A theoretical model that describes the power of a scattered Global Positioning System (GPS) signal as a function of geometrical and environmental parameters has been developed. This model is based on a bistatic radar equation derived using the geometric optics limit of the Kirchhoff approximation. The waveform (i.e., the time-delayed power obtained in the delay-mapping technique) depends on a wave-slope probability density function, which in turn depends on wind. Waveforms obtained for aircraft altitudes and velocities indicate that altitudes within the interval 5-15 km are the best for inferring wind speed. In some regimes, an analytical solution for the bistatic radar equation is possible. This solution allows converting trailing edges of waveforms into a set of straight lines, which could be convenient for wind retrieval. A transition to satellite altitudes, together with satellite velocities, makes the peak power reduction and the Doppler spreading effect a significant problem for wind retrieval based on the delay-mapping technique. At the same time, different time delays and different Doppler shifts of the scattered GPS signal could form relatively small spatial cells on sea surface, suggesting mapping of the wave-slope probability distribution in a synthetic-aperture-radar (SAR) fashion. This may allow more accurate measurements of wind velocity and wind direction.

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