# Motion Compensation for Long Integration Times and DoA Processing in Passive Radars
## 7 Experimental Results
In Figure 16, zoomed areas of the CAFs centered on the collaborative target position on the CPIs\(=4,41\), and 72 are presented to show the  
Figure 14: Detection and tracking outputs of the first step without target motion compensation of the proposed scheme. Figure 15: Results associated with Doppler migration compensation bank filter. **(a)** Bistatic tracker results for filters designed with \(f_{Dr}^{i}=\{-94.29,-47.14,0,47.14,94.29\}\) Hz/s. **(b)** Tracker performances for the collaborative target are provided by the first and second stages of the proposed scheme. SIR improvements in target motion compensation stages and how the target contributions are concentrated on fewer Doppler Shift and range cells. Using the same representation philosophy, zoomed areas of the CAFs centered on the collaborative target position on one CPIs centered at 1250 ms with \(T_{int}=750,1000\) and 1250 ms are depicted in Figure 17. At the input, the area where target contributions are concentrated is bigger as the integration time is also longer. The Doppler migration reduction can be obtained until CPI value of 1000 ms, but for 1250 ms, a non-linear variation of target Doppler (a non-constant acceleration during CPI) is presented (Figure 17c), and the correction is not so significative. With respect to the range walk, the target trajectory during CPI becomes more complex and non-linear as the time interval increases. In Figure 18a, the SIR values estimated for the target detections in the CAFs generated for the \(0^{\circ}\)-steered beam in the first and third stages of the proposed methodology during the 80 CPIs are presented. The results confirm that the target motion compensation provides an SIR improvement of around 10 dB with \(T_{int}=500\) ms. SIR values for CPIs = \(4,41\), and 72, and the corresponding DoA accuracy, are summarized in Figure 18b. The SIR after the coherent signal processing is related to the SIR before the integration, the signal bandwidth, and \(T_{int}\)[44]. As the input SIR and bandwidth are constant, the SIR improvement with respect \(T_{int}=500\) ms should be 1.76, 3, and 3.98 dB for \(T_{int}=750,1000\) and 1250 ms, respectively, with the proposed solution when the target dynamics are characterized by constant acceleration and linear movement in RDM domain. The results presented in Figure 19 confirm that controlled long-time intervals can be considered with the proposed methodology to obtain SIR improvements very close to the theoretical ones. The best relationship between CPI value, integration gain, and SIR improvement is obtained for \(T_{int}=500\) ms (Figure 16) and \(T_{int}=750\) ms (Figure 17a). The final estimated collaborative target trajectory provided by the proposed solution with \(T_{int}=500\) ms is depicted in Figure 20 on 2D map coordinates and compared with GPS data acquired on the collaborative vehicle during the acquisition time, confirming the suitability of the proposed scheme for the DVB-S based on passive radar signal processing. Figure 16: Target motion compensation results in the CAF zoomed area in different CPIs. Left, center, and right images are inputs, outputs of second stage, and outputs of third stage of the proposed scheme, respectively. Figure 17: Target motion compensation results in the CAF zoomed area with different integration times. Left, center, and right images are inputs, outputs of second stage, and outputs of third stage of the proposed scheme. Figure 18: Study of collaborative target SIR and DoA accuracy measured in CAF generated for the \(0^{\circ}\)-steered beam associated with the first and third stages of the proposed scheme and \(T_{int}=500\) ms.