Precoding for decentralized detection of unknown deterministic signals

We consider a decentralized detection problem in which a number of sensor nodes collaborate to detect the presence of 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). The aim of the work presented here is to develop effective linear precoding strategies and study their detection error exponents under the asymptotic regime where the number of sensors tends to infinity. Two precoding strategies are introduced: a random precoding scheme which generates its precoding vectors following a Gaussian distribution, and a sign-assisted random precoding scheme which assumes the knowledge of the plus/minus signs of the signal components and designs its precoding vectors with the aid of this prior knowledge. Performance analysis shows that utilizing the sign information can radically improve the detection performance. Also, it is found that precoding-based schemes are more effective than the energy detector in detecting weak signals that are buried in noise. Specifically, the sign-assisted random precoding scheme outperforms the energy detector when the observation signal-to-noise ratio (SNR) is less than 1/(π - 2). Numerical results are conducted to corroborate our theoretical analysis and to illustrate the effectiveness of the proposed algorithms.