Efficient 2-D Direction Finding Based on the Real-valued Subspace Linear Transformation with Nonuniform Circular Array
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摘要: 由于均匀圆阵(UCA)的阵列流型不具有范德蒙结构，通常采用模式空间方法构造虚拟线性阵列，因此，UCA阵列下使用结构变换已经是2维测向的必要基本假设。该文通过对虚拟信号模型进行特征分析，避免了线性阵列的结构变换，提出一种适用于UCA和非均匀圆阵(NUCA)的实值高效二维测向方法。因此，新方法利用经前/后向平滑的阵列协方差矩阵(FBACM)以及分离实虚部后的和差变换，获得了维度相互适配的阵列流型和实值子空间，理论揭示了所获实值子空间与原始复值子空间的线性张成关系，构建了无虚假目标的空间谱，且可以推广至NUCA，增强了实值算法对于圆形阵列结构的适应性。同时，理论揭示了上述方法具有秩增强优势。数值仿真实验表明，与传统UCA阵列下的模式空间方法相比，该文所提出方法能够在显着降低复杂性的情况下，提供相似的估计性能和更好的角度分辨率。同时，在考虑幅度和相位误差等情况时，所提出方法具有较强的鲁棒性。Abstract: The central symmetry based on the virtual array is a necessary fundamental assumption for the structure transformation of Uniform Circular Arrays (UCAs). In this paper, the virtual signal model for circular arrays is used to make an eigen analysis, and an efficient two-dimensional direction finding algorithm is proposed for arbitrary UCAs and Non Uniform Circular Arrays (NUCAs), where the structure transformation of linear arrays is avoided. As such, the forward/backward average of the array covariance matrix (FBACM) and the sum-difference transformation method after separating the real and imaginary parts are both utilized to obtain the manifold and real-valued subspace with matching dimensions. Moreover, the linear relationship between the obtained real-valued subspace and the original complex-valued subspace is revealed, where the spatial spectrum is reconstructed without fake targets. The proposed method can be generalized to NUCAs, enhancing the adaptability of real-valued algorithms to circular array structures. Numerical simulations are applied to demonstrate that with significantly reduced complexity, the proposed method in this paper can provide similar performances and better angle resolution as compared to the traditional UCAs based on the mode-step. Meanwhile, the proposed method demonstrates high robustness with amplitude and phase errors in practical scenarios.
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Key words:
- Direction Of Arrival (DOA) /
- Real-valued Estimation /
- Circular Array
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表 1 不同搜索类算法下CPU运行时间(单位：秒)
UCA-MUSIC UCA-Capon UCA-RB-MUSIC UCA-RV-MUSIC M=8 0.4528 0.4614 0.2270 0.2342 M=16 0.7401 0.7477 0.3593 0.3621 M=24 1.0692 1.0802 0.5208 0.5217 M=32 1.3705 1.3844 0.6491 0.6496 
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