Geometric Properties of Grassmannian Frames for <inline-formula><graphic file="1687-6180-2006-049850-i1.gif"/></inline-formula> and <inline-formula><graphic file="1687-6180-2006-049850-i2.gif"/></inline-formula>

Abstract

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.