We now come to what lies at the heart of the theoretical foundation of the HFR, namely the analytical derivation of the second-order ocean Doppler spectrum. For this we use the general description of the Doppler spectrum derived in the last chapter using the small perturbation approach and make it explicit in the case of HFR remote sensing. We recover the classical monostatic results known as Barrick’s theory and also give, in a common framework, the much less classical bistatic results. We end up with Walsh and Gill theory, which is an alternative mathematical theory to describe the bistatic second-order Doppler spectra and is not fully equivalent to Barrick’s theory.