Most of the reconstruction-based robust adaptive beamforming (RAB) algorithms require the covariance matrix reconstruction (CMR) by high-complexity integral computation. A Gauss-Legendre quadrature (GLQ) method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity. The interference angular sector in RAB is regarded as the GLQ integral range, and the zeros of the three-order Legendre orthogonal polynomial is selected as the GLQ nodes. Consequently, the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral. The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques, and it is able to provide the similar performance close to the optimal. These advantages are verified by numerical simulations.

中文翻译：

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使用Gauss-Legendre正交算法快速，准确地建立自适应波束形成的协方差矩阵

大多数基于重构的鲁棒自适应波束成形（RAB）算法都需要通过高复杂度积分计算来实现协方差矩阵重构（CMR）。为了降低复杂度，提出了一种在插值式正交算法中具有最高代数精度的高斯-勒格德勒正交（GLQ）方法。将RAB中的干扰角扇区视为GLQ积分范围，并选择三阶Legendre正交多项式的零作为GLQ节点。因此，可以通过对三个GLQ节点进行简单的求和而无需积分来有效地获得CMR。与大多数最新的基于重建的RAB技术相比，该新方法已大大降低了复杂性，并且能够提供接近最佳性能的相似性能。