Upper bounds are presented on the size of equal energy continuous time signal sets occupying a given time-bandwidth (TB) product under specified synchronous correlation constraints. Both time-limited (aperiodic) and periodic signal sets are addressed, with appropriate measures of bandwidth for each. Signal set construction techniques are derived which illustrate that the bounds for periodic signal sets are relatively tight, while those obtained for aperiodic signal sets are tight under certain conditions.

Rowe has developed an upper bound on the number of vectors possible in ad-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 Crms. 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.