Achieving optimal detection through discrete diffusion equations

It is known that sequential signal detection based on the sequential probability ratio test (SPRT) is the shortest on an average among other tests. Most of the work in sequential signal detection assumes independent, identically distributed noise. The decision thresholds are not exact. This is due to the complexity involved in doing an exact analysis of the sequential detector. In this paper, we propose a sequential sign detector for detecting constant signals in first order Markov noise. The distribution of the sufficient statistic is derived as a solution to the discrete diffusion equations. This leads to the derivation of the exact values of the decision thresholds and the average sample number