Distributed Detection of Sparse Stochastic Signals With Quantized Measurements: The Generalized Gaussian Case

Abstract

In this paper, we consider distributed detection of sparse stochastic signals with quantized measurements. Assume that both the noise and the dominant elements in sparse signals follow the generalized Gaussian (GG) distribution. Since the communication bandwidth in sensor networks is limited, the local sensors send quantized measurements instead of analog data to the fusion center. First, we propose the locally most powerful test (LMPT) detector based on quantized measurements for distributed detection of sparse signals with the GG distribution. Then, the local quantizers are designed by maximizing the efficacy of the proposed quantized LMPT detector. In particular, we obtain the near-optimal closed-form solutions of 1-bit quantizers at the local sensors using the log-concave approximation of efficacy. Multilevel quantizers at the local sensors are numerically obtained using the particle swarm optimization (PSO) algorithm. The asymptotic relative efficiency (ARE) is derived analytically to measure the performance loss of the proposed LMPT detector caused by quantization of local measurements. Simulation results corroborate our theoretical analysis of the proposed quantized LMPT detector.