# Compact Bistatic Iterative Passive Radar Based on Terrestrial Digital Video Broadcasting Signals
## 4 Results and Discussion
In Figure 9, the evolution of the error in the estimation of the three distances with respect to the true distance is shown (\(\Delta_{i}=dt_{i}-\hat{dt}_{i}\)). In this figure, the \(y\) axis shows the estimated error at each antenna during the running of the algorithm. At the beginning, the first antenna showed an error of 30 m, antenna 2 showed an error of 60 m, and antenna 3 showed an error of 50 m. These errors converge gradually to the true value, i.e., as it can be seen, by using our proposed algorithm, the estimated distances are converging to the true value exhibiting an error of 0 at the end, in this example. It can be observed that, for this example, at the beginning, distance 1 is not modified by the algorithm (the error keeps constant); however, after some iterations, it is modified until its instantaneous error is decreased. Moreover, the estimated distances are modified slightly with each further iteration, usually resulting in reduced error. The algorithm only modifies one distance at a time, although they can alternate. Inorder to illustrate the evolution of the total error throughout this process, the total error values are plotted in Figure 10. The total error is  
\[Error_{T}^{i}=\sqrt{\left(\mathbf{x}-\mathbf{\hat{x}_{i}}\right)^{2}} \tag{16}\]  
As shown for these examples, using our proposed method, the error converges to 0, although not always producing a perfect value. Moreover, at the beginning, this error can even increase with further iterations and it slowly decreases with further iterations to a perfect estimation (0 error) if the initial estimation is within a specific lock-in range, and the step divides the initial error at each distance. For comparison purposes, the alto gradient  
Figure 8: Example of the evolution of coordinates’ estimation. The true coordinates of the target are \(T_{X}=1000\) m, \(T_{Y}=-200\) m, and \(T_{Z}=5000\) m. Left part, \(X\) coordinate, middle, \(Y\) coordinate and right part, \(Z\) coordinate. Figure 9: Evolution of the error at each estimated distance with an initial error of 30, 60, and 50 m in the distance from antenna 1 (\(dt_{1}\)), 2 (\(dt_{2}\)), and 3 (\(dt_{3}\)), respectively. descend method has been used. As shown, the gradient leads to faster convergence to a local minimum that then halts the process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Description** & **Value** & **Units** \\ \hline \multicolumn{3}{c}{Standard} & 8k & - \\ \hline \(P_{tx}\) & Transmission power & 20 & dBW \\ \hline \(f_{c}\) & Transmission frequency & 482, 530, 626 & MHz \\ \hline \(N_{c}\) & N. of useful subcarriers & 6817 & - \\ \hline \(T_{u}\) & Useful symbol duration & 896 & \(\upmu\)s \\ \hline \(T_{s}\) & OFDM symbol duration & 1120 & \(\upmu\)s \\ \hline \(B\) & Bandwidth & 7.61 & MHz \\ \hline \(d\) & Distance between antennas & 2.55 & m \\ \hline \(d_{0}\) & Distance to DVB-T Tx & [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] & km \\ \hline \(T_{z}\) & Target altitude & [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15] & km \\ \hline \(T_{x}\), \(T_{y}\) & Target coordinates & [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] & km \\ \hline \(\mu\) & Update factor & 0.015 & m \\ \hline \(L\) & Max. n. of iterations & 10,000 & - \\ \hline \(K\) & Upsampling factor & 10 & - \\ \hline \(\delta\) & Target error & 0.1 & m \\ \hline \(E_{z}\) & Tx height & 10 & m \\ \hline \(\alpha_{t}\) & Target’s reflection coefficient & 0.9 & - \\ \hline DS & Doppler spectrum & Jakes & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 10: Example of the evolution of the total error for the case when true coordinates of the target are \(T_{X}=1000\) m, \(T_{Y}=-200\) m, and \(T_{Z}=5000\) m.  
After showing the different variables of the algorithm, in Figure 11, the normalized mean squared error (MSE) is shown for different SNRs at the receiver. In these simulations, the target is located in different positions, as is the DVB-T transmitter (see Table 1 for more details).