Coherence time and statistical properties of the GPS signal scattered off the ocean surface and their impact on the accuracy of remote sensing of sea surface topography and winds

A GPS transmitter-receiver pair forms a bistatic radar for ocean remote sensing when the receiving platform carries a down-looking antenna capable of collecting the GPS signal scattered off the ocean surface. The average received power versus time is derived as a function of viewing geometry, system parameters and ocean state. This waveform is crucial for the derivation of the sea surface topography (from its leading edge) or wind speed and direction (from its trailing edge). In predicting the accuracy of either measurement it is important to understand how accurately the average power can be determined in practical situations. This starts with the determination of the coherence time of the scattering, over which the received signal can be integrated for optimal signal to noise ratio. Additionally, the real signal is affected by self-noise which introduces variability from one sample to another. This work examines the coherence properties of the modeled received power as a function of sea state and scattering geometry. In particular the coherence time variability between leading and trailing edges is addressed, and its impact on the accuracy of either sea surface topography or wind speed and direction measurements is addressed. In particular, having determined the integration time necessary to produce independent samples, the incoherent summation time required for a given measurement accuracy is derived. Furthermore, the lag-to-lag correlation is addressed, leading to a covariance analysis formulation for the formal error in height retrieval