A Composite Doppler Spectrum of Forward Scattered GNSS Signal From Sea Surface and Its Application in Retrieving Coastal Wind Vector

Conventional methodologies for coastal Global Navigation Satellite System-Reflectometry (GNSS-R) are derived from the assumption of pure specular reflection, which is typically modeled using the Kirchhoff Approximation (KA). Such methods are generally considered insensitive to wind direction, thereby posing a challenge for wind direction retrieval in coastal GNSS-R. This article introduces a new theoretical assumption, wherein the signal received by a sea-looking antenna is regarded as a synthesis of specular reflection and off-specular scattering. The off-specular component follows the Bragg scattering mechanism and is modeled using the small slope approximation (SSA). Based on this assumption, a composite spectrum is theoretically derived, which effectively captures the multimodal characteristics observed in actual measured spectra. Within this composite spectrum, three key spectral characteristics, namely, the spectral width of specular reflection, the peak ratio of the positive and negative Bragg spectral components, and wave-motion-induced Doppler shift, are uniquely dependent on both wind speed and wind direction. An iterative Gaussian fitting method is proposed to separate the spectra corresponding to specular reflection and Bragg scattering, from which these three spectral characteristics are subsequently estimated. Experimental validation supports the theoretical assumption and derivation. Two Bragg scattering components, corresponding to diffraction orders 1 and 2, are successfully extracted. The estimated spectral characteristics exhibit consistent dependencies on wind speed and direction with the theoretical predictions, confirming the coexistence of specular reflection and Bragg scattering in forward GNSS-R observations. A least-square optimization approach is employed to simultaneously retrieve wind speed and direction. Comparisons between the retrieved and in situ wind vectors demonstrate good agreement. In summary, this article proposes a promising forward-scattered signal spectrum model that effectively addresses the challenge in simultaneously retrieving wind speed and direction in coastal GNSS-R.