Distributed Detection of Identical Sparse Signal With Quantized Measurements via LMPT

This paper considers the distributed detection of an identical sparse signal across sensor networks. Measurements are acquired and quantized locally at each sensor node, and the fusion center determines the global presence/absence of the sparse signal. We propose a quantized locally most powerful test (LMPT) detector to enhance detection performance under bandwidth constraints. The sparse signal follows the Bernoulli- Gaussian distribution, with a positive and near-zero degree of sparsity under the alternative hypothesis. By leveraging the Lyapunov-central limit theorem and the Berry-Esseen theorem, we establish the asymptotic Gaussianity of compressed measurements, enabling the formulation of a well-defined hypothesis testing problem. Moreover, we determine the quantization thresholds by maximizing the Fisher information, with the optimization problem solved by the Particle Swarm Optimization algorithm, thereby ensuring near-optimal performance without requiring the objective function to be concave. Simulation results demonstrate the efficacy of the quantized LMPT detector in various scenarios.