Distributed Detection of Sparse Stochastic Signals via Fusion of 1-bit Local Likelihood Ratios

TL;DR

This paper introduces an improved 1-bit local likelihood ratio detector for sensor networks that enhances detection of sparse signals by optimizing quantization thresholds, reducing the number of sensors needed compared to existing methods.

Contribution

The paper proposes an improved 1-bit LMPT detector that fuses local likelihood ratios and optimizes quantization thresholds for better detection performance in sensor networks.

Findings

Requires fewer sensors for the same detection performance.

Theoretical and numerical validation of the proposed method.

Achieves asymptotic optimality with designed thresholds.

Abstract

In this letter, we consider the detection of sparse stochastic signals with sensor networks (SNs), where the fusion center (FC) collects 1-bit data from the local sensors and then performs global detection. For this problem, a newly developed 1-bit locally most powerful test (LMPT) detector requires 3.3Q sensors to asymptotically achieve the same detection performance as the centralized LMPT (cLMPT) detector with Q sensors. This 1-bit LMPT detector is based on 1-bit quantized observations without any additional processing at the local sensors. However, direct quantization of observations is not the most efficient processing strategy at the sensors since it incurs unnecessary information loss. In this letter, we propose an improved-1-bit LMPT (Im-1-bit LMPT) detector that fuses local 1-bit quantized likelihood ratios (LRs) instead of directly quantized local observations. In addition, we design the quantization thresholds at the local sensors to ensure asymptotically optimal detection performance of the proposed detector. It is shown theoretically and numerically that, with the designed quantization thresholds, the proposed Im-1-bit LMPT detector for the detection of sparse signals requires less number of sensor nodes to compensate for the performance loss caused by 1-bit quantization.