# Bistatic Forward ISAR with DVB-T Transmitter of Opportunity
## 5 Numerical Simulation Experiment  
To illustrate the adequacy of the BFISAR geometrical and kinematical analysis, synthesis of the DVB-T waveform and BFISAR signal, and the algorithms for BFISAR signal formation and image reconstruction, a simulation experiment was carried out. Consider the following scenario depicted in the Cartesian coordinate system \(Oxyz\) (Figure 1). The stationary DVB-T transmitter and receiver were placed at heights near an airport or other zones under defense. The coordinates of the DVB-T transmitter: \(x^{s}=10\) m; \(y^{s}=100\) m; \(z^{s}=150\) m.  
The coordinates of the DVB-T receiver: \(x^{r}=1\) km; \(y^{r}=100\) m; \(z^{r}=150\) m.  
Object's trajectory parameters:  
Vector velocity modulus: \(V=12\) m/s;  
Vector velocity's guiding angles: \(\alpha=\pi/4\); \(\beta=\pi/4\); \(\gamma=\pi/2\). The coordinates of the mass-center at the moment of imaging \(p=0\):  
\(x_{00}(0)=100\) m; \(y_{00}(0)=50\) m; \(z_{00}(0)=200\) m.  
A flying object, helicopter, was illuminated by DVB-T waveform segments with the following parameters:  
Segment repetition period \(T_{p}=1\) ms;  
DVB-T symbol's width \(T=0.896\) ms;  
DVB-T segment's width \(T=1.12\) ms;  
DVB-T segment's samples \(K=1024\)\(K\);  
Central carrier frequency \(f=0.9\) GHz;  
DVB-T sample's time width \(\Delta T=0.13\) u\(\mathrm{s}\);  
Frequency bandwidth \(\Delta F=7.61\) MHz;  
Number of segments for synthesis of the aperture \(N=256\). The object' geometry is described in a 3-D coordinate system with a normalized intensity of scattering points in nodes \(a_{ijk}=0.01\) (Figure 2). The image of the helicopter is without propellers. During the flight, propellers rotate at a high speed and can be accepted as invisible. However, it is not very correct for microwaves at a frequency of 0.9 GHz. The propellers induce additional correlation noise that was ignored in the present work. The simulation experiment was carried out in the following order. First, the DVB-T waveform's coefficients were calculated. Second, geometrical and kinematical parameters and distances to the object's scattering points were calculated and sorted. Third, the BFISAR signal was created. Fourth, the image reconstruction based on the 2-D Fourier transformation realized by inverse fast Fourier transforms was implemented. The pseudo code of these stages is presented in Appendix A. The real (a) and imaginary (b) parts of the complex BFISAR signal are presented in Figure 3. The BFISAR signal structure has properties of a complex microwave hologram. Figure 2: Geometry of the flying object—helicopter. The first step of the image reconstruction is the range compression of the BFISAR signal. The pseudo code of the range compression realized by the first inverse fast Fourier transform is presented in Appendix A. The real (a) and the imaginary parts of the complex BFISAR signal compressed in the range direction are presented in Figure 4. It can be seen that the interfering structure of the BFISAR signal occupies a particular area in the range-compressed signal. The second step of the image reconstruction is the azimuth compression of the range-compressed BFISAR signal. The pseudo code of the azimuth compression realized by the second inverse fast Fourier transform is presented in Appendix A. The quadrature components of the final BFISAR complex image, i.e., the real (a) and imaginary (b) parts of the azimuth-compressed BFISAR signal obtained after range compression, are presented in Figure 5.  
In Figure 6, the amplitude and phase of the final BFISAR complex image extracted from the DVB-T BFISAR signal by applying all steps of the imag  
Figure 4: BFISAR signal after range compression: (**a**) real and (**b**) imaginary parts. Figure 3: Complex BFISAR signal presented by (**a**) real and (**b**) imaginary parts. The final amplitude image of the object has a poor range and not very satisfactory azimuth resolutions.