This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

中文翻译：

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基于几何代数的电磁矢量阵列非圆信号二维 DOA 估计

本文提出了两种基于几何代数 (GA) 的新颖方法来估计均匀矩形阵列 (URA) 的非圆形 (NC) 信号的二维 (2D) 到达方向 (DOA)。传统方法将接收到的数控信号视为长矢量，这将不可避免地失去每个电磁矢量传感器（EMVS）内部的正交性，从而丢失一些二阶统计特性的信息。此外，计算复杂度也会增加。相比之下，基于遗传算法的旋转不变技术估计信号参数（ESPRIT）和传播方法（PM）算法被提出来估计数控信号的DOA。利用遗传算法，可以保持多维信号之间的关系。首先，EMVS 的六个分量在 GA 空间中表示为多向量。然后，我们构建基于遗传算法的扩展协方差矩阵，以更充分地利用信号信息。 DOA参数可以通过ESPRIT和PM原理进行估计。所提出的基于 GA 的信号参数估计，通过用于 NC 信号处理的旋转不变技术（GANC-ESPRIT）可以以高估计精度估计 DOA。所提出的基于遗传算法的数控信号估计传播方法（GANC-PM）使用线性变换来计算角度参数。与长向量模型相比，我们的模型具有更低的内存需求和更少的计算负担。仿真结果证明了所提出的 GANC-ESPRIT 算法在角分辨率方面的鲁棒性和优越性。复杂度分析表明，所提出的 GANC-PM 算法在计算量较少的情况下性能更好。