A new beamspace method for array processing, called convolutional beamspace (CBS), is proposed. It enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. But unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure and the shift-invariance are preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space. The method also generalizes to sparse arrays by effective use of the difference coarray. For this, the autocorrelation evaluated on the ULA portion of the coarray is filtered appropriately to produce the coarray CBS. It is also shown how CBS can be used in the context of sparse signal representation with dictionaries, where the dictionaries have columns that resemble steering vectors at a dense grid of frequencies. Again CBS processing with dictionaries offers better resolution, accuracy, and lower computational complexity. As only the filter responses at discrete frequencies on the dictionary grid are relevant, the problem of designing discrete-frequency FIR filters is also addressed.

中文翻译：

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线性阵列的卷积波束空间

提出了一种新的用于阵列处理的波束空间方法，称为卷积波束空间 (CBS)。它享有经典波束空间的优点，例如较低的计算复杂度、增加的子带处理并行性以及改进的 DOA 估计分辨率阈值。但与经典的波束空间方法不同，它允许直接为 ULA 执行 root-MUSIC 和 ESPRIT，无需额外准备，因为 Vandermonde 结构和平移不变性在 CBS 变换下得以保留。该方法产生比经典波束空间更准确的 DOA 估计，并且对于相关源，比元素空间更好的估计。该方法还通过有效使用差分协阵列推广到稀疏阵列。为了这，在 coarray 的 ULA 部分上评估的自相关被适当地过滤以生成 coarray CBS。还展示了如何在具有字典的稀疏信号表示的上下文中使用 CBS，其中字典在密集的频率网格中具有类似于导向向量的列。使用字典的 CBS 处理再次提供了更好的分辨率、准确性和更低的计算复杂性。由于只有字典网格上离散频率的滤波器响应是相关的，因此还解决了设计离散频率 FIR 滤波器的问题。使用字典的 CBS 处理再次提供了更好的分辨率、准确性和更低的计算复杂性。由于只有字典网格上离散频率的滤波器响应是相关的，因此还解决了设计离散频率 FIR 滤波器的问题。使用字典的 CBS 处理再次提供了更好的分辨率、准确性和更低的计算复杂性。由于只有字典网格上离散频率的滤波器响应是相关的，因此还解决了设计离散频率 FIR 滤波器的问题。