Beamforming is a fundamental technology that not only enhances communication efficiency but also lays the foundation for massive multiple-input multiple-output~(MIMO) systems. However, its reliance on accurate channel state information (CSI) estimation introduces significant training overhead and feedback costs, especially in large-scale antenna systems. In this paper, we investigate positioning-assisted beamforming as a competitive alternative to the CSI-based methods, which circumvents the complicated CSI estimation. In particular, we analyze the outage probability of positioning-assisted systems with joint Gaussian beams and derive its closed-form expressions for both two-dimensional~(2D) and three-dimensional~(3D) scenarios. Based on these results, we also derive closed-form expressions for the optimal joint Gaussian beam pattern. The optimal solution is independent of the positioning error distribution in 2D scenarios but depends on it in 3D cases. Subsequently, the asymptotic performance of the approximation error is analyzed. Numerical results verify the derived outage probability expressions, and show the effectiveness of the beam pattern optimization.

翻译：波束成形是一项基础技术，不仅能提升通信效率，也为大规模多输入多输出（MIMO）系统奠定了基础。然而，其对精确信道状态信息（CSI）估计的依赖引入了显著的信道训练开销与反馈成本，尤其是在大规模天线系统中。本文研究定位辅助波束成形，将其作为基于CSI方法的一种有竞争力的替代方案，从而规避复杂的CSI估计。具体而言，我们分析了采用联合高斯波束的定位辅助系统的中断概率，并推导了其在二维（2D）和三维（3D）场景下的闭式表达式。基于这些结果，我们还推导了最优联合高斯波束模式的闭式表达式。该最优解在2D场景下与定位误差分布无关，但在3D场景下则依赖于该分布。随后，我们分析了近似误差的渐近性能。数值结果验证了所推导的中断概率表达式，并展示了波束模式优化的有效性。