Modeling and Analysis of GNSS-R Waveforms Sample-to-Sample Correlation

The exploitation of global navigation satellite systems Earth-reflected signals to perform ocean mesoscale altimetry from space has been originally proposed at the beginning of the 1990s. This technique is generally defined as “GNSS-R.” Since then, the versatility and availability of the GNSS-R has been the subject of studies targeting many other earth remote sensing applications, for both ocean and land. GNSS-R observables (called GNSS-R “waveforms”) are typically obtained by performing a complex cross-correlation of the received GNSS reflected signals with a locally generated replica of one of the open access GNSS signals, evaluated over a pre-defined set of delays of the local replica. The knowledge of the statistical properties of GNSS-R waveforms is of fundamental importance in order to define the retrieval algorithms to estimate the geophysical parameters and in order to optimize the accuracy of these estimations. The statistical properties of interest are mainly: 1) the correlation between realizations of GNSS-R waveforms generated at different time instants (generally defined as slow-time correlation) and 2) the correlation between the different delay samples of a given GNSS-R waveform (generally defined as fast-time or sample-to-sample correlation). The modeling and analysis of the slow-time statistical properties has been the subject of previous works. On the other hand, this paper presents for the first time a detailed analytical model describing the sample-to-sample statistics of GNSS-R waveforms. The model has been validated with real measurements of global positioning systems (GPSs) reflected signals collected by UK-DMC receiver, showing excellent agreement with the observations from space. The model is generic and can be easily extended to GNSS-R waveforms from other systems. For altimetry applications, the knowledge of waveform statistics allows to assess the dependence of altimetry performance on critical system/instrument and retrieval parameters such as the sampling frequency, the receiver bandwidth or signal-to-noise-ratio (SNR). This paper also presents an analysis of the impact of these parameters on instrument performance, the conclusions of which are general and constitute an important basis for optimization of future GNSS-R instruments.