Geometric Properties of Grassmannian Frames for and
Geometric Properties of Grassmannian Frames for and
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DOI：
10.1155/asp/2006/49850
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发表时间：
2006-02
影响因子：
1.9
通讯作者：
J. Benedetto;J. Kolesar
中科院分区：
文献类型：
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作者：
J. Benedetto;J. Kolesar
格拉斯曼帧是满足最小-最大相关标准的帧。我们将二维和三维欧几里得空间（和）的几何直观方法转化为一种新的分析方法，用于在此设置中对许多格拉斯曼框架进行分类。该方法和相关算法降低了最大帧相关性，从而产生了格拉斯曼帧的具体示例的构造。许多结果是通过其他技术已知的，甚至更普遍，因此本文可以被视为教程。然而，我们提出的分析方法的目标是开发它来解决维度希尔伯特空间中未解决的问题，希尔伯特空间作为球形码、擦除信道建模和通信理论其他方面的设置。
Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( and) into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of specific examples of Grassmannian frames. Many of the results are known by other techniques, and even more generally, so that this paper can be viewed as tutorial. However, our analytic method is presented with the goal of developing it to address unresovled problems in-dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.