It is known that compressive sensing (CS) techniques are useful for the estimation of millimeter wave (mmWave) channels. When uniform planar arrays (UPA) are used, four dictionaries, two for angles of departure (AoD) and two for angles of arrival (AoA), are constructed and mmWave channel estimation becomes a four-dimensional CS problem. The sensing matrix in the CS formulation, containing the Kronecker product of four dictionary matrices, becomes very large. The complexity is extremely high even when efficient orthogonal matching pursuit (OMP) is used. In this paper, we view the channel estimation problem for mmWave systems as a generalized Kronecker compressive sensing (G-KCS) problem that also arises in multidimensional signal processing. We show that we can solve G-KCS using successive recovery, one dimension at a time. In each one-dimensional recovery, the sensing matrix is of a much smaller size, which greatly reduces the complexity of OMP. The recovery result of a particular dimension, called decisions, can be utilized for successive decision-aided recovery (SDAR) of subsequent dimensions. The exploitation of earlier decisions allows us to have not only a more relaxed recovery condition but also further reduction in complexity. The proposed SDAR-OMP can be applied to G-KCS problems, e.g., channel estimation for mmWave channels and multidimensional signal processing. Simulations demonstrate that when SDAR-OMP is applied to channel estimation for hybrid mmWave systems, the estimation error is comparable to that of conventional OMP but the complexity is much lower.

中文翻译：

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使用广义克罗内克压缩感知 (G-KCS) 和连续决策辅助恢复的混合毫米波系统的信道估计


众所周知，压缩感知（CS）技术对于毫米波（mmWave）信道的估计非常有用。当使用均匀平面阵列（UPA）时，构建四个字典，两个用于出发角（AoD），两个用于到达角（AoA），毫米波信道估计成为四维CS问题。 CS 公式中的传感矩阵（包含四个字典矩阵的克罗内克乘积）变得非常大。即使使用高效的正交匹配追踪（OMP），复杂性也非常高。在本文中，我们将毫米波系统的信道估计问题视为广义克罗内克压缩感知（G-KCS）问题，该问题也出现在多维信号处理中。我们证明我们可以使用连续恢复来解决 G-KCS，一次一维。在每个一维恢复中，感知矩阵的尺寸要小得多，这大大降低了OMP的复杂度。特定维度的恢复结果称为决策，可用于后续维度的连续决策辅助恢复（SDAR）。利用早期决策不仅可以让我们拥有更宽松的恢复条件，还可以进一步降低复杂性。所提出的 SDAR-OMP 可应用于 G-KCS 问题，例如毫米波信道的信道估计和多维信号处理。仿真表明，当SDAR-OMP应用于混合毫米波系统的信道估计时，估计误差与传统OMP相当，但复杂度要低得多。