Sign-assisted precoding for joint decentralized detection and estimation in WSNs

We consider a joint decentralized detection and estimation problem in which a number of sensor nodes collaborate to detect and estimate an unknown deterministic vector signal. To cope with the power/bandwidth constraints inherent in wireless sensor networks (WSNs), each sensor compresses its observations using a linear precoder. The compressed messages are transmitted to the fusion center (FC), where a global decision is made by resorting to a generalized likelihood ratio test (GLRT), and a maximum likelihood (ML) estimate of the signal is formed if the signal is detected. We propose a sign-assisted random precoding scheme which utilizes the knowledge of the plus/minus signs of the signal components. Performance analysis shows that the signassisted scheme is more effective than the energy detector in detecting weak signals that are buried in noise. Specifically, it outperforms the energy detector when the observation signal-to-noise ratio (SNR) is less than 1/(π-2).