Distributed sequential detection: Dependent observations and imperfect communication

In this paper, we consider the problem of distributed sequential detection using wireless sensor networks in the presence of imperfect communication channels between the sensors and the fusion center. Sensor observations are assumed to be spatially dependent. Moreover, the channel noise can be dependent and non-Gaussian. We propose a copula-based distributed sequential detection scheme that takes the spatial dependence into account. More specifically, each local sensor runs a memory-less truncated sequential test repeatedly and sends its binary decisions to the fusion center synchronously. The fusion center fuses the received messages using a copula-based sequential test. To this end, we first propose a centralized copula-based sequential test and show its asymptotic optimality and time efficiency. We then show the asymptotic optimality and time efficiency of the proposed distributed scheme. We also show that by suitably designing the local thresholds and the truncation window, the local probabilities of false alarm and miss detection of the proposed memory-less truncated local sequential tests satisfy the pre-specified error probabilities. Numerical experiments are conducted to demonstrate the effectiveness of our approach.