## 3 Passive Radar Array Antenna Design  
### Problem Formulation  
The design of an array antenna to be part of the IDEPAR demonstrator [8], which has been used to test the algorithms, is one of the objectives of this paper. Figure 4 presents a functional block diagram of this multichannel DVB-T-based PRS. To ensure an easy maintenance and low-cost, COTS components were used as much as possible, and following this design requirement, commercial antennas were selected. The use of an antenna array and array digital signal processing could provide further benefits:  
* Reducing the direct signal interference, by creating suitable nulls in the beam pattern in the direction of transmitters. Figure 4: Functional block diagram of Improved Detection Techniques for Passive Radars (IDEPAR). Figure 3: Zero-Doppler cut of the Ambiguity Function (AF) of a simulated Digital Video Broadcasting-Terrestrial (DVB-T) signal. * Enabling the application of beamforming techniques for estimating the target azimuth location. * Increasing the angular coverage using an individual element of the array with a wide beamwidth. The Televes 4G NOVA antenna (Figure 5), which is a log-periodic antenna designed in microstrip technology for operating in the 698 MHz-960 MHz and the 1700 MHz-2700 MHz bands, was selected according to the following requirements: (a) broad beamwidth to provide the required angular coverage and a wide range of steering angles; (b) high discrimination between the main and the back lobes; (c) small physical dimension. The 3D antenna model was generated and simulated in the Ansoft HFSS (High Frequency Structure Simulator). Figure 6 shows the radiation patterns in elevation and azimuth. The 3-dB azimuth beamwidth is approximately 60\({}^{\circ}\), and the directivity is 7.98 dBi for 770 MHz (Figure 7). In a first approach, a study of Uniform-Linear Arrays (ULA) along the y-axis was carried out. Arrays of five elements were considered because the current version of the passive radar demonstrator includes six synchronized receiving chains: one for the reference channel and five for the surveillance one. In Spain, DVB-T is transmitted in horizontal polarization, which requires all antennas to be parallel to the ground. The inter-element spacing is limited by the width of the antenna, which could give rise to the appearance of grating lobes. Equation (2) is the stringent condition for no grating lobes [27], being \(\phi_{sa}\) the steering angle and \(d\) the inter-element spacing. Figure 5: Televés 4G NOVA antenna. Figure 6: Televés 4G NOVA antenna radiation pattern generated using ANSYS HFSS. \[|\sin(\phi_{sa})|<\frac{\lambda}{d}-1 \tag{2}\]  
For \(d=315\) mm, the antenna width, beam patterns generated for steering angles higher than \(13.7^{\circ}\) and lower than \(-13.7^{\circ}\) will present grating lobes at the operating frequency of 770 MHz. Although the radiation pattern of the antenna reduces the effect of grating lobes, they can be seen in Figure 8 for steering angles greater than or equal to \(15^{\circ}\). A further study revealed that the reflector shown in Figure 5 only worked at the higher frequency band (1700 MHz-2700 MHz), so we decided to remove it together with the radome, reducing the minimum inter-element spacing to 210 mm. In this case, the steering angles' interval for no grating lobes is \(|\phi_{sa}|\leqslant 58.79^{\circ}\). As the single radiating element beamwidth is \(60^{\circ}\), the realistic steering angle interval is \(|\phi_{sa}|\leqslant 30^{\circ}\). Therefore, the inter-element spacing can be increased to improve array directivity while fulfilling the no grating lobes condition expressed in Equation (2). If this condition is relaxed allowing the appearance of part of the grating lobe for a steering angle \(\phi_{sa}=30^{\circ}\), with a maximum level equal to the Sidelobe Level (SLL), the inter-element spacing can be increased to 270 mm (Figure 12b).