One-bit digital cross-correlation in the PARIS-IOD

The use of opportunity signals to make altimetric measurements is known as the PARIS (PAssive Reflectometry and Interferometry System) concept. Signals transmitted by the GPS satellite constellation reach the PARIS receiver by the direct path and are collected by a zenith looking antenna. Signals reflected on the Earth's surface reach the PARIS receiver as well and are collected by a nadir looking antenna. The instrument measures the relative delay between the instants of arrival of the direct and reflected signals. By knowing the positions of transmitters and receivers the distance to the scattering surface can be retrieved. The presented work aims to clarify if one-bit correlation can be successfully used in the PARIS-IOD, and under what limitations. It can be concluded that an upper bound has been found for the SNR of the signals at the PARIS-IOD if one-bit quantization is used and a linear cross-correlation with the same shape as the analog correlation is desired. That is, it is not possible to increase the signal SNR at any desired level without distorting the cross-correlation waveform if one-bit digitalization is used. Simulation results have been presented confirming the upper bound for the SNR of the signals.