## 2 Phased Array Radar (PAR)
### Radiation Pattern Control  
#### 2.2.1. Phased Array (PA)  
Radiation characteristics of the antenna must meet the design requirements, and they vary according to its shape and building materials, which are factors that determine the distribution of electric and magnetic fields. Typically, for a single antenna, the distribution of these fields, seen by the radiation pattern, is relatively sparse and has low values of gain [7]. However, applications such as RTS radar sensors require antennas with high gain and control, which can be made by combining several radiator elements in a single structure, called antenna array [7,8,20]. In the array, besides the geometry of elements (spatial distribution and distance) and the type of antenna (wires, loops, apertures, microstrip or a mix of them), it is possible to dynamically format the radiation pattern by controlling the amplitude and phase of excitation signals (electronic control) of each element, originating PAs [7]. Nowadays, with increasingly faster and cheaper digital processors, such control has become more common, enabling new functionalities, such as improving coverage area, quality of signal transmitted/received (greater gain) and interference suppression. This is achieved by factors like an accurate positioning of the main beam tilt, beamwidth and beam number flexibility, high scanning speeds, increased gain, reduced sidelobes and rejection of interfering signals (null positioning). To build PAs, elements are distributed along an axis (linear array), a flat surface (planar array) or 3D surface (three dimensional array). Neglecting the mutual coupling among the elements, the total fields of PA are obtained by a vector composition among fields of their elements. Therefore, high gain is achieved by the action of constructive interference in the desired direction and destructive interference in other directions. In Figure 4, there is a linear array of isotropic elements, often used to form more complex antennas. The planar array, for example, can be considered a \"linear array of linear arrays\". Planar arrays require more complex excitation schemes, although they allow greater control of the radiation characteristics, such as a symmetrical radiation pattern and smaller sidelobes. Figure 3: (**a**) Rocket Tracking System (RTS) with two radar sensors. (**b**) Flowchart of operation of the Radar No.1. The PA total far field (\(E_{T}\)) is equal to the field of an element positioned at the reference point (\(E_{el}\)) multiplied by the array field, or array factor, \(AF\), as summarized in Equation (1) [7]. This process is called multiplication of radiation patterns and can be extended to PAs of several elements [7,8]. In general, \(AF\) depends only on the geometry and excitation of PA, which eases projects designed to isotropic elements and then extrapolated to any type of element. \[E_{T}=E_{el}\cdot AF \tag{1}\]  
The \(AF\) allows, then, to match PA radiation to the desired application with the tilt angle of the main lobe ranging between broadside and endfire directions. Besides that, it reduces the level of sidelobes, avoiding interference, regions without coverage and power loss in the main direction [7,13]. In this case, the radiation pattern can be traced from the radiation intensity, \(U\), which for isotropic elements is equal to the square of \(AF\)[7]. For a linear array with variation only in tilt angle, \(\theta\), the normalized expression of \(U\), in dB, is given in Equation (2). The parameter used to quantify the level of sidelobes is the Relative Side Lobe Level (RSLL), calculated as the ratio between the amplitudes of the main lobe, \(A_{M}\), and the greater sidelobe, \(A_{S}\), according to (3) [20].