New Bounds on the Aperiodic Total Squared Correlation of Binary Signature Sets and Optimal Designs

We derive new bounds on the aperiodic total squared correlation (ATSC) of binary antipodal signature sets for any number of signatures K and any signature length L. We then present optimal designs that achieve the new bounds for several (K, L) cases. As an example, it is seen that the familiar Gold and (small or large) Kasami designs are not ATSC-optimal in general. The optimal signature set designs provided herein are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.