LAUSR

Signal-to-noise ratio (SNR) estimation for the one-bit analog-to-digital converter (ADC) is a challenging task due to the nonlinearity, lots of information loss, and complex probability distribution. And classical SNR estimators are unavailable in 1-bit sampling. Given this issue, we propose novel one-bit SNR estimators with the closed-form solution based on harmonic analysis to estimate the SNR from 1-bit measurements. We first derive the statistical characteristic of each-order harmonic caused by 1-bit sampling and then give the mathematical relationship between the expectation of harmonic amplitude (EoHA) and the SNR. The ${m}$ th-order harmonic-based estimator (mHE) with high precision is devised by this relationship. Further, an approximate alternative, the ${m}$ th- and ${n}$ th-order harmonics-based ratio estimator (mnHRE), is presented to reduce the computational complexity. Moreover, two schemes for calculating the EoHA are provided to assist the proposed one-bit SNR estimators. Simulation results verify the effectiveness and superiority of our proposed estimators.