The Order-and-Type Prediction Problem Arising from Passive Intermodulation Interference in Communications Satellites

Intermodulation (IM) effects were recently observed in communications satellites where the source of nonlinearity was traced back to passive and normally linear components. This phenomenon is sometimes called passive intermodulation (PIM) and can cause serious interference to the ultrasensitive receiver on board the spacecraft. One interesting and important aspect of the PIM study is to find the order and type of IM products causing interference in an arbitrary satellite receive band. It is shown that the problem can be reduced by the use of number theory to a Diophantine optimization problem. Two types of tree searches are formulated and proposed as viable approaches. Some additional bounds for the equal-spacing case and an iterative technique for the unequal-spacing case are described. Finally, we show, by means of an example, that the proposed techniques offer a practical method of solving the order and type prediction problem.