Binary CDMA signature sets with concurrently minimum total-squared-correlation and maximum-squared-correlation

We derive lower bounds on the maximum-squared-correlation (MSC) of binary antipodal signature sets for any number of signatures K and any signature length L with K ≤ L (underloaded systems). We establish the tightness of the bounds for all cases except K = L ≡ 1 (mod 4) and we prove that the minimum total-squared-correlation (TSC) binary antipodal signature sets that were recently designed are, in fact doubly optimal for underloaded systems: both their TSC and MSC are minimum.