Two state Markov modelling and detection of single electron spin signals

The focus of this paper is the optimal detection of piecewise constant binary valued continuous-time (C-T) signals with Markovian state transitions. One example is the classic random telegraph signal for which the number of states is two and the transitions follow a Poisson process. This signal detection problem arises in many different areas of engineering and science, notably modulation classification in digital communications and detection of digital content in continuous signals or images with high noise contamination. Our motivation is single electron-spin detection in Magnetic Resonance Force Microscopy (MRFM), which is an emerging molecular scale imaging modality. We will obtain an optimal discrete time iterative detection algorithm and an associated upper bound on the Receiver Operating Characteristic (ROC) curve. These results will be used to show that the optimal detector reduces to a simple filtered energy detector when the state transition probabilities are symmetric, the signal-to-noise ratio (SNR) is low, and the time-bandwidth product is high. In the general case when the state transition probabilities can be either symmetric or asymmetric, the optimal detector reduces to a hybrid filtered energy/amplitude/energy detector when the SNR is low and there are a large number of samples per observation.