AI 中文总结
本文针对导向矢量失配下的线性约束最小方差波束形成问题，提出基于概率约束的分布鲁棒设计，利用CES分位数、矩、支撑集及Wasserstein模糊集构建凸二阶锥规划，提升可靠性与鲁棒性。
AI 中文摘要
线性约束最小方差（LCMV）波束形成是一种基本技术，用于控制阵列对多个期望信号的响应，同时抑制干扰和噪声。然而，在实际系统中，响应约束中涉及的导向矢量常常受到到达方向误差、校准不完善以及其他阵列不确定性的影响。这种失配可能导致约束违反和显著的性能下降。本文研究了导向矢量失配下的多信号LCMV波束形成，并开发了概率约束以保证每个期望信号的预定可靠性水平。考虑了多种不确定性信息设置。当精确的失配分布已知且属于复椭圆对称分布（CES）类时，利用精确的CES分位数推导出基于分布信息的凸安全重构。当失配分布未知，仅可获得部分统计信息或经验数据时，在基于矩的模糊集、基于支撑集的不确定性和Wasserstein数据驱动模糊集下开发了鲁棒概率重构，所得确定性公式可表示为凸二阶锥规划。数值实验表明，所提出的设计提高了样本外可靠性，并降低了对导向矢量失配的波束增益敏感性，同时保持了具有竞争力的输出信干噪比（SINR）和鲁棒波束图。
英文摘要
Linearly constrained minimum variance (LCMV) beamforming is a fundamental technique for controlling the array response toward multiple desired signals while suppressing interference and noise. In practical systems, however, the steering vectors involved in the response constraints are often affected by direction-of-arrival errors, calibration imperfections, and other array uncertainties. Such mismatches may cause constraint violations and substantial performance degradation. This paper investigates multi-signal LCMV beamforming under steering-vector mismatch and develops probabilistic constraints to guarantee a prescribed reliability level for each desired signal. Several uncertainty-information settings are considered. When the exact mismatch distribution is known and belongs to the class of complex elliptically symmetric distributions (CES), a distribution-informed convex safe reformulation is derived using exact CES quantiles. When the mismatch distribution is unknown, and only partial statistical information or empirical data is available, robust probabilistic reformulations are developed under moment-based ambiguity, support-based uncertainty, and Wasserstein data-driven ambiguity, and the resulting deterministic formulations can be expressed as convex second-order cone programs. Numerical experiments show that the proposed designs improve out-of-sample reliability and reduce beam-gain sensitivity to steering-vector mismatch, while maintaining competitive output signal-to-interference-plus-noise (SINR) ratio and robust beampatterns.
