Distributed Detection of Sparse Stochastic Signals With 1-Bit Data in Tree-Structured Sensor Networks

In this paper, we consider the problem of detection of sparse stochastic signals based on 1-bit data with tree-structured sensor networks (TSNs). In the literature, distributed detection of sparse signals with parallel sensor networks (PSNs) has previously been studied, and detectors using the locally most powerful test (LMPT) strategies with analog data and 1-bit data have been proposed, respectively. However, parallel topology does not always reflect the practical scenario, such as in the case where some nodes are outside the communication range of the fusion center (FC). In this paper, we design a new detector for TSNs with extremely limited resources and let each local sensor node send 1-bit data to its immediate successor. For the proposed detector, we devise 1-bit quantizers at the local sensor nodes and the decision fusion rule with the 1-bit data collected at the FC, based on quantization of likelihood ratios and the LMPT strategy. We also present the procedure to obtain the near optimal quantization thresholds numerically for nodes at different levels by characterizing the detection performance in terms of the Fisher Information. In particular, in two-level two-degree (2L-2D) TSNs, compared with the analog LMPT detector with Q nodes that transmit analog data hierarchically, the proposed 1-bit LMPT detector asymptotically needs 1.74Q nodes to compensate for the performance loss induced by local quantization. Simulation results validate our theoretical analysis.