四阶累积量稀疏表示的DOA估计方法

针对现有稀疏重构DOA估计算法不能抑制噪声项以及在高斯色噪声背景下不再适用的问题，本文提出了基于四阶累积量稀疏重构的DOA估计方法。首先，利用接收数据的四阶累积量构建了稀疏表示模型，该模型抑制了噪声项；其次对四阶累计量矩阵进行奇异值分解，化简了稀疏表示模型，通过奇异值分解，不仅减小了数据规模，而且进一步抑制了噪声。对于稀疏表示模型的求解，先利用信号子空间与噪声子空间的正交特性选取权值矢量，然后利用加权l1范数法对模型求解实现DOA估计。理论分析和仿真实验表明本文算法在高斯白噪声和色噪声背景下均适用；能够处理非相干和相干信号，且在低信噪比条件下，对相干信号有更高的估计精度；较之同类的稀疏重构算法，本文算法具有较低的算法复杂度和更高的角度分辨力。 

DOA estimation method by sparse representation of fourth-order cumulant

The existing sparse reconstruction algorithms for DOA estimation algorithms couldn’t suppress noise and be applied in the background of colored Gaussian noise. In order to solve these problems, an approach for DOA estimation based on sparse reconstruction of fourth-order cumulant matrix was proposed in this paper. Firstly, we constructed sparse representation model using fourth-order cumulants of received data. Noise is suppressed in the model. Secondly, singular value decomposition was used upon forth-order cumulant matrix to simplify the sparse representation model. Through singular value decomposition, we not only reduced the scale of data, but also further suppressed noise. Aiming at solving the model, we selected weight vector using orthogonality between signal subspace and noise subspace. Then we solved the model by weighted 1 norm algorithm to achieve DOA estimation. Theoretical analysis and experimental results show that the algorithm proposed in this paper can be applied in the background of white Gaussian noise and colored Gaussian noise. The algorithm has the capability of processing both incoherent and coherent signals and achieves more accurate estimation for coherent signal in the case of low SNR. Compared with the same kind of sparse reconstruction algorithms, the algorithm has lower calculation complexity and higher angle resolution.