Geometry of the Welch Bounds

A geometric perspective is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric k-tensors, tight frames, homogeneous polynomials, and tdesigns. Index Terms – Frames, Grammian, Homogeneous polynomials, Symmetric tensors, t-designs, Welch bounds