# Motion Compensation for Long Integration Times and DoA Processing in Passive Radars
## 5 IDEPAR Demonstrator for DVB-S  
IDEPAR is a PR technological demonstrator developed in the University of Alcala [5; 31; 36]. The acquisition chain is composed of two universal software radio peripheral (USRP) software defined radio (SDR) devices. Each one can perform full-coherent digitalization of four channels with a maximum instantaneous bandwidth of 100 MHz per channel. An \(N_{a}=7\) element surveillance array was built using low-cost commercial single elements. Each single antenna uses a different acquisition channel. The eighth channel was reserved for acquiring the reference signal using a parabolic reflector antenna with higher gain. The surveillance array is composed of axially corrugated conical horns and low noise blocks (LNPs) with conversion gains greater than 50 dB (Figure 4a). Horizontal or vertical polarization can be selected [37]. The simulation results presented in [31] showed that the single element achieves a maximum realized gain of 13.9 dBi with a symmetrical HPBW\(=38.4^{\circ}\) in both E and H planes (Figure 4b). The planar array architecture is shown in Figure 5. The main parameters are an angular resolution of 3.2\({}^{\circ}\); maximum directivity \(D_{max}=22.3\) dBi; and a side lobe level (SLL) of 12.2 dB in the worst case [31]. For an azimuth pointing direction of 12\({}^{\circ}\), the grating lobe appears at \(-14.3^{\circ}\), reaching almost the same directivity level as the main desired lobe. The steering margin to unambiguous DoA (Direction of Arrival) estimation must be limited to \([-12^{\circ};12^{\circ}]\), reducing the azimuth coverage area to 24\({}^{\circ}\). IDEPAR signal processing scheme, proposed in [8], is shown in Figure 6:
* The reception stages include RF-front ends and digitalization processes. In the processing stages, zero Doppler interference rejection techniques are applied to obtain the snapshot defined in the time domain: \(\mathbf{s}_{surv}[n]=[s_{surv,1}[n],s_{surv,21}[n],\ldots,s_{surv,N_{a}}[n]]^{T}\), where \(T\) denotes the transpose vector. These techniques are applied to reduce DPI (direct path interference), multipath, and stationary clutter sources. * The acquisition time is divided into CPIs of duration \(T_{int}\), and independent CAFs are calculated for each single radiating element signal \(s_{surv,i}[n]\), \(i=1,\ldots,N_{a}\). These are denoted as CAFs \(\mathbf{s}_{CAF}[m,p]=[s_{CAF,1}[m,p],s_{CAF,2}[m,p],\ldots,s_{CAF,N_{a}}[m,p]]\). * Digital beamforming is applied in the CAF domain to generate \(N_{BF}\) orthogonal beams pointing to azimuths \(\Phi=[\phi_{BF,1},\phi_{BF,2},\ldots,\phi_{BF,N_{BF}}]\) within the azimuth coverage without grating lobes ambiguities. The use of orthogonal beams guarantees that a signal arriving along the maximum radiation axis of a beam will have no output in any other beam, and that a signal that is not along the maximum radiation axis will appear in the side lobes of the other beams [38]. The result is a three dimensional matrix called \(\mathbf{S}_{CAF}=\left[s_{CAF}[m,p,\phi_{BF,1}],\ldots,s_{CAF}[m,p,\phi_{BF,N_{ BF}}]\right]\). * 3D reference window CFAR constant false alarm rate: (a) For each \([m,p]\) pair, the cell under test (CUT) is the cell \(s_{CAF}[m,p,\phi_{BF,i}]\) for the \(\phi_{BF,i}\) value where the maximum power of the echo was received; (b) a 3D reference window with dimensions \(R_{R}xR_{D}xN_{\phi_{BF}}\) (range x Doppler x steering angle) was generated using the neighbour cells around the CUT, excluding the guard cells defined along range and Doppler for all of the steering angles. This 3D reference window also excludes \(s_{CAF}[m,p,\phi_{BF,i}]\), \(i=1,\ldots,N_{\phi_{BF}}\). * The detection matrix generated by the 3D reference window CFAR is applied to a bistatic tracker. The linear functions that govern the dynamic model in the bistatic range-Doppler domain, and the direct relation with the measurement vector, make the linear Kalman filter the optimum solution in terms of root-mean-square error (RMSE) [39].