Characterizing the Coherent Reflected Power Dependence on Rough Surface Height at Low Signal Levels

Abstract

The Global Navigation Satellite System reflectometry (GNSS-R) community has traditionally used the Kirchhoff approximation to model how the coherent reflected power reduces as a function of the RMS height of the rough surface observed. While this approximation has been valid for most GNSS-R applications to date, the community has recently raised the question of the model's validity when the normalized coherent reflected power is very low $(\leq-20\mathrm{dB})$ due to increased interest in measuring the coherent reflected power in situations where the incoherent reflected power is dominant. To investigate the trend of the normalized coherent reflected power below −20dB, Monte Carlo simulations were performed by randomly generating Gaussian rough PEC surfaces with various RMS heights and averaging over multiple realizations at each RMS height to obtain a reflected power whose incoherent component has been averaged out, leaving only the coherent reflected power behind. In this process, the statistics of the Rician random variable obtained when coherent specular scattering from a rough surface is measured must also be considered, and it can be shown that the accuracy of the coherent power estimate is dependent on the number of realizations used and the ratio of the coherent and incoherent powers. This analysis also shows that a large number of averages can be required to obtain reasonable accuracy in estimating the coherent power in the limit of low coherent to incoherent power ratio.