A generalized sequential sign detector for binary hypothesis testing

It is known that for fixed error probabilities sequential signal detection based on the sequential probability ratio test (SPRT) is optimum in terms of the average number of signal samples for detection. But, often suboptimal detectors like the sequential sign detector are preferred over the optimal SPRT. When the additive noise statistic is independent and identically distributed (i.i.d.), the sign detector is preferred for its simplicity and nonparametric properties. However, in many practical applications such as the usage of high speed sampling devices the noise is correlated. A generalized sequential sign detector for detecting binary signals in stationary, first-order Markov dependent noise is studied. Under the i.i.d. assumptions, this reduces to the usual sequential sign detector. The optimal decision thresholds and the average sample number for the test to terminate are derived. Numerical results are given to show that the proposed detector exploits the correlation in the noise and hence results in quicker detection. The method can also be extended to Mth order Markov dependence by converting it to a first-order dependence in an extended state space.