The Beam Hopping Pattern Design Algorithm of Low Earth Orbit Satellite Communication System
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摘要: 低轨卫星资源调度是长时间的连续资源分配过程，这一过程中低轨卫星保持高速移动，跳波束图案的设计需要考虑星地链路的切换。针对这种切换，即卫星覆盖区域间的服务目标迁移，所导致的多星资源联合调度需求，该文提出一种资源自适应权衡分配的多星联合跳波束图案设计算法。该算法通过设计星间联合调度框架和多星联合调度权重，将多星资源联合分配问题转化为星座内单星资源调度问题，轻量化设计跳波束图案。经过与多种权重设计方法的对比验证，仿真结果表明，所提算法的轻量化设计思路合理，并且可以有效地保障受迁移影响区域内小区的服务质量，可为低轨卫星系统长时资源调度设计提供参考。Abstract:
Objective The resource scheduling in Low Earth Orbit (LEO) satellite communication systems using Beam Hopping (BH) technology is a continuous, long-term allocation process. Unlike geostationary earth orbit (GEO) satellites, LEO satellites exhibit high-speed mobility relative to the ground during communication. The design of BH patterns typically occurs within regular time windows, ranging from tens to hundreds of milliseconds, leading to the switching of satellite-to-cell interaction links during certain BH periods. This switching implies that cells migrate between satellite coverage areas, each with varying capacity and delay requirements, which inevitably affects the performance of the receiving satellite. Additionally, the requirements of migrating cells during the switching time slot are directly related to the resource tilt provided by the source satellite before the switch. Therefore, there is a strong correlation between the BH pattern design strategies for different satellites, requiring multi-satellite joint resource scheduling to maintain service quality of cells in regions affected by migration. Methods In order to characterize the demands of joint scheduling for multiple satellites and maximize the minimum traffic satisfaction rate, an optimization problem is proposed for dynamic scenarios involving satellite-to-cell interaction link switching. This optimization problem simultaneously considers co-channel interference, traffic demands with differentiated temporal and spatial distributions, and traffic delay—all factors that affect the service quality of BH systems. To solve this NP-hard problem, a design algorithm of Multi-Satellite Joint BH Pattern based on Resource Adaptive Tradeoff Allocation (RATMJ-BHP) is proposed. First, an inter-satellite joint scheduling framework is proposed to model the complex impact of cell migration on satellite resource scheduling, transforming the multi-satellite scheduling problem into a single-satellite BH pattern design problem. Then, within this framework, a weight design method for multi-satellite joint scheduling is proposed, which quantifies the intensity of service urgency based on the capacity and delay requirements of cells. Finally, this joint scheduling weight is used to design the BH pattern. Results and Discussions Based on the optimization problem modeled in this paper, the satellite optimization region is divided into two areas: the stable region and the immigration region. A comprehensive evaluation, considering both regions within individual satellites and across adjacent satellites, is essential for analyzing the performance of the proposed algorithm. Thus, this paper examines the simulation results from two perspectives: the minimum traffic satisfaction rate and the variation in the minimum traffic satisfaction rate across different regions. Additionally, convergence speed is a key indicator of the algorithm’s performance; therefore, the number of iterations required to produce results for each time slot is counted. The key contributions of this research are as follows: Firstly, the average and maximum convergence times of the proposed algorithm are significantly lower than those of the enumeration method, demonstrating its efficiency in terms of time complexity ( Table 3 ). Specifically, with three satellites, the maximum complexity value of the proposed algorithm is 39.05, compared to that for the enumeration method. Secondly, the proposed algorithm outperforms the comparison algorithms in terms of minimum traffic satisfaction rates under different load rates, with a minimum value above 69.34% across various satellites (Fig. 3a ) (Fig. 4a ) (Fig. 5a ). These results show that the RATMJ-BHP algorithm effectively ensures high traffic satisfaction rates for cells in affected regions, demonstrating robustness across different traffic demand rates. Thirdly, the proposed algorithm exhibits a smaller disparity in minimum traffic satisfaction rates across regions, with values remaining close to zero, unlike other algorithms. This indicates its ability to maintain high traffic satisfaction rates for most cells in service areas (Fig. 3b ) (Fig. 4b ) (Fig. 5b ). Finally, simulation results from both perspectives demonstrate consistent performance across different satellites and varying traffic demand rates, highlighting the general applicability of the proposed algorithm in LEO satellite BH systems.Conclusions This paper addresses the design of BH patterns for dynamic scenarios involving satellite-to-cell interaction link switching. To meet the demands of multi-satellite joint resource scheduling in such scenarios, while considering performance factors such as co-channel interference, traffic demands, and traffic delay, the RATMJ-BHP algorithm is proposed. Simulation results show that the proposed algorithm effectively ensures the service quality of cells in migration-affected areas, and its lightweight design demonstrates broad applicability within LEO constellations. This paper contributes to the design strategy of BH patterns in dynamic scenarios during long-term resource scheduling processes, offering a solution to maintain continuous high-quality service to cells throughout prolonged satellite motion. It provides a reference for the design of long-term beam scheduling strategies in LEO satellite BH systems. However, several challenges remain in resource scheduling strategies for LEO satellite BH systems. For instance, the relationship between resource scheduling across BH periods and its impact on long-term system performance has yet to be fully explored. Additionally, while the proposed algorithm focuses on resource scheduling for the forward link of LEO satellite systems, further research is needed for uplink scenarios. -
1 RATMJ-BHP算法
1 输入：$ {G_{\rm{th}}} $ 2 初始化：$ \forall s \in \mathcal{S},{{\boldsymbol{X}}_s} = \varnothing $,$ \forall k \in (1,K),{{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} = \varnothing $ 3 For $ t = 1,2, \cdots ,T $ 4 If $ \forall s \in \mathcal{S},{\text{ }}\exists {t^{'}} \in \iota _s^{({\mathrm{in}})},{\text{ }}{\mathrm{s.t}}.{\text{ }}{t^{'}} = = t{\text{ or }}\exists {t^{''}} \in \iota _s^{({\mathrm{out}})} $,
${\mathrm{s.t.}}{\text{ }}{t^{''}} = = t{\text{ }} $5 $ {{\mathcal{N}}}_s^{(t)} = {{\mathcal{N}}}_s^{(t)} + {{\mathcal{N}}}_s^{({t^{'}})} - {{\mathcal{N}}}_s^{({t^{''}})} $, $ {{\mathcal{N}}}_{{\mathrm{set}}}^{(s)} = {{\mathcal{N}}}_s^{(t)} $ 6 根据式(11)和式(12)更新$ \sigma _{s,t}^{({\mathrm{out}})} $, $ \sigma _{s,t}^{({\mathrm{in}})} $ 7 End If 8 $ \forall {n_s} \in {{\mathcal{N}}}_s^{(t)} $，根据式(20)和式(21)计算$ \overline \beta _{{n_s}}^{(t)} $，式(23)和
式(24)计算$ \overline D _{{n_s}}^{(t)} $9 For $ k = 1,2, \cdots ,K $ 10 For $ s = 1,2, \cdots ,S $ 11 If $ D_{{\mathrm{now}},{n_s}}^{(t)} > R_{{\mathrm{unit}}}^{({n_s})} $ 12 依据策略(3)和(4)计算$ \varpi _{{n_s}}^{(t)} $，选择候选服务小区$ n_s^{'} $ 13 $ n_s^{'} \leftarrow {{\mathcal{N}}}_{{\mathrm{set}}}^{(s)} $；$ {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} \leftarrow n_s^{'} $ 14 Else 15 依据策略(1)和(2)计算$ \varpi _{{n_s}}^{(t)} $，并选择候选服务小区$ n_s^{'} $ 16 $ n_s^{'} \leftarrow {{\mathcal{N}}}_{{\mathrm{set}}}^{(s)} $；$ {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} \leftarrow n_s^{'} $ 17 End If 18 End For 19 依据4种策略对$ {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} $中的小区排序 20 While $ {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} \ne \varnothing $ 21 选择$ {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} $中的第一个小区$ n_s^{'} $。 22 If $ \exists {n_{{s_1}}},\max \left\{ {G_{k_s^{'},{k_{{s_1}}}}^{({\rm{tx}})},G_{{k_{{s_1}}},k_s^{'}}^{({\rm{tx}})}} \right\} \ge {G_{\rm{th}}} $,
$ {s_1} \in \mathcal{S},{n_{{s_1}}} \in {{\boldsymbol{X}}_{{s_1}}},{k_s} \ne {k_{{s_1}}} $23 $ n_s^{'} \leftarrow {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} $ 24 对于卫星$ s $，转至步骤11， 25 Else 26 $ x_{k_s^{'}}^{(t)} = n_s^{'} $ 27 $ n_s^{'} \leftarrow {{\mathcal{N}}}_{{\mathrm{sort}}}^{(k)} $ 28 End If 29 End While 30 End For 31 End For 32 输出跳波束图案$ {{\boldsymbol{X}}_1},{{\boldsymbol{X}}_2}, \cdots ,{{\boldsymbol{X}}_s},s \in \mathcal{S} $ 
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表 1 仿真参数
参数 值 卫星数目 3 高度(km) 508 卫星初始经度(°) [–3.81, 0.65, 5.55] 卫星初始纬度(°) [26.45, 31.01, 35.39] 初始小区数目 [38, 37, 40] 卫星迁出、迁入小区数目 [3, 4, 4, 4, 4, 3] 载波频率(MHz) 1 990 带宽(MHz) 40 星上总功率(dBW) 14 接收机天线模型 全向天线 极化方式 圆极化 业务包大小(MHz) 2 波束数目 8 跳波束时隙长度(ms) 30 跳波束周期长度(时隙) 35 时延门限(时隙) 5 干扰增益门限(dBi) 10
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表 2 相控阵天线参数
参数 参数值 最大阵元增益(dBi) 5 阵元水平方向3 dB波束宽度(°) 65 阵元垂直方向3 dB波束宽度(°) 65 前后比(dB) 30 阵元水平方向间隔 0.5 阵元垂直方向间隔 0.5 水平方向阵元数目 32 垂直方向阵元数目 32
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表 3 迭代次数
卫星数目 1 2 3 平均迭代次数 28.1 32.29 36.95 最大迭代次数 31.58 35.71 39.05 枚举法 $ {\mathrm{C}}_{{\text{38}}}^{\text{8}} $ $ {\mathrm{C}}_{{\text{38}}}^{\text{8}} \cdot {\mathrm{C}}_{{\text{37}}}^{\text{8}} $ $ {\mathrm{C}}_{{\text{38}}}^{\text{8}} \cdot {\mathrm{C}}_{{\text{37}}}^{\text{8}} \cdot {\mathrm{C}}_{{\text{40}}}^{\text{8}} $
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