Knowledge-Enhanced 1-Bit Compressive Sensing in Noisy Wireless Sensor Networks

One-bit compressive sensing (1-bit CS) is an attractive low-bit-resolution signal processing technique that has been successfully applied to the design of large-scale wireless networks. In this work, we consider the problem of 1-bit CS in wireless sensor networks (WSNs), where the fusion center (FC) aims to recover a sparse signal based on a few binary measurements received from local sensor nodes and corrupted by channel-induced bit-flipping errors. In contrast to most existing 1-bit CS approaches that rely solely on the sign information of measurements, we propose a knowledge-enhanced signal recovery framework to improve robustness against bit-flipping errors without requiring prior knowledge of the signal support or sparsity level. In our algorithm, we first identify the signal support using a simple energy detector. Based on the estimated support, we then derive the optimal representation level of local 1-bit quantizers in closed form by minimizing the mean square error resulting from quantization error, local sensing noise, and bit-flipping errors at the FC. Leveraging the optimal representation level and the support estimate, we develop a weighted single-sided ℓ₁-minimization-based algorithm for signal reconstruction. Computer simulations are used to illustrate the effectiveness of the proposed scheme.