  This paper considers the sequential composite hypothesis test with multiple
sensors. The sensors observe random samples in parallel and communicate with a
fusion center, who makes the global decision based on the sensor inputs. On one
hand, in the centralized scenario, where local samples are precisely
transmitted to the fusion center, the generalized sequential likelihood ratio
test (GSPRT) is shown to be asymptotically optimal in terms of the expected
sample size as error rates tend to zero. On the other hand, for systems with
limited power and bandwidth resources, decentralized solutions that only send a
summary of local samples (we particularly focus on a one-bit communication
protocol) to the fusion center is of great importance. To this end, we first
consider a decentralized scheme where sensors send their one-bit quantized
statistics every fixed period of time to the fusion center. We show that such a
uniform sampling and quantization scheme is strictly suboptimal and its
suboptimality can be quantified by the KL divergence of the distributions of
the quantized statistics under both hypotheses. We then propose a decentralized
GSPRT based on level-triggered sampling. That is, each sensor runs its own
GSPRT repeatedly and reports its local decision to the fusion center
asynchronously. We show that this scheme is asymptotically optimal as the local
thresholds and global thresholds grow large at different rates. Lastly, two
particular models and their associated applications are studied to compare the
centralized and decentralized approaches. Numerical results are provided to
demonstrate that the proposed level-triggered sampling based decentralized
scheme aligns closely with the centralized scheme with substantially lower
communication overhead, and significantly outperforms the uniform sampling and
quantization based decentralized scheme.
