# Analysis of the correlation properties of digital satellite signals and their applicability in bistatic remote sensing

#### Abstract

Numerous studies have demonstrated that the shape of code-correlation waveform of forward-scattered Global Positioning System signals may be used to measure ocean surface roughness and related geophysical physical parameters such as wind speed. In those studies, the surface roughness was estimated by inverting a scattering model to fit measurements of the correlation waveform shape. The research done in this thesis applies the same concept to digital communication signals, which are available over a range of frequencies from S-band to Ku-band along with lower frequencies down in UHF/VHF bands. As an example, this thesis particularly presents a study of relevant correlation properties of signals transmitted from commercial digital XM satellite radio (XM) in order to evaluate their potential use as “Signals of Opportunity” for bistatic remote sensing. More specifically, the work described in this thesis is an attempt to obtain sea surface roughness (statistics) based on the waveform shape of the reflected XM signals. In order to do so, the model for the ambiguity function of the XM transmission (2332.5 to 2345.0 MHz) was computed analytically, using published information on the modulation schemes and bandwidth, under the assumption that the transmitted data was an infinitely long, random sequence. XM signals were recorded and used to experimentally verify this model. Realistic values for the signal strength on the surface of the Earth, and the receiver noise floor, were obtained from the published specification of currently operating digital satellite signals and used in a link budget analysis to predict the received signal to noise ratio (SNR). This model agreed with a measured SNR to within 0.1 dB. Next, the ambiguity function was integrated into a scattering model originally developed for reflected Global Navigation Satellite System (GNSS-R) signals. This model was used to compute the cross-correlation waveform of the XM signals reflected from a random rough surface. A recent experiment collected ocean-reflected XM signals from an aircraft, which were used to experimentally demonstrate the generation of a waveform through cross-correlating direct and reflected signals and the predicted widening of this waveform upon reflection from a rough surface. The waveform generated from airborne data was found to agree very well with a model waveform generated using a scattering model and ocean-roughness data from nearby buoys. A simulation, based upon this scattering model, was then used to generate synthetic waveforms with realistic SNR. A non-linear weighted least squares method was applied to invert the scattering model, estimating the slope variances of the probability density function (PDF) that best fits the synthetic waveforms, thus simulating the retrieval for ocean surface roughness from reflected XM signals. A Monte-Carlo approach was then used to generate a statistically significant set of simulated retrievals from an airborne receiver, to estimate their error. From these simulations, the standard deviation of the retrieved ocean mean square slope (MSS) was predicted to be 0.5%, or equivalent to an error of 0.07 m/s for a wind speed of 14 m/s. For comparison, the same simulation, using a typical GPS signal, predicted errors of 9% and 1.25 m/s.

#### Degree

M.S.E.

#### Advisors

Garrison, Purdue University.

#### Subject Area

Engineering|Aerospace engineering

Off-Campus Purdue Users:

To access this dissertation, please **log in to our
proxy server**.