Online Design of Precoders for High Dimensional Signal Detection in Wireless Sensor Networks

In this paper, we present an efficient methodology to design precoders for distributed detection of unknown high dimensional signals. We consider a wireless sensor network, where several distributed sensors collaborate to perform binary hypothesis testing based on observations of an unknown high dimensional signal corrupted by noise. The sensors collect data over both temporal and spatial domains. Due to network resource constraints, each sensor performs a linear compression (through precoding) of the observed high dimensional signal at each time instant and forwards the compressed signal to the fusion center (FC). The FC then employs the generalized likelihood ratio test (GLRT) to make a decision on the presence or absence of the signal. We propose online linear precoding/compression strategies for such sensors that collect data over spatio-temporal domain, so that the detection performance at the FC is maximized under certain network resource constraints. Through the measure of non-centrality parameter and receiver operating characteristics (ROC), we show that our proposed precoder design achieves very good detection performance.