# Compact Bistatic Iterative Passive Radar Based on Terrestrial Digital Video Broadcasting Signals
## 3 Proposal Description
### Operational Time  
During the operational time, at each frame, the channel is estimated at each antenna, and the power delay profile (PDP) is obtained for each antenna. When a target appears, it is likely that the reflections into this channel will affect its propagation characteristics, causing the channel's estimation to change and new reflections (taps) to appear in the estimation of time-domain channel, as shown in Figure 7 for receiver antenna 2 (all antennas will exhibit similar behavior). In this figure, the PDP is the plot. As shown in this figure, a multi-path channel with two taps is simulated without any target on the left side, and with the target on the right side. This channel may appear in a scenario in  
Figure 6: Pilot locations within the DVB-T frame structure [27]. The time index is vertical, and the frequency index is horizontal. Edge pilots are repeated with each OFDM symbol in the frame at subcarrier 0, while scattered pilots swipe in positions at each OFDM time symbol. This pilot structure of DVB-T is exactly the same as the pilot pattern PP1 in DVB-T2. Figure 7: Effect on the time-domain channel’s estimation (power delay profile) of the target. Left part is when there is no target and the right part is when there is a target reflecting the signal. which there is a main reflector (clutter) like a building or a mountain. Thus, by comparing both estimations, new taps can be identified. For the purposes of localization, the first new tap (\(\tau_{n}\)) will make the main contribution to the target reflection; thus, we chose to use it because our goal is to estimate its position and not to identify the channel for coherent demodulation. At this point, it is notable that, for our proposal, the important value to take into account is the delay in the new tap in inferring the total distance to this antenna, and not the amplitude. Thus, we can consider the time of this first new tap to be the time of arrival for the reflection on the target; then, assuming the speed of the light (\(c\)), we can calculate the distance using \(d=c\times\tau_{n}\). It is important to note that, in more complex scenarios with multiple clutters, since the algorithm operates based on the difference in PDP, the first new tap also provides a reliable estimate for the target's distance. Once we have estimated the three total distances to each antenna, the Equation (9) can be used to estimate the position. If our estimations of the distances were perfect, Equation (9) would provide the exact coordinates of the target. However, small mismatches in the distances will result in erroneous estimations. Indeed, this equation is quite robust if the distance to the antenna is large. For example, if the antennas are separated by several km, this formula only produces minimal errors, even for errors of 10 or more meters in the estimation of distances. This is the case when several receivers are used and has been extensively evaluated in the existing literature. The reason behind is that the error on distances compared to the distance between antennas is small. However, it is usually challenging to use several synchronous receivers for this purpose. In our design of a compact receiver with antennas separated by a few meters, an error of even 1 m has the same order of magnitude as the distances between antennas. Therefore, the impact on the estimation accuracy is huge. Looking at Equation (10), two factors can be easily identified. The first involves a pseudo-inverse and identity matrix, which only depends on the coordinates of the antennas and their distances from the transmitter (\(d_{0}\)) and its height, \(E_{z}\); it is essentially a 1/2 factor (in matrix form). The second part of the expression depends on \(\mathbf{z}\), \(\mathbf{r}\), and \(R_{t}\). Examining \(\mathbf{z}\) in more detail, we can see that whether the antennas are co-located, the coordinates \(Rx_{i}\), \(Ry_{i}\), and \(Rz_{i}\) will be small in comparison to \(d_{0}\) and \(dt_{i}\); thus, the vector will be dominated by \(d_{0}^{2}\) and \(dt_{i}^{2}\).