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Robust sparse array design for adaptive beamforming against DOA mismatch

机译：针对DOA不匹配的自适应波束形成的鲁棒稀疏阵列设计

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Highlights•Different array configurations exhibit differed sensitivities towards the uncertainty in the source arrival direction, which was ignored by the previous work on robust beamforming in the literature.•This work proposes enhancing the receiver's robustness through optimizing array configurations in terms of output SINR.•We formulate both unconstrained and constrained sparse array design problems for robust MVDR and LCMV beamforming respectively and solve them through a series of iterative convex programming algorithms.AbstractThe performance of an adaptive beamformer is significantly influenced by its array configuration. The problem of optimum array configuration for minimum variance distortionless response (MVDR) beamformers has been recently investigated under the assumption of accurate estimate or prior exact knowledge of the source direction of arrival (DOA). Inaccuracies in DOA can lead to significant performance degradation. Improving the robustness of MVDR beamformers has commonly been achieved by adding appropriate constraints in the determination of beamforming weights, such as the linearly constrained minimum variance (LCMV) beamformer. This work examines the sensitivity of different sparse array configurations towards uncertainty in the source DOA. It proposes enhancing system robustness through optimizing array configurations. The sparse array design problem is formulated in terms of maximizing the output signal-to-interference-plus-noise ratio (SINR) of the MVDR and LCMV beamformers. The constrained maximization problem is expressed as the fraction of matrix determinants, and a sequential convex programming algorithm is adopted for the solution of the corresponding non-convex problem. Numerical examples are presented to validate the robustness of configured sparse array MVDR and LCMV beamformers for small errors in source directional angles.
机译： 突出显示 • 不同的阵列配置对源到达方向的不确定性表现出不同的敏感性，这在先前文献中关于鲁棒波束成形的工作中已被忽略。 • 此作品提议通过根据输出SINR优化阵列配置来增强接收机的鲁棒性。 • 我们制定了不受约束的d分别约束了健壮的MVDR和LCMV波束成形的稀疏阵列设计问题，并通过一系列迭代凸规划算法来解决。 摘要 自适应波束形成器的性能受其阵列配置的影响很大。最近，在对源到达方向（DOA）进行精确估计或事先知道的前提下，研究了最小方差无失真响应（MVDR）波束形成器的最佳阵列配置问题。 DOA中的错误会导致性能显着下降。通常通过在确定波束成形权重时添加适当的约束（例如线性约束最小方差（LCMV）波束成形器）来提高MVDR波束成形器的鲁棒性。这项工作研究了不同稀疏阵列配置对源DOA中不确定性的敏感性。它建议通过优化阵列配置来增强系统的鲁棒性。稀疏阵列设计问题是根据最大化MVDR和LCMV波束形成器的输出信噪比（SINR）来制定的。将约束最大化问题表示为矩阵行列式的分数，并采用顺序凸规划算法求解相应的非凸问题。通过数值算例验证了配置的稀疏阵列MVDR和LCMV波束形成器对于源方向角中的小误差的鲁棒性。

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