Signal Sets with Optimal Correlation Properties

Rowe has developed an upper bound on the number of vectors possible in a
d
-dimensional space, given that the vectors of the set are divided into orthogonal alphabets and subject to an appropriately defined root-mean-square correlation constraint C
rms
. Here, signal set design procedures are presented that are near optimal with respect to Rowe's upper bound. The specific parameters of these signal set construction techniques are significant as they illustrate the tightness of the upper bound for situations that have not been previously addressed. Finally, a signal set design procedure is presented that serves as an improvement to a lower bound originally reported by Rowe.