This article proposes a new recursive linearly constrained minimum variance (LCMV) beamformer based on the extended instrumental variable (EIV) method for planar radial coprime arrays (PRCAs) under spatially colored noise. The proposed recursive LCMV beamformer is able to deal with multiple constraints with high precision and low complexity and can be applicable to various array geometrical configurations. Taking advantage of the EIV vector, the proposed beamformer can effectively combat the additive color noise with unknown noise covariance matrix. We develop our recursive LCMV beamformer based on the square-root (SR) EIV algorithm due to its improved numerical stability than the conventional EIV-based algorithms. Furthermore, we studied a class of planar arrays called PRCAs, which consists of a set of linear coprime arrays arranged radially at various azimuth angles. The coprime array property is utilized to enlarge the array aperture leading to higher resolution and stronger interference rejection and it offers additional flexibility in the tradeoffs between array complexity and performance. Simulation results demonstrate that the proposed recursive SREIV-based LCMV beamformer outperforms the conventional QR decomposition based LCMV beamformers in the resolution and suppression of interferences under various scenarios. The PRCAs tested outperform the uniform rectangular arrays with the same number of elements. Moreover, better performance can be achieved with more linear subarrays at the expense of increased complexity.

中文翻译：

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空间有色噪声下平面径向互质阵列的基于递归扩展仪器变量的 LCMV 波束形成器


本文提出了一种基于扩展工具变量（EIV）方法的新型递归线性约束最小方差（LCMV）波束形成器，用于空间有色噪声下的平面径向互质阵列（PRCA）。所提出的递归LCMV波束形成器能够以高精度和低复杂度处理多种约束，并且可以适用于各种阵列几何配置。利用EIV向量，所提出的波束形成器可以有效地对抗具有未知噪声协方差矩阵的加性颜色噪声。我们开发了基于平方根 (SR) EIV 算法的递归 LCMV 波束形成器，因为它比传统的基于 EIV 的算法提高了数值稳定性。此外，我们研究了一类称为 PRCA 的平面阵列，它由一组以不同方位角径向排列的线性互质阵列组成。利用互质阵列特性来扩大阵列孔径，从而实现更高的分辨率和更强的干扰抑制，并且它在阵列复杂性和性能之间的权衡中提供了额外的灵活性。仿真结果表明，所提出的基于 SREIV 的递归 LCMV 波束形成器在各种场景下的干扰分辨率和抑制方面均优于传统的基于 QR 分解的 LCMV 波束形成器。测试的 PRCA 优于具有相同元件数量的均匀矩形阵列。此外，通过更多的线性子阵列可以实现更好的性能，但代价是增加复杂性。