Optimal sequence sets meeting Welch's lower bound

摘要

Welch's lower bounds on total periodic and odd correlation energyof an equi-energy set of sequences are presented. It is shown that bothbounds are simultaneously achieved precisely when the sequence set formsan aperiodic complementary sequence set, which has been extensivelystudied and is of independent interests. Then a lower bound closelyrelated to an approximate SNR formula of Pursley (1977) for asynchronousDS/SSMA is derived. Our results are an extension of the works of Masseyand Mittelholzer (see Sequences II: Methods in Communication, Security,and Computer Science, R. Capocelli, et al., Eds. New York:Springer-Verlag, 1993) for synchronous DS/SSMA