## 3 Multi-Beam Fast Tracking and Satellite Capture Method  
### Overall Scheme of Multi-Beam  
According to the multi-beam array antenna's characteristics, the array antenna is divided into multiple sections. When the moving carrier is in a normal state, the entire array antenna runs as a whole and completes stable tracking of the communication satellite through methods such as conical scanning. When the carrier is in a high maneuvering moving state, the SOTM array antenna is divided into multiple beams in order to prevent the antenna beam from losing track of the communication satellite. Each beam should be pointed to multiple locations near the current position. Then, through demodulation analysis and combining the energy distribution characteristics of the main lobe of the array antenna, the accurate antenna pointing direction can be quickly determined. The previous section introduced the directivity of array antennas. This section uses the graphical representation of array antenna directivity, i.e., the directional pattern, to design a method for fast-tracking satellites by array antennas under a high maneuvering state. Figures 4 and 5 show the wide-angle directional pattern and the main lobe beam directional pattern, respectively. Figure 4: A sketch of the wide-angle holography antenna pattern. Figure 5: A sketch of the main lobe beam holography antenna pattern. After dividing the entire array antenna into multiple beams by block, the main lobes of each beam become \"fatter,\" resulting in a larger beam coverage for the array antenna. When the SOTM carrier's high maneuvering moving characteristics cause significant deviation in the tracking direction of the array antenna beam, if the array antenna works as a single beam due to its narrow beam, the satellite may deviate from the beam range of the array antenna due to the beam center being too far away from the communication satellite, leading to the loss of tracking the communication satellite by the array antenna. At this time, multiple \"fatter\" beams can scan simultaneously, resulting in an expansion of the beam scanning coverage range; this significantly increases the probability of the satellite being within the beam coverage range. Based on this, the rapid tracking scheme of this paper is designed. The division of the array antenna into four beams is used as an example to illustrate the method of this paper. Assume that Figure 6 represents the entire SOTM array antenna, where the black squares represent the elements. The number of black squares does not represent the specific number of elements in the array antenna; it is for illustration purposes only. The array antenna is divided into four sub-blocks, each of which can form an independent beam, as shown in the schematic diagram in Figure 7. It is necessary for the number of elements in each sub-block to be equal. In this way, each beam will point to a location close to the direction of the SOTM array antenna when it runs as a single beam; this corresponds to four points on the directional pattern, and the schematic diagram for multi-beam taking points on the directional pattern is shown in Figure 8, in which, the black dots represent the pointing values of the 4 sub-beams, while the blue dot represents the theoretical target pointing value of the beam when the array antenna is running as a whole. After achieving different pointing directions for each sub-beam in the multi-beam setup, carrier analysis is performed on each sub-beam and, combined with the energy distribution characteristics of the array antenna's main lobe, the coordinate values of each sub-beam pointing direction in the directional pattern shown in Figure 8 are calculated separately. Figure 6: Sketch of the SOTM array antenna. Figure 7: A sketch of the multi-beam scheme of the SOTM array antenna. Figure 9 shows a schematic diagram of the design proposal. Each sub-beam is processed through its own synthesis network, and the processed data is sent to its own detection component.