Detection of Sparse Signals in Sensor Networks via Locally Most Powerful Tests

We consider the problem of detection of sparse stochastic signals with a distributed sensor network. Multiple sensors in the network are assumed to observe sparse signals, which share the joint sparsity pattern. The Bernoulli-Gaussian (BG) distribution with sparsity-enforcing capability is imposed on the sparse signals. The sparsity degree in the BG model is positive and close to zero in the presence of the sparse signals and is zero in the absence of the signals. Motivated by this, the problem of detection of the sparse signals with a distributed sensor network is formulated as the problem of close and one-sided hypothesis testing on the sparsity degree. For this problem, we propose a detector based on the locally most powerful test (LMPT) to decide on the presence or absence of sparse signals with sensor networks. The proposed LMPT detector does not require signal recovery, which alleviates the complexity of the detection system in sensor networks. Simulation results illustrate the performance of the proposed LMPT detector and corroborate our theoretical analysis. Simulation results also show that, compared to the detector based on matching pursuit, the proposed LMPT detector significantly reduces the computational burden without noticeable performance loss.