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中文摘要：
针对现有稀疏重构DOA估计算法不能抑制噪声项、在高斯色噪声背景下不适用以及能够分辨的最大信源数小于阵元数的问题,首先利用阵列输出数据的四阶累积量矩阵构建稀疏表示模型,该模型抑制了噪声项,并通过产生虚拟阵元实现了阵列扩展;然后对累积量矩阵进行奇异值分解来化简模型,化简后的模型不仅减小了数据规模而且进一步抑制了噪声。在利用加权l1范数法对稀疏表示模型求解时,不需要选取平衡重构残差与解的稀疏性的正则化参数。理论分析与仿真实验表明所提算法在高斯白噪声以及色噪声背景下均适用,能够分辨的最大信源数大于阵元数且具有较高的角度分辨力。
英文摘要：
The existing sparse reconstruction algorithms for DOA estimation cannot suppress noise and are not applicable under colored Gaussian noise, and the maximum number of sources that could be handled by these algorithms is smaller than the number of array elements. In order to solve these problems, a sparse representation model is constructed based on the fourth-order cumulant of received data, which suppresses the noise and realizes array extension by producing virtual array elements. And then, singular value decomposition is used upon the cumulant matrix to simplify the model. The simplified model not only reduces the scale of data, but also further suppresses noise. When the sparse representation model is solved by using weighted l1 norm algorithm, it’s unnecessary to select the regularization parameter which balances reconstruction residual with the sparsity of solution. Theoretical analysis and experimental results show that the proposed algorithm is applicable under both the white or colored Gaussian noise, and the maximum number of sources that can be handled is larger than the number of array elements, with higher angle resolution.
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