Robust Beamforming Method for Dense LEO Satellite Network Assisted Terrestrial Communication
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摘要: 面向密集低轨道卫星网络辅助的星地无线通信系统，该文提出一种基于非完美信道状态信息的多低轨卫星鲁棒波束赋形方法来改善频谱效率。具体地，在多低轨卫星全频复用场景下，提出了一个多卫星下行通信系统和速率最大化问题，并联合考虑卫星发射功率、卫星与用户关联关系，以及馈线链路容量约束。为了求解该优化问题，原优化问题被分解成卫星-用户关联和卫星传输波束赋形两个子问题，然后使用加权最小均方误差方法和连续凸近似方法对问题进行求解。仿真结果验证了即使在非理想信道条件下，该文所提出的多星频率复用和鲁棒波束赋形设计方法能有效提高系统吞吐量。Abstract:
A robust beamforming method based on imperfect Channel State Information (CSI) is proposed for dense Low-Earth Orbit (LEO) satellite network-assisted terrestrial wireless communication systems to enhance spectral efficiency. Specifically, in scenarios where multiple LEO satellites use full frequency reuse, a multi-LEO satellite downlink sum rate maximization problem is formulated, considering constraints on satellite transmit power, satellite-User Terminal (UT) association, and satellite feeder link capacity. To solve the optimization problem, it is decomposed into two subproblems: satellite-UT association and satellite transmit beamforming. Weighted minimum mean-squared error and successive convex approximation methods are then employed to address the non-convex challenges. Simulation results confirm that the proposed multi-satellite full frequency reuse scheme and robust beamforming design effectively improve system throughput, even under non-ideal channel conditions. Objective As the LEO satellite constellation becomes denser, spectrum resources will become scarcer, and co-channel interference among satellites will intensify. Therefore, transmission methods with higher spectrum efficiency are needed. To mitigate the effects of severe satellite-terrestrial wireless channels and enhance system throughput, multi-beam beamforming and phased-array antennas are employed in LEO satellites to achieve higher antenna gain. However, most existing studies assume perfect knowledge of CSI, which is often impractical. Therefore, considering the complex satellite-terrestrial channel conditions and channel estimation errors, a robust beamforming method is preferable. Under dense satellite constellations, the increasing number of satellites and the presence of inter-satellite co-channel interference make the design of robust transmission methods for multi-LEO satellite networks essential. Thus, this paper aims to investigate the design of an efficient robust beamforming method for dense LEO satellite networks under given channel uncertainty. Methods To enable frequency reuse across multiple LEO satellites, this paper proposes a dense LEO satellite network architecture that incorporates a gateway or Geostationary Earth Orbit (GEO) satellite as the centralized controller. In this system architecture, multiple LEO satellites can reuse spectrum, thereby improving spectral efficiency. Additionally, a system sum-rate maximization problem is formulated, considering imperfect Angular-Of-Arrival (AoA) based CSI. The problem incorporates constraints on satellite-user association, multi-satellite downlink transmit beamforming, and satellite feeder link capacity. Results and Discussions The simulation results show that the system sum-rate increases with the satellite transmit power budget, as higher transmit power improves received signal quality ( Fig. 3 ). Additionally, the proposed robust beamforming method significantly enhances the system sum-rate compared to existing methods (Fig. 3 ). Furthermore, the results indicate that the communication rate of the UT is constrained by satellite feeder link capacity, and higher feeder link capacity leads to an increase in the system sum-rate (Fig. 4 ). However, the rate of increase in the system sum-rate slows once the satellite feeder link capacity exceeds a certain threshold. The results also reveal that larger AoA uncertainty reduces the system sum-rate, highlighting the significant impact of AoA uncertainty on system performance (Fig. 5 ). Lastly, increasing the number of antennas effectively improves channel quality and further increases the system sum-rate (Fig. 6 ).Conclusions This paper investigates a robust beamforming method for dense LEO satellite networks and proposes a full frequency reuse scheme to enhance spectral efficiency and increase system throughput. Given the challenges in obtaining accurate CSI, an angular-information-based channel uncertainty model is adopted to reflect non-ideal channel conditions. A system sum-rate maximization problem is then formulated to evaluate system performance, considering satellite-UT association and satellite transmit beamforming. To address the non-convex optimization problem, the WMMSE and SCA methods are employed. Simulation results demonstrate that channel uncertainty significantly impacts system performance. When channel uncertainty is small, the performance gap between the proposed robust beamforming method and the ideal CSI case is minimal. Furthermore, the proposed multi-LEO satellite robust beamforming method outperforms other existing schemes. -
Key words:
- Dense LEO satellites /
- MIMO /
- Robust beamforming /
- Frequency reuse
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1 求解问题式(9)的迭代优化算法
1：初始化:给定可行的波束赋形向量$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( 0 \right)}} \right\}$和二进制关联值$\left\{ {a_{i,s}^{\left( 0 \right)}} \right\}$，设置容差$\varepsilon \gt 0$，迭代索引$n = 0$，最大迭代次数${N_{\max }}$。 2：repeat 3：根据式(10)，将不确定信道进行均匀离散化； 4：给定$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( n \right)}} \right\}$，更新$v_{s,i}^{{\text{opt}}}$, $ u_{s,i}^{{\text{opt}}} $和$e_{s,i}^{{\text{opt}}}$，得到式(14)中的$ {\tilde R_{s,i}} $； 5：给定$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( n \right)}} \right\}$和$\left\{ {a_{i,s}^{\left( n \right)}} \right\}$，利用内点法求解问题式(15)得到$\left\{ {a_{i,s}^{\left( {n + 1} \right)}} \right\}$。 6：给定$\left\{ {a_{i,s}^{\left( {n + 1} \right)}} \right\}$，得到式(16)中的$ {\tilde R_{s,i}} $； 7：给定$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( n \right)}} \right\}$和$\left\{ {a_{i,s}^{\left( {n + 1} \right)}} \right\}$，采用式(19)，得到${\tilde R_{s,i}}$的上界$\tilde R_{s,i}^{\mathrm{U}}$； 8：给定$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( n \right)}} \right\}$和$\left\{ {a_{i,s}^{\left( {n + 1} \right)}} \right\}$，利用内点法求解问题式(20)得到$\left\{ {{\boldsymbol{w}}_{s,i}^{\left( {n + 1} \right)}} \right\}$。 9：设置$ n = n + 1 $。 10：Until：目标函数式(9)收敛或者$n = {N_{\max }}$。 
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