Adaptive beamforming with sidelobe-level control in the presence of signal steering vector uncertainty is investigated. Unlike the traditional multiconstrained optimization strategy using the interior point method, iterative optimization algorithms with the aid of the alternating direction method of multipliers (ADMM) framework are proposed. The uncertainty set constraint and the sidelobe constraint are formulated into two optimization subproblems and handled with the Lagrange multiplier method. By introducing matrix decomposition techniques, subproblem 1 is transformed into a polynomial root-finding problem that can be solved with low computational complexity. For subproblem 2, a closed-form solution can be obtained directly. Furthermore, for the continuously receiving snapshots case, iterative gradient minimization is introduced and embedded into the ADMM iterations to give an approximate solution free from matrix decompositions. Theoretical analyses and simulations verify the low complexities and performance advantages of the proposed algorithms in the low sample support, steering vector mismatch, and real-time snapshot update scenarios.

中文翻译：

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使用乘法器交替方向方法进行旁瓣电平控制的鲁棒最小方差波束形成


研究了在存在信号引导矢量不确定性的情况下具有旁瓣电平控制的自适应波束形成。与使用内点法的传统多约束优化策略不同，提出了借助乘子交替方向法（ADMM）框架的迭代优化算法。将不确定性集约束和旁瓣约束表述为两个优化子问题，并用拉格朗日乘子法处理。通过引入矩阵分解技术，子问题1转化为多项式求根问题，可以用较低的计算复杂度来求解。对于子问题2，可以直接得到闭式解。此外，对于连续接收快照的情况，引入迭代梯度最小化并将其嵌入到 ADMM 迭代中，以给出无需矩阵分解的近似解。理论分析和仿真验证了该算法在低样本支持、导向向量失配和实时快照更新场景下的低复杂度和性能优势。