基于稀疏子阵列空间平滑的相干信号波达方向欠定估计

Recently, the difference co-array generated by directly vectorizing the covariance matrix of the measurements from some sparse arrays, provides a solution to detect more sources than the number of sensors. However, this exciting result requires that all the impinging sources are uncorrelated and their corresponding source covariance matrix should be full-rank and diagonal. In this project, we focus on how to solve the nonsingular and/or rank deficient problem of source covariance matrix resulted from the presence of coherent sources. Firstly, we will design a new sparse array geometry, which contains a set of overlapped subarrays, and investigate a subarray-based spatial smoothing technique. Compared with the conventional spatial smoothing technique, our proposed technique can effectively restore the deficient rank for non-uniform linear array, since the subarray-based spatial smoothing is applied to a set of overlapping uniform sub-arrays, instead of to the whole sparse array. Then, we try to compute sparse representations of the vectorized full-rank spatial smoothed covariance matrix using kronecker bases. In order to reduce the dimension of the kronecker dictionary, an effective joint sparse recovery strategy will be investigated via making use of the block diagonal properties of the smoothed covariance matrix. In the end, we plan to conduct some experiments based on microwave arrays and microphone arrays to validate the effectiveness of the proposed arrays and algorithms.

基于稀疏阵列的互阵列技术，由于其通过矢量化信号协方差矩阵产生虚拟阵列，可用于提高阵列的自由度，成为欠定波达估计的有效方法。然而互阵列技术依赖于满秩且对角的信源协方差矩阵，要求入射信号相互正交，限制了其在实际中的应用。本课题致力于解决相干信号入射背景下的欠定波达估计问题，具体工作如下：首先，拟提出一种新的稀疏阵列结构，该阵列包含多个相互重叠的稀疏子阵列，进而利用子阵列相互平滑达到恢复协方差矩阵秩的目的。由于所提子阵列平滑技术只要求子阵列具有平移特性，因此能适用于整体结构不规则的稀疏阵列。其次，将研究一种通过平滑后的满秩协方差矩阵实现欠定波达估计的方法。拟通过利用协方差矩阵的块对角特性约束主对角元素与其他元素之间的关系，降低kronecker基空间的维度和自由度，达到低复杂度联合稀疏重构的目的。最后，拟通过射频天线阵列和麦克风阵列采集相干入射信号，验证和分析所提稀疏阵列结构和估计算法的性能。

基于稀疏阵列的互阵列波达估计技术，由于其通过矢量化信号协方差矩阵产生虚拟阵列，可用于提高阵列的自由度，成为欠定波达估计的有效方法。然而互阵列技术依赖于满秩且对角的信源协方差矩阵，要求入射信号相互正交，限制了其在实际中的应用。本课题提出了一套解决相干信号入射背景下的欠定波达估计问题的有效方法，形成成果如下：首先，提出两种新的稀疏阵列结构，该阵列包含多个相互重叠的稀疏子阵列，进而利用子阵列相互平滑达到恢复协方差矩阵秩的目的。由于所提子阵列平滑技术只要求子阵列具有平移特性，因此能适用于整体结构不规则的稀疏阵列。其次，提出了一种通过平滑后的满秩协方差矩阵实现欠定波达估计的方法。通过利用协方差矩阵的块对角特性约束主对角元素与其他元素之间的关系，通过迭代方法逐次分离出非相关信号协方差矩阵中的对角元素，通过对剔除主对角元素的剩余协方差矩阵进行估计，寻找最大似然角度空间，最终达到对相关信号入射角度估计的目的。最后，拟通过射频天线阵列和麦克风阵列采集相干入射信号，验证和分析所提稀疏阵列结构和估计算法的有效性。本项目的研究成果提供了一种相干信号欠定波达估计的有效方法，对未来实际应用中目标被动探测与识别具有重要的应用价值。