Signal to Noise Ratio Estimation for a Space-borne Swept-Frequency Intensity-Modulated CO2 Laser Absorption Spectrometer

Abstract:

The Signal to Noise Ratio (SNR) in the digital lock-in detection for a space-borne swept-frequency Intensity-Modulated Continuous-Wave (IM-CW) CO₂ Laser Absorption Spectrometer (LAS) has a direct influence on the accuracy of the CO₂ measurement. According to the Maximum Likelihood Estimation (MLE) method, we have theoretically analyzed a linear swept-frequency sine wave signal in an additive high Gaussian-distributed noise with a constant variance, which is a good approximation for the detector-noise-limited system or the solar background noise dominated space-borne IM-CW CO₂ LAS. The general MLE equations for the amplitude and the phase of the swept-frequency IM_CW signal have been generated and solved by a nonlinear optimization procedure. The variances of the amplitude and the phase have been obtained by using the Cramer-Rao lower bound, a lower bound on the variance of the estimated parameters. Under the large sampling numbers, the SNR, signal amplitude divided by the square-root of the amplitude variance, increases as the square-root of the total sampling numbers. Thousands of numerical simulations with randomly generated uniform distributed Gaussian noise were completed for the statistical verification of the estimation. The estimation has also been applied to a space-borne IM-CW CO₂ LAS with typical parameters under averaged daytime solar background to confirm the feasibilities of the instrument design of the space-borne IM-CW CO₂ LAS.