Robust Beamforming Algorithm Based on Double-layer Estimation of Steering Vector and Covariance Matrix Reconstruction
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摘要: 针对干扰加噪声协方差矩阵(INCM)重构过程中Capon功率谱(CPS)估计分辨率低的问题，该文提出两种稳健自适应波束形成（RAB）算法。该算法首先通过搜索CPS的峰值确定积分区间，然后对各区间积分所得的协方差矩阵进行特征值分解。通过合理设置判定门限确定区间内所含的入射信源数量，并将较大特征值所对应的特征向量作为信源导向矢量(SV)的初步估计。而后通过最大化估计功率的方法，在初步估计SV的正交空间内搜索其与真实SV之间的误差。该算法1利用最小特征值所对应的特征向量，向初步估计的SV中添加正交比例梯度，得到双层估计的SV。与算法1不同，算法2通过求解2次优化(QP)问题得到修正的SV。最后通过重构INCM获得阵列最优权值矢量。通过计算机仿真实验，验证了所提算法有效解决了CPS估计分辨率低的问题，较其他算法综合性能更优，具备更高的稳健性。
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关键词:
- 稳健自适应波束形成 /
- 协方差矩阵重构 /
- 导向矢量估计 /
- Capon功率谱估计
Abstract: Considering the problem of the low resolution of the Capon Power Spectrum (CPS) in the reconstruction of Interference plus Noise Covariance Matrix (INCM), two Robust Adaptive Beamforming (RAB) algorithms are proposed. The proposed algorithm first searches the peaks of CPS to determine the integration intervals and then eigen-decomposes the covariance matrixes obtained from the integration of each interval. The number of incident sources in the interval is determined by reasonably setting the decision threshold, and the eigenvectors corresponding to the larger eigenvalues are used as the preliminary estimation of the Steering Vectors (SV). Then, by maximizing the estimated power, the gap between the nominal SV and the real SV is searched in the orthogonal space of the nominal SV. The first proposed algorithm uses the eigenvector corresponding to the minimum eigenvalue to add the orthogonal proportional gradient to the initial estimated SV to obtain the double-layer estimated SV. The second proposed algorithm obtains the modified SV by solving a Quadratic Programming (QP) problem. Finally, the optimal weight vector of the array is obtained by reconstructing the INCM. Simulation results demonstrate that the proposed algorithm solves effectively the problem of the low resolution of the CPS estimation and is superior to other algorithms. -
表 1 所提算法步骤
序号 内容 步骤 1 利用式(13)计算CPS，并搜索CPS的峰值； 步骤 2 利用峰值确定积分区间，并使用式(17)计算区间积分； 步骤 3 利用式(18)特征值分解积分所得的矩阵，使用式(19)确定入射信号数量； 步骤 4 算法1利用式(20)构造一组SV，并计算最优SV；
算法2利用式(23)求解误差向量，并计算最优SV；步骤 5 利用式(21)和式(22)重构INCM，使用式(24)计算阵列权值矢量。 
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