Online Linear Compression with Side Information for Distributed Detection of High Dimensional Signals

In this paper, we propose a novel near-optimal linear compression strategy at the local sensors for the distributed detection of unknown high dimensional signals in a wireless sensor network (WSN). The WSN consists of multiple sensors distributed in a region of interest (RoI) and a fusion center (FC). The signal is assumed to be unknown to the local sensors and the FC; however, we assume that the sensors have some side information about the signal to be detected. Specifically, the sensors possess the knowledge of the signs of the individual components of the signal vector. Using this sign information, we design a linear compression strategy which is employed by the local sensors to compress the collected spatio-temporal data before forwarding it to the FC. We analytically show that the proposed compression strategy can achieve near-optimal error exponents. Further, the proposed compression strategy provides robust performance which is unaffected by the signal dimension as opposed to other state-of-the-art compression strategies whose error exponents are shown to decay with the signal dimension.