Amplitude-aided 1-Bit compressive sensing over noisy wireless sensor networks

One-bit compressive sensing (CS) is known to be particularly suited for resource-constrained wireless sensor networks (WSNs). In this letter, we consider 1-bit CS over noisy WSNs subject to channel-induced bit flipping errors, and propose an amplitude-aided signal reconstruction scheme, by which 1) the representation points of local binary quantizers are designed to minimize the loss of data fidelity caused by local sensing noise, quantization, and bit sign flipping, and 2) the fusion center adopts the conventional ${\ell-1}$-minimization method for sparse signal recovery using the decoded and de-mapped binary data. The representation points of binary quantizers are designed by minimizing the mean square error (MSE) of the net data mismatch, taking into account the distributions of the nonzero signal entries, local sensing noise, quantization error, and bit flipping; a simple closed-form solution is then obtained. Numerical simulations show that our method improves the estimation accuracy when SNR is low or the number of sensors is small, as compared to state-of-the-art 1-bit CS algorithms relying solely on the sign message for signal recovery.