**Figure 3.** Space–time distribution of the Doppler frequency shift of the first-order sea clutter for a coast-transmit ship-receive (CTSR) bistatic HFSWR at different headings when the shipborne platform was anchored: (**a**) 0◦, (**b**) 45◦, and (**c**) 90◦.

Based on the two-dimensional space–time distribution plots presented in Figure 3, simulation results of the first-order sea clutter spectrum of a coast–ship bistatic HFSWR with different headings on a single channel can be obtained, as shown in Figure 4.

**Figure 4.** Simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR at different headings: (**a**) 0◦, (**b**) 45◦, and (**c**) 90◦.

It can be seen from Figure 4 that the broadening ranges of the right first-order sea clutter spectrum and left first-order sea clutter spectrum were symmetrical. As ϕ*<sup>R</sup>* = 45◦, θ*R*<sup>1</sup> = 46◦, and ϕ*<sup>R</sup>* < θ*R*1, the widths of both the right sea clutter spectrum and the left sea clutter spectrum at the headings of 0◦ and 45◦ were equal. The minimum value of the width of the sea clutter spectrum was obtained when ϕ*<sup>R</sup>* = 90◦. In addition, owing to the change of heading, the angle of the wind direction relative to the principal axis of the receiving array was equivalent to that change, which induced the amplitude variation of the sea clutter spectrum.

The space–time distribution of the Doppler frequency shift of the first-order sea clutter and the simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR at three different headings when the shipborne platform was navigating with velocity of 11.5 km/h are shown in Figures 5 and 6, respectively. In those cases, the broadening ranges of the right first-order sea clutter spectrum and left first-order sea clutter spectrum were asymmetrical and their widths were not equal.

**Figure 5.** Space–time distribution of the Doppler frequency shift of the first-order sea clutter for a CTSR bistatic HFSWR at different headings when the shipborne platform was navigating: (**a**) 0◦, (**b**) 45◦, and (**c**) 90◦.

**Figure 6.** Simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR navigating at different headings: (**a**) 0◦, (**b**) 45◦, and (**c**) 90◦.

## *3.2. Simulation 2: Simulated Space–Time Distribution for Di*ff*erent Shipborne Platform Velocities*

The space–time distribution of the Doppler frequency shift of the first-order sea clutter and the simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR at different velocities are shown in Figures 7 and 8, respectively. Here, we set the elliptical eccentricity as e = 0.22, frequency as 4.7 MHz, heading ϕ*<sup>R</sup>* = 115◦, and wind direction as 90◦. Simulation results of a monostatic shipborne HFSWR with the same operating conditions are presented for comparative analysis in Figure 8.

**Figure 7.** Space–time distribution of the Doppler frequency shift of the first-order sea clutter for a CTSR bistatic HFSWR at different velocities: (**a**) *vR* = 11.48 km/h (6.2 knots) and (**b**) *vR* = 22.2 km/h (12 knots).

**Figure 8.** Simulation results of the first-order sea clutter spectrum for a CTSR bistatic HFSWR at different velocities: (**a**) *vR* = 11.48 km/h (6.2 knots) and (**b**) *vR* = 22.2 km/h (12 knots).

It can be seen from Figure 8a that the range of broadening of the first-order sea clutter spectrum of a coast–ship bistatic HFSWR increased when the platform velocity increased, meaning that the range of the blind area caused by first-order sea clutter was widened, which had a greater effect on moving targets falling within these velocity ranges. This is very disadvantageous to target detection. Conversely, with the increase of platform velocity, the echo amplitude of the first-order sea clutter decreased gradually, which led to a higher signal-to-clutter ratio. This is more conducive to the detection and highlighting of moving targets falling into and becoming submerged in the blind area caused by first-order sea clutter.

As can be seen from Figure 8b, the range of broadening of the first-order sea clutter spectrum for a monostatic shipborne HFSWR was obviously larger than that of the coast–ship bistatic HFSWR under the same platform velocity, and even the left and right sea clutter spectra were almost superimposed when the velocity was greater than 24 km/h. For a CTSR bistatic HFSWR, only the receiving station was on the moving platform, while both the transmitting and the receiving stations were on the moving platform in a monostatic shipborne HFSWR system. Therefore, the Doppler shift of the first-order sea clutter spectrum and the related blind area of a coast–ship CTSR bistatic HFSWR were smaller than those of a monostatic shipborne HFSWR.
