Drive the dish in a small circle around the predicted location, while measuring the signal amplitude as a function of time and position, to keep the orbital parameters up to date.

If the reason that you can't predict the orbital track is due to atmospheric drag, then just let the project slide for a week or two and the requirement will probably go away (due to reentry).

By the way, why are you using a "large" reflector for a LEO satellite. If it's LEO, then a smaller dish (with a wider beam width, making tracking easier) should suffice. Are you trying to detect an on-board LO?

 

Monopulse tracking consist of a lot more than the coupler (hybrid coupler) used. The coupler is just one small part of the complete antenna and receiver system which generates as outputs both the received data and the position-error feedback signals for the antenna servos.

What kind of system are you considering? simpler single channel, dual channel, or a full-blown three-channel with dual polarization, receivers, and combiners?

Note, I assumed that you are tracking for data or telemetry downlink/uplink, and not monopulse radar tracking.

Ohhh, that sustained atmospheric drag gets me all hot and bothered!  

John D