基于通道压缩的原子范数最小化DOA估计算法

A channel compression DOA estimation algorithm based on atomic norm minimization

针对波达方向(DOA)估计算法的精度以及分辨率受通道数目影响的问题,本文提出了基于通道压缩的原子范数最小化(CC-ANM)无网格DOA估计算法。该算法首先对通道数进行压缩,然后对压缩之后数据的协方差矩阵进行特征值分解,利用分解得到的特征值和特征向量构建新的观测向量,以此来构建单快拍模型下的ANM问题,最后根据半正定规划问题的最优解建立Toeplitz矩阵,通过其Vandermonde分解获得信号DOA参数的估计结果。仿真实验验证了CC-ANM算法在阵元数为20,压缩率为2,信噪比为20 dB,快拍数为200时,估计精度可以达到0.1°以下。对于角度间隔2°以上的信号可以达到100%的测量。对仪器接收入射角度为0°实测数据进行测试,该算法估计精度在0.3°以下,要优于同等条件下的压缩感知类算法。

The accuracy of the direction of arrival(DOA) estimation algorithm and the resolution are limited by the number of channels. To address these issues, this article proposes a meshless DOA estimation algorithm based on channel compression-atomic norm minimization(CC-ANM). First, the algorithm compresses the number of channels. Then, the eigenvalue decomposition is performed on the covariance matrix of the compressed data. The decomposed eigenvalues and eigenvectors are used to construct a new observation vector to solve the ANM problem under the single snapshot model. Finally, the Toeplitz matrix is established according to the optimal solution of the positive SDP problem. The DOA parameter estimation result of the signal is achieved through its Vandermonde decomposition. Simulation experiments show that the CC-ANM algorithm can achieve an estimation accuracy below 0.1° when the number of array elements is 20, the compression rate is 2, the SNR is 20 dB, and the number of snapshots is 200. The 100% measurement is possible for signals with an angular separation of more than 2°. The test data received by the instrument with an incident angle of 0° show that the estimation accuracy of the algorithm is below 0.3°, which is better than the compressed sensing algorithm under the same condition.