The maximum squared correlation, sum capacity, and total asymptotic efficiency of minimum total-squared-correlation binary signature sets

The total squared correlation (TSC), maximum squared correlation (MSC), sum capacity (C_sum), and total asymptotic efficiency (TAE) of underloaded signature sets, as well as the TSC and C_sum of overloaded signature sets are metrics that are optimized simultaneously over the real/complex field. In this present work, closed-form expressions are derived for the MSC, C_sum, and TAE of minimum-TSC binary signature sets. The expressions disprove the general equivalence of these performance metrics over the binary field and establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible. The sum-capacity loss of the recently designed minimum-TSC binary sets is found to be rather negligible in comparison with minimum-TSC real/complex-valued (Welch-bound-equality) sets.