Geometric Properties of Grassmannian Frames for R 2 and R 3
Geometric Properties of Grassmannian Frames for R 2 and R 3
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发表时间：
2004
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通讯作者：
J. Benedetto;J. Kolesar
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作者：
J. Benedetto;J. Kolesar
Grassman帧是满足最小-最大相关准则的帧。我们将二维和三维欧氏空间(R2和R3)的几何直观方法转化为一种新的解析方法，用于在这种情况下对许多Grassman标架进行分类。该方法和相关算法降低了最大帧相关性，从而产生了Grassman帧的具体例子的构造。许多结果是通过其他技术已知的，甚至更广泛地说，因此本论文可以被视为教程。然而，我们的分析方法的目的是发展它来解决d维Hilbert空间中的未解决问题，d维Hilbert空间用作球形码、擦除信道建模和通信理论的其他方面的设置。
Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for twoand three-dimensional Euclidean space (R2 andR3) 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 d-dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.