# Bistatic Forward ISAR with DVB-T Transmitter of Opportunity
## 7 Conclusions  
BFISAR geometrical and kinematical features, models of the waveform and signal structure, and an algorithm for extraction of the image were the focus of the present study. A BFISAR scenario with a DVB-T transmitting station of opportunity and receiver, and an object crossing baseline was analytically described by kinematical and position vector equations. The DVB-T waveform and BFISAR signal were defined by mathematical expressions. Based on the model of the BFISAR signal, an algorithm for image extraction was drawn. Transformation of the 3-D coordinates of the scattering points into their 2-D coordinates on the imaging plane was described in detail. The imaging algorithm includes the following steps: signal compression in range direction by inverse Fourier transformation, and compression in the azimuth direction by inverse Fourier transformation; the image was improved by compensation of the phases induced by object motion of higher order. To justify the correctness of the analytical and geometrical models describing the BFISAR scenario, waveform, signals, and the algorithm for extraction of the object image, graphical results of the simulation experiment were provided. Conceptualization, methodology, formal analysis, investigation, writing--original draft preparation, writing--review and editing final manuscript, A.D.L. ; data curation and processing, software implementation, T.P.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. A pseudo code for calculation of DVB-T coefficients c(m, l, k):  
\( \begin{array}{l}\text{fqam = 20''10''8};\\ \text{quadrature = nchoosek ([-4,-2,2,4],2);}\\ \text{qam\_coeff = [2 2 4 4 - 2 - 2 - 4 - 4 - 2 - 2 - 4 - 2 2 4 4 ; 2 4 2 4 - 2 - 4 - 2 - 4 - 2 - 4 - 2 - 4 - 2 - 4 - 2 - 4 - 2 - 4 ];}\\ \text{am = sqrt(qam\_coeff(1,:).^2+qam\_coeff(2,:).^2);}\\ \text{ph = exp(lj).*(2.*pi.*fqam + atan(qam_coeff(1,:)./qam_coeff(2,:)).*180./pi));} \\ \end{array} \)qam = am. *ph; c_mlk = zeros(M,68,6817); pilot = [0 48 54 87 141 156 192 201 255 279 282 333 432 450 483 525 531 618 636 714 759 765 780 804 873 888 918 939 942 969 984 1050 1101 1107 1110 1137 1140 1146 1206 1269 1323 1377 1491 1683 1704 1752 1758 1791 1845 1860 1896 1905 1959 1983 1986 2037 2136 2154 2187 2229 2235 2322 2340 2418 2463 2469 2484 2508 2577 2592 2622 2643 2646 2673 2688 2754 2805 2811 2814 2841 2844 2850 2910 2973 3027 3081 3195 3387 3408 3456 3462 3495 3549 3564 3600 3609 3663 3687 3690 3741 3840 3858 3891 3933 3939 4026 4044 4122 4167 4173 4188 4212 4281 4296 4326 4347 4350 4377 4392 4458 4509 4515 4518 4545 4548 4554 4614 4677 4731 4785 4899 5091 5112 5160 5166 5199 5253 5268 5304 5313 5367 5391 5394 5445 5544 5562 5595 5637 5643 5730 5748 5826 5871 5877 5892 5916 5985 6000 6030 6051 6054 6081 6096 6162 6213 6219 6222 6252 6258 6318 6381 6435 6489 6603 6795 6816] + 1; c_mlk(1:M.;pilot + 1) = 4/3; data = find(c_mlk = =0); for f = 1: length(data) c_mlk(data(f,1)) = ph(round((rand)*15) + 1); end Pseudo code for calculation of coordinates and distances of scattering points: p_v= (0: N\(-\)1); % N is the number of emitted segments. \(\chi\)s = \(-\)kron(x00,ones(num,N)) + kron(xrs,ones(num,N))-kron(Vx*(N/2-p_v)*Tp,ones (num,1)) + kron(transf_xyz(1,:),ones(N,1)). '; Ys = \(-\)kron(y00,ones(num,N)) + kron(yrs,ones(num,N))-kron(Vy*(N/2-p_v)*Tp,ones (num,1)) + kron(transf_xyz(2,:),ones(N,1)). '; Zs = \(-\)kron(z00,ones(num,N)) + kron(zrs,ones(num,N))-kron(Vz*(N/2-p_v)*Tp,ones (num,1)) + kron(transf_xyz(3,:),ones(N,1)). '; Xr = kron(xrr,ones(num,N))-kron(x00,ones(num,N))-kron(Vx*(N/2-p_v)*Tp,ones(num, 1))-kron(transf_xyz(1,:),ones(N,1)). '; Yr = kron(yrr,ones(num,N))-kron(y00,ones(num,N))-kron(Vy*(N/2-p_v)*Tp,ones(num, 1))-kron(transf_xyz(2,:),ones(N,1)). '; Zr = kron(zrr,ones(num,N))-kron(z00,ones(num,N))-kron(Vz*(N/2-p_v)*Tp,ones(num, 1))-kron(transf_xyz(3,:),ones(N,1)).