Stochastic voltage model and experimental measurement of ocean-scattered GPS signal statistics

Information about the roughness of the ocean surface and related geophysical parameters, such as wind speed, is present in the shape of the code-correlation waveform of forward-scattered Global Positioning System (GPS) signals. A model is developed for the statistics of this waveform to be used in designing retrieval algorithms and predicting their accuracy in the estimation of geophysical parameters. One potential application of this model is to assess the feasibility of bistatic GPS measurements from satellite orbits. Time and frequency domain models for the complex "voltage" correlation waveform are developed and compared against experimental results. The voltage model can be applied to determine the upper limit for predetection integration time. The resulting temporal and spatial correlation function has a form similar to the van Cittert-Zernike theorem in that it can be expressed in terms of two-dimensional Fourier transform. The fast Fourier transform is, thus, used for efficient computation. Waveforms were generated from measurements of reflected GPS signals recorded in 1999 from an airborne receiver at an altitude of 3200 m during a flight near Puerto Rico. Complex voltage correlations were produced using the coarse-acquisition code with a 1-ms integration time over a range of code delay "bins". The Doppler compensation frequency was set equal to the Doppler frequency obtained by tracking the direct line-of-sight GPS signal. The resulting spectra and derived correlation times of the voltage signal time series in each delay bin were compared with the predictions of the model. The model agreed well with the experimental data, near the specular point, showing correlation times between 4-6 ms.