## 2 Phased Array Radar (PAR)  
### Rocket Tracking System (RTS)  
#### 2.1.1 Features, Requirements and Functions  
RTS is the main component of the tracking area and consists of radar sensors that collect and process data from the target trajectory. However, despite the current knowledge about radars, the construction of an RTS involves significant technical challenges because the target may have a reduced cross section and be hundreds of miles away, which leads to the need for high power transmitters (peak values of hundreds of kW) and antennas with fast scanning and high precision. Figure 1 shows a block diagram of a tracking radar. The devices that perform the tasks of each block must be designed so as to meet various operational radar requirements, such as accurate tracking in three-dimensional position, long distances range, high reliability, easy maintenance, low probability of false alarms, detection at extreme conditions (stealth targets or those with very high or very low speeds), clutter suppression, noise filtering in RF circuits and interference inhibition caused by commercial transmitters or countermeasures (e.g., jammers) [9]. Moreover, in the most difficult operating conditions, both processor and antenna deserve special attention. The antennas will be examined in Section 2.2. As for the processors, there has been great progress in technology of digital signals through the high integration of semiconductors, miniaturized microwave integrated circuits and computational-aided designs for microwave circuits. Signal and data processing must extract information from the target, such as format, position and speed, as well as cancel clutter, noise and interference, which could saturate the receiver, preventing detection of real targets or generating false target detection [11,24]. Data filtering is a part of this process, which removes data generated by error detection and calculates future position data in order to direct antennas. In this case, the tracking success depends on selecting the appropriate dynamic models of target movement [25,26], considering that targets in general, such as commercial aircrafts, rockets or missiles, can be characterized by three basic dynamic movements: constant speed motion, accelerated motion and rotational motion [27]. A dynamic model widely used is the Kalman filter, which is the basis for the development of many others models [28]. Thus, the main measurement of radar systems, both for tracking and surveillance, are the three-dimensional position coordinates of the target (\(x\), \(y\) and \(z\), in Cartesian coordinates). The basic difference is that tracking seeks to detect and pursue a specific target, while surveillance monitors a region of space to detect unknown targets [29]. Hence, when tracking, in addition to position detection, the sensor must provide a quick and accurate estimation of future kinematic parameters of the target [30]. Thereby, considering the scanning time, the tracking processing must be much faster (around milliseconds) than the surveillance one (about 5 s [25]). Figure 1: Block diagram of a tracking radar. Apart from processing, the functions of tracking and surveillance differ in terms of radar-target distance and response speed of the radar. In general, during surveillance, as in air traffic control, the target is moving with its main axis approximately parallel to the velocity vector and is far from the radar [31], so it is reasonable to assume that the target and radar are in the same horizontal plane [32, 33]. However, in tracking, this assumption cannot be considered, especially for the so-called platform or pad radars. These radar sensors are positioned near the launching site, aiming to track rockets since ignition time, so they are subject to quick changes in elevation angle, which requires a high response speed to the radar beam motion. In normal operation, another difference is the beamwidth.