*2.1. The Geometry of Shore-To-Air Bistatic Hf Radar*

The geometry of shore-to-air bistatic HF radar is shown in Figure 2. The x axis is assumed as the direction of the radar beam and the y axis is perpendicular to the x axis. The z axis is vertical to the sea surface. The incident electromagnetic wave (the wavenumber vector is −→*k*<sup>0</sup> ) lies on x-z plane and the incident angle *θ<sup>i</sup>* is the angle of the incident radar wave from the z axis. For the near-grazing incident wave, *<sup>θ</sup><sup>i</sup>* <sup>≈</sup> *<sup>π</sup>* <sup>2</sup> . *<sup>θ</sup><sup>s</sup>* is the angle of the scattered radar wave (the wavenumber vector is −→*k*sc) from the z axis. *ϕ<sup>s</sup>* is the azimuthal angle of the scattered radar wave from the incidence plane. The half angle between the transmitter and the projection in the x-y plane of the receiver as viewed from the scatter patch is *ϕ*0, which satisfies the equation *ϕs*=180◦ − 2*ϕ*0. The scattering coefficients of bistatic HF radar can be approximated as the sum of the first-order and second-order scattering coefficients

$$
\sigma(\omega) = \sigma^{(1)}(\omega) + \sigma^{(2)}(\omega). \tag{1}
$$

The equation of the perfectly conducting rough time-varying surface *z* can be expressed as a Fourier series:

$$z = f(\mathbf{x}, y, t) = \sum\_{mnl} P(m, n, l) \exp\left\{ (-j(\frac{2\pi m}{L}\mathbf{x} + \frac{2\pi n}{L}y) - j\omega lt) \right\} \tag{2}$$

where the triple summation extends from −∞ to +∞ for *l*, *m*, and *n*, *P*(*m*, *n*, *l*) are the Fourier expansion coefficients, and *T* = 2*π*/*ω* is the time period of the Fourier expansion and corresponds to the spatial period *L* (assumed to be large).

**Figure 2.** Geometry of shore-to-air bistatic HF radar.
