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Sparse DOA Estimation Method Based on Riemann Averaging under Strong Intermittent Jamming
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摘要: 针对复杂电磁环境下雷达干扰增多且靠近强干扰信号的目标信号难以准确估计的问题，该文提出了一种强间歇干扰下基于黎曼平均的稀疏波达方向(DOA)估计方法。首先，在扩展互质阵列接收数据模型下，利用在整个采样周期内目标信号持续活动而强干扰信号间歇性活动的特性，引入黎曼平均对干扰信号进行抑制；然后，将经过处理的数据协方差矩阵向量化，得到虚拟阵列接收数据；最后，在虚拟域中运用稀疏迭代协方差估计(SPICE)算法对稀疏信号进行重构，得到目标信号的DOA估计。仿真结果表明，在信号源数目未知的情况下，该方法可以对角度与强干扰信号紧密相邻的弱目标信号进行高精度的DOA估计。与现有子空间算法和稀疏重构类算法相比，所提算法在较小快拍数和低信噪比下具有更高的估计精度和角度分辨力。Abstract: Aiming to address the problem of increased radar jamming in complex electromagnetic environments and the difficulty of accurately estimating the target signal close to a strong jamming signal, this paper proposes a sparse Direction of Arrival (DOA) estimation method based on Riemann averaging under strong intermittent jamming. First, under the extended coprime array data model, the Riemann averaging is introduced to suppress the jamming signal by leveraging the property that the target signal is continuously active while the strong jamming signal is intermittently active. Then, the covariance matrix of the processed data is vectorized to obtain virtual array reception data. Finally, the sparse iterative covariance-based estimation method, which is used for estimating the DOA under strong intermittent interference, is employed in the virtual domain to reconstruct the sparse signal and estimate the DOA of the target signal. The simulation results show that the method can provide highly accurate DOA estimation for weak target signals whose angles are closely adjacent to strong interference signals when the number of signal sources is unknown. Compared with existing subspace algorithms and sparse reconstruction class algorithms, the proposed algorithm has higher estimation accuracy and angular resolution at a smaller number of snapshots, as well as a lower signal-to-noise ratio.
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图 2 连续信号和间歇性干扰信号活动示意图
Figure 2. Schematic diagram of continuous and intermittent interfering signal activity
图 4 不同算法分辨性能对比
Figure 4. Comparison of the resolution performance of different algorithms
图 5 不同算法下相干信号空间谱对比
Figure 5. Comparison of spatial spectrum of coherent signals under different algorithms
图 6 不同参数条件下的DOA估计精度
Figure 6. Accuracy of DOA estimation under different parameter conditions
图 7 不同参数条件下的成功检测概率
Figure 7. Successful resolution under different parameter conditions
图 8 算法估计精度和分辨率随快拍数的变化
Figure 8. Algorithmic estimation of accuracy and resolution as a function of number of snapshots
图 9 所提算法在不同参数条件下的DOA估计精度
Figure 9. Accuracy of DOA estimation of the proposed algorithm under different parameter conditions
1 基于黎曼平均的虚拟域SPICE算法
1. A virtual domain SPICE algorithm based on Riemann averaging
输入：协方差矩阵的黎曼均值${\hat {\boldsymbol{R}}_{\mathrm{R}}}$，过完备网格点${\boldsymbol{\varTheta}} $，迭代终止阈值${\delta _{\min }}$，最大迭代次数Q； 输出：空间谱${\boldsymbol{P}}_{\mathrm{S}}^{(i)}$ 1 根据式(22)得到虚拟阵列数据r并通过式(23)剔除r中重复元素得到$\tilde {\boldsymbol{r}}$； 2 初始化：初始迭代次数$i = 1$，初始阈值${\delta _0} = 1$，分别根据式(35)、式(36)、式(24)和式(34)依次初始化$p_c^{(0)}$, ${\boldsymbol{P}}_{\mathrm{S}}^{(i)}$, R和${\rho ^0}$，$\sigma _n^2$初始化为
$ \sigma _n^2 = \min \left\{ {p_c^{(0)}} \right\} $；3 迭代开始：根据式(32)和式(33)更新$p_c^{(i + 1)}$和$\sigma _n^{(i + 1)}$； 4 根据式(36)、式(24)和式(34)依次更新${\boldsymbol{P}}_{\mathrm{S}}^{(i)}$, ${{\boldsymbol{R}}^{(i)}}$和${\rho ^{(i)}}$； 5 根据式(37)更新$\delta $，如果$\delta > {\delta _{\min }}$且$i < Q$，则返回步骤3； 迭代结束 
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表 1 算法计算复杂度对比表
Table 1. Comparison table of computational complexity of algorithms
算法 复杂度 SS-MUSIC算法 $ O(L{G^2} + 2{(MN + 1)^3} + C{(MN + 1)^2} - CK(MN + 1)) $ SS-SPICE算法 $ O({G^3}CQ + G{C^{^2}}Q + L{G^2}) $ SS-EQSPICE算法 $ O({G^3}CQ' + G{C^{^2}}Q' + L{G^2}) $ 本文所提算法 $ O({G^3}CQ + G{C^{^2}}Q + L{G^2} + {G^3} + {G^2}) $
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