Generalized Locally Most Powerful Tests for Distributed Sparse Signal Detection

In this paper we tackle distributed detection of a localized phenomenon of interest (POI) whose signature is sparse via a wireless sensor network. We assume that both the position and the emitted power of the POI are unknown, other than the sparsity degree associated to its signature. We consider two communication scenarios in which sensors send either (i) their compressed observations or (ii) a 1-bit quantization of them to the fusion center (FC). In the latter case, we consider non-ideal reporting channels between the sensors and the FC. We derive generalized (i.e. based on Davies' framework (Davies, 1977)) locally most powerful detectors for the considered problem with the aim of obtaining computationally-efficient fusion rules. Moreover, we obtain their asymptotic performance and, based on such result, we design the local quantization thresholds at the sensors by solving a 1-D optimization problem. Simulation results confirm the effectiveness of the proposed design and highlight only negligible performance loss with respect to counterparts based on the (more-complex) generalized likelihood ratio.