Generalized even-odd transforms and correlation lower bounds for M-PSK/CDMA sequences

For asynchronous BPSK/CDMA, the odd correlation properties of the signature sequences in use are as important as their periodic (or even) counterparts. A class of odd correlation lower bounds for equi-energy complex-valued sequences were first derived by Sarwate (1979) using correlation identities. More general odd correlation bounds were later obtained by the present author (1994). The even-odd transforms (EOT) were introduced for converting a complex sequence set into another set with their periodic and odd correlation levels exchanged. Since the EOT changes only the phases but not the magnitudes of the elements of a sequence, the lowest maximum odd correlation level must be identical to the lowest maximum periodic correlation level for equi-energy (or constant envelope) complex-valued sequences. This fact trivializes some widely accepted formulations of odd correlation bounds. In this work, the EOT and the odd correlation bounds are generalized for the M-phase correlation functions.