Sampling Schemes for Sequential Detection With Dependent Observations

Several sampling schemes and their corresponding sequential detection procedures in autoregressive noise are presented in this paper. Two of them use uniform sampling procedures with high and low sampling rates, respectively. The other two employ groups of samples, which are separated by long intergroup delays such that the intergroup correlations are negligible. One of the group-sampling schemes also employs optimal signaling waveforms to further improve its energy-efficiency. In all the schemes, data sampling and transformation are designed in such a way that Wald's sequential probability ratio test (SPRT) can still be implemented. The performances of different schemes, in terms of average termination time (ATT), are derived analytically. When all the schemes employ the same sampling interval and under a constant signal amplitude constraint, their performances are compared through analytical and numerical methods. In addition, under a constant power constraint, their ATTs and energy-efficiency are compared. It is theoretically proved that the scheme using groups of samples with the optimal signaling waveform is the most energy-efficient.