Abstract— In a slot-synchronized wireless communication system, a set of signature sequences can be derived by circularly shifting a base sequence with good auto correlation properties. In a time-dispersive channel, the sequences with different circular time shifts can be uniquely identified as long as their minimum separation in time is greater than the channel’s maximum delay spread. In this paper, we extend this approach further to the Doppler domain by introducing an additional circular frequency offset to the delay shifted sequences. When the base sequence is carefully designed through applying some delay-Doppler radar signal design principles, the results of this two-dimensional generalization are a much larger set of sequences with better correlation properties than some existing designs. Moreover, the new design is also suitable in channels that are both time and frequency selective as long as the minimum Doppler separation of the sequences is greater than the channel’s ...