Strategy of Multi-Beam Spot Allocation for GEO Data Relay Satellite Based on Modified K-Means Algorithm

With the booming development of satellite applications, the giant constellations of low Earth orbit (LEO) satellites have introduced challenges for the data relay service. The multi-beam satellite not only offers concurrent access to a large number of objects, but can also meet the high data requirements toward specific coverage of the LEO constellation. However, the multi-beam satellite often faces the mismatch problem of spot allocation and data requirements, which can cause an overload traffic jam or a waste of resources. An optimization algorithm on spot beam allocation is necessary to automatically place the spot centers with appropriate beam widths in line with the density of the traffic demands and to realize the uniformity of the beam occupation. Compared with the conventional K-means algorithm, two adjustable parameters α and β are introduced: one for tuning the ratio of two components making up the distance matrix, and the other for setting the obligatory minimum number of objects per beam. In this paper, the whole process of the proposed method is demonstrated, including the establishment of the low-orbit satellite constellation model, the extraction of the distribution features, and the implementation and evaluation of the modified K-means algorithm. The results prove the validity of the proposed algorithm. A larger value of β with a relative smaller value of α tends to obtain the uniformity of beam occupation; the minimum standard deviation of objects per beam is achieved when α is 0.2 and β is 0.8. This demonstrates that the uniformity of objects per beam can be realized by adjusting the parameters of the distance determination matrix and the obligatory minimal number of objects in each beam. The impact of parameter range on the results is also analyzed.