Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems
Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems
复制标题
DOI：
10.1109/tsp.2008.917929
复制
发表时间：
2008-07-01
影响因子：
5.4
通讯作者：
Del Galdo, Giovanni
中科院分区：
文献类型：
--
作者：
Haardt, Martin;Roemer, Florian;Del Galdo, Giovanni
多维谐波恢复问题在多种信号处理应用中都会遇到，包括雷达、声纳、通信、医学成像以及从多输入多输出（MIMO）信道测量中估计主要多径分量的参数。基于R维子空间的方法，例如R - D酉ESPRIT、R - D RARE或R - D MUSIC，经常用于这项任务。由于测量数据是多维的，当前的方法需要将各维度堆叠成一个高度结构化的矩阵。然而，在传统的子空间估计步骤中，例如通过对后一个矩阵进行奇异值分解（SVD），这种结构并没有被利用。在本文中，我们定义了一个测量张量，并通过高阶奇异值分解来估计信号子空间。这使我们能够在算法的第一步就利用测量数据中固有的结构，从而更好地估计信号子空间。我们展示了前后向平均的概念以及中心厄米特矩阵到相同大小实值矩阵的映射如何能够扩展到张量。作为示例，我们开发了R - D标准张量 - ESPRIT和R - D酉张量 - ESPRIT算法。然而，这些新概念可以应用于任何基于多维子空间的参数估计方案。如果R个维度中至少有一个维度所具有的传感器数量大于信源数量，那么所得到的参数估计精度会有显著提高。这在二维情况下就已经可以观察到。
Multidimensional harmonic retrieval problems are encountered in a variety of signal processing applications including radar, sonar, communications, medical imaging, and the estimation of the parameters of the dominant multipath components from MIMO channel measurements. R-dimensional subspace-based methods, such as R-D Unitary ESPRIT, R-D RARE, or R-D MUSIC, are frequently used for this task. Since the measurement data is multidimensional, current approaches require stacking the dimensions into one highly structured matrix. However, in the conventional subspace estimation step, e.g., via an SVD of the latter matrix, this structure is not exploited. In this paper, we define a measurement tensor and estimate the signal subspace through a higher-order SVD. This allows us to exploit the structure inherent in the measurement data already in the first step of the algorithm which leads to better estimates of the signal subspace. We show how the concepts of forward-backward averaging and the mapping of centro-Hermitian matrices to real-valued matrices of the same size can be extended to tensors. As examples, we develop the R-D standard Tensor-ESPRIT and the R-D Unitary Tensor-ESPRIT algorithms. However, these new concepts can be applied to any multidimensional subspace-based parameter estimation scheme. Significant improvements of the resulting parameter estimation accuracy are achieved if there is at least one of the R dimensions, which possesses a number of sensors that is larger than the number of sources. This can already be observed in the two-dimensional case.