Carrier Frequency Offset Estimation in Ambient Internet of Things

Ambient Internet of Things (IoT), with its low-cost and battery-free characteristics, holds substantial promise for future green IoT. However, such characteristics usually impose a strict constraint on the adopted radio frequency (RF) devices, resulting in undesirable RF link. One of the most important issues is carrier frequency offset (CFO), which adversely affects communication reliability. Noticing the signal sparsity in frequency domain, compressed sensing (CS) provides potential solutions to CFO estimation. In this paper, we decompose CFO into on-grid frequency and off-grid deviation, based on which two estimation algorithms are derived. In particular, the fast maximum likelihood-approximate message passing (FML-AMP) algorithm estimates the off-grid deviation with maximum likelihood estimator (MLE) and the on-grid frequency with AMP algorithm. The key is the derivation of the closed-form marginal distribution of the off-grid deviation, which enables the fast implementation of MLE and so facilitates the design of FML-AMP. To reduce complexity, a Newtonized orthogonal matching pursuit (NOMP) algorithm is further designed, which alternately applies Newton's method to estimate the off-grid deviation and orthogonal matching pursuit (OMP) to estimate the on-grid frequency. Numerical results demonstrate that both algorithms outperform existing methods and approach the Cramér-Rao bound at medium to high signal-to-noise ratio (SNR) regime.