Detection of Sparse Stochastic Signals With Quantized Measurements in Sensor Networks

In this paper, we consider the problem of detection of sparse stochastic signals with quantized measurements in sensor networks. The observed sparse signals are assumed to follow the Bernoulli-Gaussian distribution. Due to the limited bandwidth in sensor networks, the local sensors are required to send quantized measurements to the fusion center. First, we propose a detector using the locally most powerful test (LMPT) strategy, called the quantized LMPT detector, for the problem of distributed detection of sparse signals with quantized measurements. Then, the local quantizers are designed to guarantee the near optimal detection performance of the proposed quantized LMPT detector. When the designed quantization thresholds are applied at the local sensors, we show that 1) the proposed 1-bit LMPT detector with 3.3L sensors achieves approximately the same detection performance as the clairvoyant LMPT detector with L sensors; 2) the proposed LMPT detector with 3-bit measurements can achieve detection performance comparable to the clairvoyant LMPT detector. Simulation results demonstrate the performance of the proposed quantized LMPT detector and corroborate our theoretical analysis.