Within the realm of rapidly advancing wireless sensor networks (WSNs), distributed detection assumes a significant role in various practical applications. However, critical challenge lies in maintaining robust detection performance while operating within the constraints of limited bandwidth and energy resources. This paper introduces a novel approach that combines model-driven deep learning (DL) with binary quantization to strike a balance between communication overhead and detection performance in WSNs. We begin by establishing the lower bound of detection error probability for distributed detection using the maximum a posteriori (MAP) criterion. Furthermore, we prove the global optimality of employing identical local quantizers across sensors, thereby maximizing the corresponding Chernoff information. Subsequently, the paper derives the minimum MAP detection error probability (MAPDEP) by inplementing identical binary probabilistic quantizers across the sensors. Moreover, the paper establishes the equivalence between utilizing all quantized data and their average as input to the detector at the fusion center (FC). In particular, we derive the Kullback-Leibler (KL) divergence, which measures the difference between the true posterior probability and output of the proposed detector. Leveraging the MAPDEP and KL divergence as loss functions, the paper proposes model-driven DL method to separately train the probability controller module in the quantizer and the detector module at the FC. Numerical results validate the convergence and effectiveness of the proposed method, which achieves near-optimal performance with reduced complexity for Gaussian hypothesis testing.

翻译：在快速发展的无线传感器网络（WSNs）领域，分布式检测在众多实际应用中扮演着重要角色。然而，关键挑战在于在有限带宽和能量资源约束下保持稳健的检测性能。本文提出了一种新颖方法，将模型驱动深度学习（DL）与二元量化相结合，以在WSNs中实现通信开销与检测性能之间的平衡。我们首先基于最大后验（MAP）准则建立了分布式检测的检测错误概率下界。此外，我们证明了在所有传感器上采用相同局部量化器的全局最优性，从而最大化相应的Chernoff信息。随后，本文推导了在传感器间实施相同二元概率量化器时的最小MAP检测错误概率（MAPDEP）。同时，本文建立了利用所有量化数据与其平均值作为融合中心（FC）检测器输入之间的等价性。特别地，我们推导了Kullback-Leibler（KL）散度，用于衡量真实后验概率与所提检测器输出之间的差异。以MAPDEP和KL散度作为损失函数，本文提出了模型驱动深度学习方法，分别训练量化器中的概率控制模块和融合中心的检测器模块。数值结果验证了所提方法的收敛性和有效性，该方法在高斯假设检验中能以较低复杂度实现接近最优的性能。