The Study of the Bistatic Cross-Correlation Function of Two Signals Separated in Frequency Reflected by the Water Surface

Abstract

The purpose of this study is to analyze the applicability conditions for the significant wave height (SWH) measurement approach based on measuring the cross-correlation function of two signals with similar frequencies reflected by the sea surface in the bistatic problem statement (the transmitting antenna and the receiving antenna are separated in space). When implementing this approach, the modulus of the normalized cross-correlation function for several pairs of signals with different frequency bases will be measured in the experiment. The advantage of this approach over the traditional method for radar altimetry, based on the analysis of the shape of the reflected pulse, is the high accuracy in measuring the SWH for weak waves. In the bistatic formulation of the problem, an important advantage of the approach under study is the possibility of obtaining analytical formulas for solving the direct problem. This paper presents the derivation of a formula for the modulus of the normalized cross-correlation function of reflected signals, which expresses an explicit relationship with the parameters of sea waves and the measurement geometry in the bistatic formulation of the problem. This paper considers the influence on the modulus of the normalized cross-correlation function of the antenna patterns of the transmitting and receiving antennas, the distances to the sea surface, the wave slope variances, the SWH and the frequency base of the transmitted signals. The optimal variants of the measurement scheme are discussed. The results and conclusions obtained can be easily expanded to underwater acoustic sounding.