We consider the problem of optimal (fixed) wireless sensor network (WSN) design for distributed detection of a randomly-located target. A distributed one-dimensional (1-D) WSN model with equal spacing d between any two adjacent nodes is assumed We first model the target as being randomly located following an exponential distribution with a known parameter, and the channel between the nodes and the fusion center to be AWGN with path loss attenuation. A simplified decision fusion rule for the high observation signal-to-noise ratio (SNR) regime and its Bayesian error probability are derived, which then is used to optimize the parameters of the WSN. The optimal sensor placements are obtained in the limit of a large sensor system and the analytical properties of the obtained solution are discussed with corresponding numerical examples. It is shown that in many cases deviation from optimal inter-node spacing can cost significant performance penalty. Finally, the results are generalized to a fading wireless channel and for any target-location distribution specified only via its second-order statistics. It is shown that the optimal sensor placements essentially stays the same regardless of whether the channel is AWGN or fading, and are insensitive to operating SNR's either at the fusion center or at the local sensor nodes.
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