**1. Introduction**

Since the discovery of the Bragg effects on the transmission of electromagnetic fields over the ocean surface in 1955 [1], high-frequency (HF) radars have been largely used in ocean remote sensing, from oceanographic applications (e.g., [2,3]) to target detection and tracking (e.g., [4,5]). HF radars can be presented in two configurations with respect to the relative positions of the transmitter and receiver: Monostatic, where the distance between the transmitter and receiver is much smaller than the distance between them and the scattering object, to the point that they can be considered co-located; and bistatic (or multistatic), where the distance between the transmitter and receiver (or multiple receivers) is comparable to the distance between them and the scattering object. Due to the ubiquity of HF radar systems installed in monostatic configurations and the relative simplicity of geometric and mathematical considerations when compared to a bistatic radar, most of the research developed in the past decades has been dedicated to monostatic HF radar systems.

Although early works on the bistatic radar cross-section of the ocean surface in C-band were published in 1966 [6], the first efforts to implement bistatic HF radars for radio oceanography would only come later in that decade [7–9]. Barrick started exploring the scattering theory of bistatic HF radars in 1970 [10], proposing an expression for the radar cross-section of the ocean surface for HF radars in 1972 [11]. Bistatic scattering coefficients from the ocean surface were later derived by Johnstone [12]. In 1987, Barrick's theory for the radar cross-section of the ocean surface was expanded by Anderson [13], and was later validated through experiments; e.g., [14,15]. In the past two decades, the generalized functions method introduced in [16] has been applied to the development of a scattering theory for bistatic HF radars [17–23], with its validity being experimentally verified [24].

In the development of the scattering theory for the ocean surface in both monostatic and bistatic radar configurations, small-height and small-slope approximations are commonly applied, respectively restricting the scattering analysis to ocean surfaces where wave heights are small compared to the radar wavelength and the surface slopes are sufficiently small [16,25]. In mathematical terms, the small-height approximation limits the scattering analysis of the ocean surface roughness scales *k*0*Hs* to be much smaller than one, where *k*<sup>0</sup> is the wavenumber that represents the central radar transmitting frequency *ω*0, defined as

$$k\_0 = \frac{\omega\_0}{c}\_{\prime}$$

where *c* is the speed of light and *Hs* is the significant wave height of the ocean surface, while the small-slope approximation restricts the surface slope |∇ *f*(*x*, *y*; *t*)| to values smaller than unity. Therefore, when the ocean surface violates these restrictions, the validity of the currently-used theory cannot be guaranteed [26], and the development of a scattering theory that would be valid in such circumstances is desirable.

The present work aims to expand the narrow-beam bistatic HF radar scattering theory to ocean surfaces with large roughness scales, allowing arbitrary wave heights. The expression for the electric field scattered from an ocean surface with arbitrary heights and received in a bistatic radar configuration is presented in Section 2, while the radar cross-section expression is derived in Section 3. The simulation results and discussion are presented respectively in Sections 4 and 5, while the concluding remarks are presented in Section 6.
