Fast Two-dimensional DOA Estimation for Coherently Distributed Noncircular Signals with Automatic Pairing
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摘要: 在相干分布式非圆信号2维波达方向(DOA)估计中，针对利用非圆特性后维数扩展带来的较大复杂度问题，且现有的低复杂度算法均需要额外的参数匹配，该文提出一种基于互相关传播算子的自动匹配2维DOA快速估计算法。该算法考虑L型阵列，在建立相干分布式非圆信号扩展阵列模型的基础上，首先证明了L阵中两个子阵的广义方向矢量(GSV)均具有近似旋转不变特性，然后通过阵列输出信号的互相关运算消除了额外噪声，最终利用子阵GSV的近似旋转不变关系通过传播算子方法得到中心方位角与俯仰角估计。理论分析和仿真实验表明，所提算法无须谱峰搜索和协方差矩阵特征分解运算，具有较低的计算复杂度，并且能够实现2维DOA估计的自动匹配；同时，相比于现有的相干分布式非圆信号传播算子算法，所提算法以较小的复杂度代价获得了性能的较大提升。Abstract: In the two-dimensional Direction Of Arrival (DOA) estimation of coherently distributed noncircular sources, the problem of large complexity is caused by dimension expansion after exploiting noncircular property, meanwhile the existing low-complexity algorithms all require additional parameter pairing procedure. To solve these problems, a rapid DOA estimation algorithm with automatic pairing is proposed for coherently distributed noncircular sources based on cross-correlation propagator. The L-shaped array is considered. Firstly, the extended array manifold model is established by exploiting the noncircularity of the signal, and then it is proved that there are approximate rotational invariance relationships in the Generalized Steering Vectors (GSVs) of two subarrays of the L array. At the same time, the extra noise can be eliminated by the cross-correlation matrix of the array output signals. Finally, on the basis of the approximate rotational invariance relationships of the sub-arrays, the center azimuth and elevation DOAs can be obtained by propagator method. Theoretical analysis and simulation experiments show that without the spectrum searching and eigenvalue decomposition of the sample covariance matrix, the proposed algorithm has low computational complexity. Moreover, it can automatically pair the estimated central azimuth and central elevation DOAs. In addition, compared with the existing propagation method for coherently distributed noncircular sources, the proposed algorithm can achieve higher estimation accuracy with the small complexity cost.
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表 1 计算复杂度对比
算法 计算量 SOS $O\left(8{M^3} + 4{M^2}N + L({K^3} + 2{K^2}M)\right)$ TLS-ESPRIT $O\left({(2M + 1)^3} + {(2M + 1)^2}N + 2M{K^2} + 2{K^3}\right)$ CDNC $O\left(64{M^3} + 16{M^2}N + \left(\frac{{11}}{9}M - 4\right){K^2} + 2{K^3}\right)$ NC-PM $O\left(2(4M - 1)KN + 2{K^3} + {K^2}\right)$ 本文算法 $O\left(4{M^2}N + 22{M^2}K + 3{K^3} - 12{K^2}\right)$ 
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