Distributed Detection of Weak Signals From One-Bit Measurements Under Observation Model Uncertainties

Abstract

We consider the distributed detection of weak signals from one-bit measurements collected by a sensor network where observation model uncertainties exist at all the sensor nodes. To solve this problem, a one-bit locally most powerful test (LMPT) detector is proposed in this letter. Moreover, asymptotically optimal one-bit quantizers at all the sensor nodes are designed for the proposed one-bit LMPT detector. In this letter, model uncertainties are interpreted as multiplicative noise and its variance represents the strength of model uncertainties. Theoretical analysis indicates that, when the strength of model uncertainties is finite, the proposed detector using one-bit data with $\pi N/2$ sensors approximately achieves the same detection performance as the clairvoyant detector that directly uses analog measurements with $N$ sensors. Simulation results corroborate our theoretical analysis and show that, compared to the one-bit generalized likelihood ratio test detector, the proposed one-bit LMPT detector provides better detection performance in the presence of model uncertainties.