# A Beam Hopping Scheme Based on Adaptive Beam Radius for LEO Satellites
## 2 Related Work  
All kinds of advantages are driving researchers to research beam-hopping in any other aspects. Here is a summary of the current research on beam-hopping resource allocation: Currently, researchers model the beam-hopping problem as a convex or non-convex problem, depending on whether the inter-beam interference can be neglected or not. If the problem is a convex problem, a numerical solution can be obtained easily by solving the convex optimization problem; however, in practice, without interference isolation measures, co-frequency interference can result in significant bandwidth and power wast-age, leading to a severe degradation in system throughput. Therefore, the following meth-ods are commonly adopted to mitigate interference:  
* Clustering beams to avoid co-interferences intra beam [4; 5; 6]. * Setting the interference distance as a guideline to avoid co-interferences within the intra beam [7; 8]. * Adopting some algorithm to cancel interferences [9]. * Adopting the algorithm that is driven by data [10; 11; 12; 13; 14]. Among the aforementioned interference avoidance methods, there are many different approaches, each with distinct implementation details. Taking the commonly practiced method of setting interference avoidance thresholds as an example, we conduct analysis and discussion: [PERSON] [7] used distance as the independent variable to simulate and visualize the relationship between signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR). Based on this simulation, the authors identified the distance at which SINR is approximately equal to SNR and determined a threshold distance at which interference from co-channel beams can be neglected. This is a feasible method for interference avoidance, and this approach will be continued in this paper, with relevant discussions placed in Section 3.6. On the one hand, this paper adopts interference avoidance strategies from related works, while on the other hand, it identifies the lack of utilization of beam flexibility in previous works. Therefore, building upon prior research, this paper proposes a communication strategy that utilizes beams of three different radii to serve ground users. The following is a summary and analysis of previous works:  
In recent years, researchers have gradually realized the beam flexibility thanks to the advancement of phase array antennas and the computing capability on board, and some papers have begun to study the use of phased array antennas based on their flexible beam pointing and the ability to dynamically change the beam radius to fully serve terrestrial users. [PERSON] et al. [15; 16] used the P-Center algorithm to determine the beam center and radius based on the user distribution, which is difficult to realize in practice on one hand, and on the other hand, when the number of users in the non-hot spot area is small, the determination of the beam center and radius only relying on the user distribution leads to unreasonable distribution. [PERSON] et al. [17] proposed an iterative algorithm and reinforcement learning to allocate resources to users, although both of these algorithms have very high computational complexity. [PERSON] et al. [18] found the sparsest user by the user location matrix and user density vector, and then gradually expanded the radius to accommodate more users, until the beam could not meet the users' demands or all the users had been assigned to beams. This algorithm belongs to the iterative algorithm, which has a large time and space complexity. [PERSON] [19] gave a simple and easy beam scheduling method by comprehensively considering the user traffic demand and distribution, but the method does not consider the system delay, which plays an important role in user quality of service (QoS). [PERSON] et al.