## 2 Passive Radar Performance Principle
### Bistatic Radar Cross-Section  
The bistatic RCS, \(\sigma_{bis}\), is a function of the transmitted signal (frequency and polarization), the shape and materials of the target and the incidence and scattering directions. In the bistatic RCS region, characterized by bistatic angles higher than \(5^{\circ}\) and lower than \(180^{\circ}\), the bistatic RCS is usually lower than the monostatic RCS for complex targets. Exceptions include [27]:  
1. Some target aspect angles that generate a low monostatic RCS and a high bistatic specular RCS at specific bistatic angles. 2. Targets that are designed for low monostatic RCS over a range of aspect angles. 3. Shadowing that sometimes occurs in a monostatic geometry and not in a bistatic one. Taking into consideration the scenario geometry depicted in Figure 6 and the possible incidence and scattering directions, the monostatic and the bistatic RCSs of a car were estimated using the program POFACETS, developed at the Naval Postgraduate School [28]. Incidence and scattering directions are defined by pairs \((\theta,\phi)\), where \(\theta\) represents the elevation angle (measured with respect to the Earth's surface perpendicularly) and \(\phi\) the azimuth one (measured in the plane tangent to the Earth's surface, with respect to the north). A basic car model made of perfect electrical conductor (PEC) with dimensions 6 m (L) \(\times\) 2 m (W) \(\times\) 1.6 m (H) was used, and the simulations were performed for \(f=9.65\) GHz and vertical polarization. The RCS has dimensions of area, so an RCS value equal to \(a(m^{2})\) corresponds to \(A(dBsm)=10\cdot\log_{10}(a)\). For the monostatic study, two cases were simulated: _Monostatic-1_ (\(\theta_{m1}=15^{\circ}\) and \(\phi_{m1}\in[0,360^{\circ}]\)), and _Monostatic-2_ (\(\theta_{m2}=65^{\circ}\) and \(\phi_{m2}\in[0,360^{\circ}]\)). In Figures 8 and 9 the results obtained for the monostatic study cases, _Monostatic-1_ and _Monostatic-2_, are depicted in 3D and in cartesian coordinates. Figure 7: Study of different coverage areas for a fixed passive radar (PR) position as a function \(L/(R_{T}R_{R})\) assuming \(R_{T}\cdot R_{R}=1\) km\({}^{2}\): \(L/(R_{T}R_{R})=1.5\) in red, \(L/(R_{T}R_{R})=2\) in blue and \(L/(R_{T}R_{R})=3\) in green. In the bistatic case, incidence and scattering directions must be considered. The estimation of an average bistatic RCS was performed using the following methodology:  
* For each value of incidence elevation angle, \(\theta_{i1}=15^{\circ}\) and \(\theta_{i2}=65^{\circ}\), the incidence azimuth angle, \(\phi_{i}\), was varied from \(0^{\circ}\) to \(180^{\circ}\), taking into consideration the symmetry of the car in the XY plane. * For each incidence direction \((\theta_{i},\phi_{i})\), the elevation angle of the scattered wave was fixed to \(\theta_{s}=~{}90^{\circ}\), and the azimuth scattering angle, \(\phi_{s}\), was varied from \(0^{\circ}\) to \(360^{\circ}\). Figures 10 and 11 show results obtained for \(\theta_{i1}=15^{\circ}\) and \(\theta_{i2}=65^{\circ}\), respectively. Figure 8: Results obtained for the Monostatic 1 case using POFACETS : (**a**) 3D model of the target and 3D monostatic radar cross-section (RCS); (**b**) Monostatic RCS in Cartesian coordinates. Figure 9: Results obtained for the Monostatic 2 case using POFACETS: (**a**) 3D model of the target and 3D monostatic RCS; (**b**) Monostatic RCS in Cartesian coordinates. * For each scattering direction, \((\theta_{s},\phi_{s})\), and incidence elevation angle \(\theta_{i}\), an average bistatic RCS was calculated as the mean value of the bistatic RCSs estimated for the set of \(\phi_{i}\) values ranging from \(0^{\circ}\) to \(180^{\circ}\). The study carried out for \(\theta_{i1}=15^{\circ}\) was denoted as _Bistatic-1_ and the study for \(\theta_{i2}=65^{\circ}\) was denoted as _Bistatic-2_.