Cooperative positioning with multiple low earth orbit (LEO) satellites is promising in providing location-based services and enhancing satellite-terrestrial communication. However, positioning accuracy is greatly affected by inter-beam interference and satellite-terrestrial topology geometry. To select the best combination of satellites from visible ones and suppress inter-beam interference, this paper explores the utilization of flexible beam scheduling and beamforming of multi-beam LEO satellites that can adjust beam directions toward the same earth-fixed cell to send positioning signals simultaneously. By leveraging Cram\'{e}r-Rao lower bound (CRLB) to characterize user Time Difference of Arrival (TDOA) positioning accuracy, the concerned problem is formulated, aiming at optimizing user positioning accuracy under beam scheduling and beam transmission power constraints. To deal with the mixed-integer-nonconvex problem, we decompose it into an inner beamforming design problem and an outer beam scheduling problem. For the former, we first prove the monotonic relationship between user positioning accuracy and its perceived signal-to-interference-plus-noise ratio (SINR) to reformulate the problem, and then semidefinite relaxation (SDR) is adopted for beamforming design. For the outer problem, a heuristic low-complexity beam scheduling scheme is proposed, whose core idea is to schedule users with lower channel correlation to mitigate inter-beam interference while seeking a proper satellite-terrestrial topology geometry. Simulation results verify the superior positioning performance of our proposed positioning-oriented beamforming and beam scheduling scheme, and it is shown that average user positioning accuracy is improved by $17.1\%$ and $55.9\%$ when the beam transmission power is 20 dBw, compared to conventional beamforming and beam scheduling schemes, respectively.

翻译：协作定位通过多颗低地球轨道（LEO）卫星协同工作，在提供基于位置的服务和增强星地通信方面具有广阔前景。然而，定位精度受到波束间干扰和星地拓扑几何构型的显著影响。为从可见卫星中选择最佳组合并抑制波束间干扰，本文探索了多波束LEO卫星的灵活波束调度与波束成形技术，使卫星能够将波束方向对准同一地球固定小区并同时发送定位信号。通过利用克拉美-罗下界（CRLB）表征用户到达时间差（TDOA）定位精度，我们构建了相关优化问题，目标是在波束调度和波束发射功率约束下优化用户定位精度。针对该混合整数非凸问题，我们将其分解为内部波束成形设计子问题和外部波束调度子问题。对于前者，首先证明用户定位精度与其感知信干噪比（SINR）之间的单调关系以重构问题，进而采用半定松弛（SDR）方法进行波束成形设计。对于外部子问题，提出一种低复杂度启发式波束调度方案，其核心思想是调度信道相关性较低的用户以缓解波束间干扰，同时寻求合适的星地拓扑几何构型。仿真结果验证了所提出的面向定位的波束成形与波束调度方案具有优越的定位性能，研究表明：在波束发射功率为20 dBw时，与传统波束成形和波束调度方案相比，平均用户定位精度分别提升17.1%和55.9%。