New Bounds and Optimal Binary Signature Sets - Part II: Aperiodic Total Squared Correlation

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 interesting -arguably- side results, we show that individual maximal merit factor sequences (for example Barker sequences) are single-user ATSC-optimal, while neither the familiar Gold nor the Kasami set designs are ATSC-optimal in general. The ATSC-optimal signature set designs provided in this work are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.