Model-Driven Deep Learning for Distributed Detection with Binary Quantization

TL;DR

The paper addresses robust distributed detection in wireless sensor networks under bandwidth and energy constraints by combining binary quantization with a model-driven deep learning pipeline. It derives MAP-based performance bounds, proves the global optimality of identical quantizers via Chernoff information, and formulates a MAP-dependent detection loss (MAPDEP) for quantizer design. It further shows that fusing all quantized data or their mean yields equivalent detection performance and introduces a KL-divergence-based loss to train a detector that approximates the true posterior. A two-stage training scheme learns a probability controller at sensors and a detector at the fusion center, achieving near-optimal performance with substantially reduced computational complexity in Gaussian-hypothesis testing scenarios.

Abstract

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.

Figures (5)

• Figure 1: System Model.
• Figure 2: Proposed Binary Quantizer.
• Figure 3: Proposed Detector.
• Figure 4: Training loss of probability controller and detector.
• Figure 5: Probability of detection error vs. the number of sensors under different SNRs.

Theorems & Definitions (6)

• Lemma 1
• Remark 1
• Lemma 2
• Proposition 1
• Theorem 1
• Proposition 2