Speaker: Douglas Cochran (DARPA/ASU)

Title: Geometry of the Welch Bounds


In 1976, L. R. Welch developed a family of lower bounds on the maximal inner product modulus between any two vectors from a set of unit vectors in a finite-dimensional space. These Welch bounds have since proven important in a number of waveform design applications for communications and radar. In this presentation, a geometric perspective will be used to derive the entire family of Welch bounds – in contrast to Welch's analytical derivation. The geometric point of view unifies a number of observations regarding tightness of the bounds and their connections to tight frames for the space of symmetric k-tensors and also to homogeneous polynomials and t-designs. This is joint work with Somantika Datta and Stephen Howard.