In this paper, we study energy transmission for decentralized detection in wireless powered sensor networks (WPSN) in which the sensor nodes are powered by harvesting the radio frequency signals transmitted from dedicated energy access points (E-AP). We present a joint design of the transmit covariance matrices at E-APs and sensor precoders to minimize the probability of error. To this end, we maximize the error exponents by employing Dinkelbach's method and semidefinite relaxation. We present an iterative algorithm to solve the relaxed problem and prove that the relaxation is tight. Simulation results demonstrate that the proposed design results in a superior detection performance in comparison to the conventional techniques.
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