The design and detection of signature sequences in time-frequency selective channel

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 channelpsilas 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 channelpsilas maximum Doppler spread. The detection of the sequences essentially consists of correlating the received signal with all valid hypotheses, and can be carried out efficiently if the base sequence is properly designed. Simulation results show that given a sequence length that is large enough, exact number of multiple devices can be accurately detected in very challenging conditions with a single threshold test.