Discretization Bias in GNSS-R Terrestrial Reflectivity: Characterization and Correction for Tianmu-1

DDM is the primary Level-1 observable of spaceborne Global Navigation Satellite System Reflectometry (GNSS-R). Over the past decade, the discretization strategy of Delay-Doppler Map (DDM) systems has been primarily optimized for ocean remote sensing. This study highlights the impact of discretization effects in DDM sampling on land applications. The discretization effect in the Doppler dimension is first evaluated by comparing simulated and observed DDM slices at the Doppler bin corresponding to the DDM peak. The results indicate that the noise in DDM observations can be approximated as additive thermal noise. Based on an ideal autocorrelation function template, a matched filtering analysis is then applied to estimate the optimized specular point delay and reconstruct the peak power. Using multi-constellation observations from Tianmu-1, the results show that the original DDM peak delay exhibits a systematic delay relative to the optimized specular point delay, with biases of approximately 0.02 chips for GPS and GLONASS, and 0.17 chips for BDS (BeiDou) and Galileo. For BOC(1,1) signals in BDS and Galileo, the reflectivity remains underestimated by ~1.4 dB even at a delay sampling interval of 1/8 chip. The results indicate that under coherent scattering conditions over land, direct use of the DDM peak leads to underestimation of reflectivity due to discretization. The correction proposed in this study reduces the relative differences in reflectivity observations among the four GNSS systems. This study suggests that peak under-sampling should be considered in GNSS-R applications, and higher delay sampling resolution is required for land observations.