In this paper, we investigate a binary decentralized detection problem in which a network of wireless sensors provides relevant information about the state of nature to a fusion center. Each sensor transmits its data over a multiple access channel. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. We consider the scenario where the sensor network is constrained by the capacity of the wireless channel over which the sensors are transmitting, and we study the structure of an optimal sensor configuration. For the problem of detecting deterministic signals in additive Gaussian noise, we show that having a set of identical binary sensors is asymptotically optimal, as the number of observations per sensor goes to infinity. Thus, the gain offered by having more sensors exceeds the benefits of getting detailed information from each sensor. A thorough analysis of the Gaussian case is presented along with some extensions to other observation distributions.

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Abstract-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.

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