基于原子范数最小化的单比特稀疏双极子阵列的波达角估计

DOA estimation of one-bit sparse cross-dipole array based on atomic norm minimization

现有的单比特稀疏双极子阵列的波达角估计方法为子空间方法,其估计精度依赖于信号的统计特征,并且没有充分利用协方差矩阵的结构,导致其估计精度较低.为了提高该阵列的波达角估计精度,本文提出了一种基于原子范数最小化的无网格稀疏化波达角估计方法.该方法将稀疏双极子阵列的波达角估计转化为标量阵波达角估计,并根据参数空间的连续性构造基于原子集的阵列信号稀疏模型,随后利用单比特采样下噪声的稀疏特征,将该波达角估计问题转化为l1范数约束下的原子范数最小化问题,并且给出一种基于交替方向乘子法的快速迭代求解方法.仿真结果表明:相较于现有的方法,本文所提方法有着更高的估计精度,在嵌套阵上,当信噪比为-5 dB时,其估计精度均方误差降低了17.9 dB;将求解原子范数最小化的计算复杂度由O(N6.5)降低为O(N3),其中N为与稀疏阵具有相同孔径和相同阵元间距的均匀线阵的阵元个数.

The existing direction of arrival(DOA)estimation methods for one-bit sparse cross-dipole arrays are all methods for subspace.The DOA estimation accuracy is affected by the decreasing of statistical efficiency and lacking usage of the structure of the covariance matrix.In order to improve the DOA estimation accuracy by one-bit sparse cross-dipole arrays,a DOA estimation method based on atomic norm minimization is proposed in this paper.The proposed method transforms the DOA estimation of sparse cross-dipole array into that of a scalar array with the same configuration,and then constructs an atomic set-based sparse model of the received signal according to the continuity of parameter space.By using the sparsity of noise under one-bit sampling,an additional-norm constraint is introduced to make the model suitable for one-bit data.A fast method based on alternating direction multiplier is then developed to reduce the computational complexity of atomic norm minimization.Numerical results show that the proposed method outperforms the existing ones from the viewpoint of estimation accuracy,the mean square error of its estimation accuracy is reduced by 17.9 dB on a nested array when the signal-to-noise ratio is−5 dB.The proposed method is also suitable for large array due to its low complexity as O(N^(3)),where N is the number of a uniform linear array(ULA)which has the same array length and the sensor spacing.