How dense should a sensor network be for detection applications?

A binary decentralized detection problem is studied in which a collection of wireless sensor nodes provides relevant information about their environment to a fusion center. The observations at the nodes are samples of a finite state Markov process under each hypothesis. The nodes transmit their data to a fusion center over a multiple access channel. Upon reception of the information, the fusion center selects one of the two possible hypotheses. It is assumed that the sensor system is constrained by the capacity of the multiple access channel over which the sensor nodes are transmitting. Thus, as the node density increases, the sensor observations get more correlated, and, furthermore, fewer bits can be transmitted by each sensor node. A framework is presented in this paper for deriving design guidelines relating sensor density to system performance under a total communication constraint. The framework is based on large deviation theory applied to the asymptotic regime where the number of sensor nodes is large. This framework is applied to a specific example to compare the gains offered by having a higher node density with the benefits of getting detailed information from each sensor.