# Compact Bistatic Iterative Passive Radar Based on Terrestrial Digital Video Broadcasting Signals
## 4 Results and Discussion  
In order to evaluate our proposal, we present several simulations. In all of them, the DVB-T transmitter has an equivalent isotropic radiated power (EIRP) of 20 dBW and the noise level is adjusted to the specified signal-to-noise ratio (SNR). The target is placed in different positions, as is the receiver. The distance between antennas at the receiver is \(d=2.55\) m and the three antennas (1,2,3) are moved 1, 2, and 3 m along the \(z\) axis once the calibration is finished in order to avoid the occurrence of a rank-deficient matrix \(S\). The frequencies used were 482, 530, and 626 MHz (if applicable). The other parameters of this simulation can be found in Table 1. Although parameter \(d\) does not directly affectthe algorithm, it is important to highlight that the distance between antennas is \(2d\). In order to achieve diversity, a separation of at least \(\lambda/4\) or \(\lambda/2\) is needed. However, within traditional estimation algorithms, the larger this distance is, the better the performance and the lower the permissible error, as indicated earlier in this paper. For this reason, to maintain a compact design, a value of approximately 10 times the wavelength of the frequency range is used. To clarify the simulation process, the procedure for generating each realization is outlined below. The first step is to randomly generate the distance from the transmitter (Tx), denoted as \(d_{0}\), within the range of 1 to 10 km. As specified in Table 1, the Tx's height is set to 10 m, which is a typical value for a DVT-T transmitter. Next, a random channel is generated between the Tx and the four receiver (Rx) antennas, with some correlation considered among the antennas. Following this, a target is placed at a random position within the specified range (see Table 1). The channel with the target present is then calculated, taking into account potential reflections. The path loss between the Tx and each antenna is determined. To simulate the adequate signal-to-noise ratio, the noise value is calculated to achieve the desired SNR. If, due to the randomness of positioning, the value generated cannot meet the desired SNR value, this position is discarded and another one is generated (e.g., the SNR being simulated is very high and the random position for Tx and Target only with the path loss exceeds the SNR, and thus, noise should be negative to reach the desired value. In this case, another position is randomly generated). Additionally, the path loss between the Tx and the target, as well as between the target and the antennas, is computed. For each realization, eight frames (approximately 600 ms) are simulated using the same channel. The channel at each antenna is estimated using pilot sequences within the signal, and the power delay profile is obtained. The same procedure is repeated with the target included in the simulation. Next, the difference between the PDPs is calculated, and the distances are estimated. Finally, the algorithm is applied to refine the estimated coordinates based on these initial distance estimates. As indicated, the algorithm runs until the \(TargetError\) is met (0.1 m) or the maximum number of iterations is reached (10,000). In Figures 8 and 9, the evolution of the coordinates' estimation and the evolution of the error at each distance as the iterations progress are shown in a synthetic example, wherein the estimated distances 1, 2, and 3 exhibited a relatively large error of 30, 60, 50 m, respectively, that is, if the theoretical estimated distance at antenna 1 is 1000 m, it estimates 30 more meters. As shown in Figure 8, for example, the original estimation is completely erroneous when the error in the estimated distances is large; eventually, however, they converge to the correct estimation at the end due to the refinement process. Interestingly, this convergence is not monotonous. This is one of the reasons that Jacobian descent and other similar methods cannot adequately address this problem.