Enhancing 1-Bit Compressive Sensing With Support Estimation 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. Here, neither the signal support nor its cardinality is assumed to be known. The proposed signal processing protocol for distributed sparse signal recovery consists of the following three steps: (i) each local sensor employs a sparse sensing vector to efficiently compress its observation into a scalar, (ii) to conserve energy and bandwidth, only sensors with informative scalar measurements will quantize their real-valued compressed measurements into one bit, and (iii) these sensors then forward their quantized data to the FC for global signal recovery. In contrast to most existing 1-bit CS methods, which rely fully on the sign message of measurements, we propose a new amplitude-assisted signal retrieval scheme to enhance robustness against bit-flipping errors. In our algorithm, we first identify the signal support using a simple energy detector and derive an analytical performance guarantee for perfect support recovery. After obtaining the support knowledge, we then analytically 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. With the aid of the optimal representation level and the support estimate, we develop a modified single-sided <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell_{1}$</tex-math></inline-formula>-minimization based algorithm to enhance signal reconstruction performance. A theoretical analysis of the convergence of the proposed algorithm is also provided. Computer simulations are used to illustrate the effectiveness of the proposed scheme.