*2.1. Target Representation with a Bistatic Compact HFSWR*

Compared with a monostatic HFSWR, a bistatic HFSWR represents a target differently due to different geometry. The target detection geometry of a T/R-R HFSWR system, defined by the position of a transmitter (Tx), a receiver (Rx), and a target using a two-dimensional north-referenced coordinate system, is illustrated in Figure 1.

**Figure 1.** The radar configuration geometry of a T/R-R high-frequency surface wave radar (HFSWR) system. The transmitter and receiving array 1 are deployed at the transmitting station (Tx), while receiving array 2 is deployed at the receiving station (Rx). The transmitter serves the two receiving arrays simultaneously. The distance *L* between the transmitter and receiver is called the bistatic range or simply the baseline. *ϕ* denotes the angle between the baseline and East direction. Denote *ψ<sup>T</sup>* and *ψ<sup>R</sup>* , respectively, as the radar look directions of receiving array 1 and receiving array 2 with respect to true North. *β* is the bistatic angle.

In Figure 1, the transmitter and receiving array 1 are deployed at the transmitting station (Tx), while receiving array 2 is deployed at the receiving station (Rx). The transmitter serves the two receiving arrays simultaneously. The distance *L* between the transmitter and receiver is called the bistatic range or simply the baseline. *ϕ* denotes the angle between the baseline and East direction. Denote *ψ<sup>T</sup>* and *ψR*, respectively, as the radar look directions of receiving array 1 and receiving array 2 with respect to true North. *β* is the bistatic angle. For a moving target with a velocity of magnitude *V* and aspect angle *φ* referenced to the bistatic bisector, the monostatic radar represents a target as a plot with a state vector [*RT θ<sup>T</sup> vdT*] in a polar coordinate, with *RT*, *θT*, *vdT* being the range, azimuth, and Doppler velocity measured at the transmitting station. Similarly, the bistatic radar represents a target as a plot with a state vector [*RR θ<sup>R</sup> vdR*], with *RR*, *θR*, *vdR* being the range, azimuth, and Doppler velocity calculated at the receiving station. As the estimation methods of *RT*, *θT*, and *vdT* for monostatic HFSWR has been investigated [11], only the estimation methods of *RR*, *θR*, and *vdR* for the bistatic HFSWR are discussed here.

Like the monostatic case, a target azimuth *θ<sup>R</sup>* is also estimated using the digital beaming forming (DBF) method for a bistatic HFSWR with a linear phased array as its receiving antenna. *θ<sup>R</sup>* takes negative values on the left side of the radar boresight, and positive values on the other side. However, the estimation methods for range and Doppler velocity are different from those used in a monostatic HFSWR. Firstly, the distance directly measured by a bistatic radar is the sum of *RT* and *RR*, the total transmitter-to-target-to-receiver scattering path, instead of *RR*. Target positions with the same range

sum, i.e., the isorange contour, form an ellipse with foci at the transmitter and receiver sites. The bisector of the bistatic angle *β* is orthogonal to the tangent of the ellipse and passes through a target position. Thus, a target position can be determined by its range sum and estimated azimuth *θR*. As can be seen from Figure 1, either (*RR*, *θR*) or (*RT*, *θT*) can be exclusively used for target location representation. For monostatic HFSWR, *RR* = *RT*, and *θ<sup>R</sup>* = *θT*, thus its target tracking methods cannot be directly applied to the bistatic case. Considering that the target azimuth *θ<sup>R</sup>* is directly measured by the receiving antenna array 2 with respect to its normal direction, (*RR*, *θR*) instead of (*RT*, *θT*) is chosen to specify the target position for bistatic HFSWR. i.e., *RR* is used to represent the target range and is derived as follows.

According to the bistatic triangle (i.e., the transmitter–target–receiver triangle shown in Figure 1) relationship, the following relation can be obtained:

$$\left|R\_T\right|^2 = R\_R\,^2 + L^2 - 2R\_RL\cos(\frac{\pi}{2} - \psi\_R - \theta\_R - \varphi). \tag{1}$$

Denote *R* = *RT* + *RR*, *θ* = *ψ<sup>R</sup>* + *θ<sup>R</sup>* + *ϕ*, then *RR* can be calculated as

$$R\_R = \frac{R^2 - L^2}{2(R - L\sin\theta)}.\tag{2}$$

Once the radar configuration is set, *ψR*, *L*, and *ϕ* are known. *R* and *θ<sup>R</sup>* can be determined from the data collected by the linear receiving array 2, then *RR* can be calculated by Equation (2). The calculated *RR* and the estimated *θ<sup>R</sup>* can also specify the location of the target. However, unlike the monostatic case, the calculated range *RR* is a function of the estimated target azimuth *θR*. The coarse azimuth resolution of a compact HFSWR leads to large estimation errors in *RR*, which brings greater challenges for target detection and tracking with bistatic compact HFSWR.

Another difference from a monostatic radar is the estimated Doppler velocity. The Doppler velocity measured by a monostatic radar is along the radial direction in the polar coordinate system with origin at the radar site, while the Doppler velocity estimated from a range-Doppler spectrum of a bistatic radar is along the direction of the bistatic bisector. It is the resultant velocity combining the Doppler velocities measured from the transmitting and receiving stations. The estimated elliptical Doppler velocity can be calculated as

$$\begin{split} V\_{dR} &= \frac{\mathrm{d}R}{\mathrm{d}t} = \frac{\mathrm{d}R\_T}{\mathrm{d}t} + \frac{\mathrm{d}R\_R}{\mathrm{d}t} \\ &= V\cos(\phi + \frac{\beta}{2}) + V\cos(\phi - \frac{\beta}{2}) \\ &= 2V\cos\phi\cos(\frac{\beta}{2}). \end{split} \tag{3}$$

It can be concluded that the magnitude of the bistatic Doppler velocity is related to the bistatic angle and is never greater than that of a monostatic radar. In practice, the measured Doppler velocity *vdR* is obtained from the Doppler shift *fd* extracted from a bistatic range-Doppler spectrum by

$$
\sigma\_{d\mathbb{R}} = (f\_d \cdot \mathfrak{c}) / f\_{\mathfrak{o}\_{\prime}} \tag{4}
$$

where *fd* denotes the radar operating frequency, *c* is the light speed.

Sea surface target detection using compact HFSWR is typically affected by either ocean clutter or ionospheric clutter, which can mask the returns from targets at their corresponding Doppler points and make them undetectable. In addition to parameter representations of a target discussed above, the first-order sea clutter should also be considered for target detection with a bistatic HFSWR. Without the effect of surface current, for stationary transmitting and receiving antennas, the Doppler shift of the first-order sea clutter for a bistatic HFSWR [22] can be written as

$$f\_b = \pm \sqrt{\frac{g \cos(\beta/2)}{\pi \lambda}},\tag{5}$$

where *λ* denotes the radar wavelength, *g* is the gravity acceleration. Equation (5) indicates that the first-order Bragg shift of a bistatic HFSWR is a function of the bistatic angle *β*. It is less than that of a monostatic HFSWR, which can be expressed as *f <sup>b</sup>* = ± *g πλ* . For a compact HFSWR, its detection range is limited due to the lower transmitting power; and its beamwidth is wider due to the smaller aperture size. Thus, the bistatic angle *β* always takes a relatively larger value leading to a spread first-order spectrum, which may mask the targets and increases the challenge for target detection.
