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Sparsity-aware DOA estimation of quasi-stationary signals using nested arrays

机译：使用嵌套数组的准平稳信号的稀疏感知DOA估计

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Highlights•The redundant components in the signal subspace can be eliminated effectively through a linear transformation.•Formulate a sparse reconstruction problem including a reweightedℓ1-norm minimisation subject to a weighted Frobenius norm.•An explicit upper bound for error-suppression is provided for robust signal recovery.•The proposed sparse-aware DOA estimation technique is extended to the wideband signal scenario.AbstractDirection of arrival (DOA) estimation of quasi-stationary signals (QSS) impinging on a nested array in the context of sparse representation is addressed in this paper. By exploiting the quasi-stationarity and extended virtual array structure provided inherently in the nested array, a new narrowband signal model can be obtained, achieving more degrees of freedom (DOFs) than the existing solutions. A sparsity-based recovery algorithm is proposed to fully utilise these DOFs. The suggested method is based on the sparse reconstruction for multiple measurement vector (MMV) which results from the signal subspace of the new signal model. Specifically, the notable advantages of the developed approach can be attributed to the following aspects. First, through a linear transformation, the redundant components in the signal subspace can be eliminated effectively and a covariance matrix with a reduced dimension is constructed, which saves the computational load in sparse signal reconstruction. Second, to further enhance the sparsity and fit the sampled and the actual signal subspace better, we formulate a sparse reconstruction problem that includes a reweightedℓ1-norm minimisation subject to a weighted error-constrained Frobenius norm. Meanwhile, an explicit upper bound for error-suppression is provided for robust signal recovery. Additionally, the proposed sparsity-aware DOA estimation technique is extended to the wideband signal scenario by performing a group sparse recovery across multiple frequency bins. Last, upper bounds of the resolvable signals are derived for multiple array geometries. Extensive simulation results demonstrate the validity and efficiency of the proposed method in terms of DOA estimation accuracy and resolution over the existing techniques.
机译： 突出显示 • 可以通过线性变换有效地消除信号子空间中的冗余分量。 • 制定一个稀疏的重建问题，包括重新加权的 ℓ 1 -范数最小化受加权Frobenius范数的约束。 • 提供了明确的错误抑制上限，以实现可靠的信号恢复。 < / ce：list-item> • 建议的稀疏已知的DOA估计技术已扩展到宽带信号场景。 摘要 在稀疏表示的情况下，撞击在嵌套阵列上的准平稳信号（QSS）的到达方向（DOA）估计。通过利用嵌套阵列中固有提供的准平稳性和扩展虚拟阵列结构，可以获得新的窄带信号模型，与现有解决方案相比，可以实现更多的自由度（DOF）。提出了一种基于稀疏性的恢复算法来充分利用这些自由度。所建议的方法基于对新信号模型的信号子空间的多次测量矢量（MMV）的稀疏重构。特别地，所开发方法的显着优点可以归因于以下方面。首先，通过线性变换，可以有效地消除信号子空间中的冗余分量，并构建一个尺寸减小的协方差矩阵，从而节省了稀疏信号重建中的计算量。其次，为了进一步增强稀疏性并更好地拟合采样信号和实际信号子空间，我们提出了一个稀疏的重构问题，其中包括重新加权的 ℓ 1 -范数最小化受加权误差约束的Frobenius范数的约束。同时，为鲁棒的信号恢复提供了明确的错误抑制上限。此外，通过在多个频率仓上执行组稀疏恢复，将提出的稀疏感知DOA估计技术扩展到宽带信号场景。最后，针对多个阵列几何体导出可分辨信号的上限。大量的仿真结果证明了该方法在DOA估计精度和分辨率方面优于现有技术的有效性和有效性。

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