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

In this paper, we derive closed-form expressions for the maximum squared correlation (MSC), total asymptotic efficiency (TAE), and sum capacity (Csum) of minimum total squared correlation (TSC) quaternary signature sets. While TSC, MSC, TAE, and Csum are equivalent optimization metrics over the real/complex field, our developments show that such equivalence does not hold, in general, over the quaternary field. We establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible.