A Statistical Model and Simulator for Ocean-Reflected GNSS Signals

Global Navigation Satellite Systems Reflectometry (GNSS-R) methods sense ocean roughness by cross correlating scattered GNSS signals with a locally generated replica of the transmitted signal. The resulting delay-Doppler map (DDM) is related to surface slope statistics through established scattering models. DDM samples are correlated in time and between delay and Doppler coordinates, limiting the number of independent samples available to reduce measurement error. Performance predictions for future GNSS-R missions depend on a model with sufficient fidelity to represent these statistics. A previously developed model for the correlation in time and a new model for the correlation between delays are used to create a GNSS-R signal simulator. A change of variables reduces these models to the numerically efficient form of a single integral and a convolution. Independent normally distributed white noise is passed through a filter bank implementing these models to generate an ensemble of synthetic noisy measurements having realistic correlation in time and between delay bins. Correlation between Doppler bins, however, is not represented by this model. The output of this simulator is compared to 1-D (delay-only) DDMs collected during a 2009 airborne experiment in the North Atlantic, with winds from 5 to 25 m/s. Good agreement is found in the variance, time correlation, and covariance matrix. The probability density functions show reasonable agreement. A bias between the synthetic and observed data was found to result from a bias in the wind/roughness retrieval. Agreement was worse for the low-wind (5.8 m/s) example, perhaps due to a component of specular reflection. One application of this simulator is in generating synthetic DDMs, maintaining accurate representation of statistics following nonlinear processing (e.g., incoherent averaging). The simulator presents a numerically efficient method for generating large statistically significant ensembles of DDMs under identical conditions.