Further analysis of the second-order high frequency radar ocean surface cross section for an antenna on a floating platform

When the transmitting and/or receiving antennas of a high high-frequency (HF) radar are mounted on a floating platform, which is subject to sway, it is known that motion introduces additional features in the Doppler spectra of the signal scattered from the ocean surface. Following techniques in earlier work which examined these features up to second order for scatter from a patch of ocean remote from the antennas, we consider second-order effects arising from a single scatter near the antennas followed or preceded by a scatter on the remote patch. The derivation begins with a general expression for the bistatically received second-order electric field in which platform sway is introduced. This is then reduced to the monostatic case. Having developed the monostatic equations, and assuming the ocean surface to be representable as zero-mean Gaussian process, the corresponding second-order monostatic radar cross section (RCS) is developed. As in the earlier analyses for patch scatter, the new contributions to the RCS appear as Bessel functions, which give rise to extra spectral content not appearing in the fixed-antenna results. However, simulations of the new RCS, including antenna sway under a variety of sea states, suggest that while the new second-order effects are visible in the spectrum, they are generally smaller than first-order effects, except at specific Doppler frequencies.