Asymptotic results for decentralized detection in power constrained wireless sensor networks

In this paper, we study a binary, decentralized detection problem in which a set of sensor nodes provides partial information about the state of nature to a fusion center. Sensor nodes have access to conditionally independent and identically distributed observations, given the state of nature, and transmit their data over a wireless channel. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. Specifically, we extend existing asymptotic results about large sensor networks to the case where the network is subject to a joint power constraint, and where the communication channel from each sensor node to the fusion center is corrupted by additive noise. Large deviation theory is used to show that having identical sensor nodes, i.e., each node using the same transmission scheme, is asymptotically optimal. Furthermore, a performance metric by which sensor node candidates can be compared is established. We supplement the theory with examples to illustrate how the results derived in this paper apply to the design of practical sensing systems.