The on board steps are similar to the ones in Low Resolution Mode. Some parts of the hardware are commonly shared between both modes. However the pulses need to be transmitted with a PRF high enough so they remain coherent. The PRF value would depend on the satellite orbit and the transmission pattern.
After a burst of pulses is successfully transmitted and received, some corrections should be applied before packing the data and send it to the ground station for further processing.
The Block diagrams of the SIRAL altimeter is shown below.
In this case, both LRM, SAR and SARIn data is received and routed to the Processing Unit. There the LRM pulses are transformed into range domain and averaged. The SAR pulses would remain in time domain and the Fourier transformation will be performed by the ground processor.