Sequential decentralized detection under noisy channels

We consider decentralized detection through distributed sensors that perform level-triggered sampling and communicate with a fusion center (FC) via noisy channels. Each sensor computes its local log-likelihood ratio (LLR), samples it using the level-triggered sampling, and upon sampling transmits a single bit to the FC. Upon receiving a bit from a sensor, the FC updates the global LLR and performs a sequential probability ratio test (SPRT) step. We derive the fusion rules under various types of channels. We further provide non-asymptotic and asymptotic analyses on the average detection delay for the proposed channel-aware scheme, and show that the asymptotic detection delay is characterized by a KL information number. The delay analysis facilitates the choice of appropriate signaling schemes under different channel types for sending the 1-bit information from sensors to the FC.