From the radar equation to the model

The radar equation, that is the signal immediately after the pulse compression in the digital part of the onboard processing, is given by:

The first term in this expression is a descriptive equation describing the outgoing pulse and its phase shifts due to onboard changes, the doppler effect, temperature changes and ageing. This quantity is convolved with the replica chirp in the onboard processing. A full description of this is provided in the project TN-02 document (see documents).

This equation is squared in the signal processing onboard the satellite, to provide the LRM mode power detection. It is a descriptive equation. In order to convert it into a form that can be used in waveform retracking, a set of assumptions are made. To highlight this, we created the Derivation Diagram, which shows the different assumptions and approximations involved in deriving a model for the waveform.