A Fast Algorithm for Sorting and Counting Third-Order Intermodulation Products

This paper presents a fast algorithm that performs a selective counting of the third-order intermodulation products generated when several carriers of various types are transmitted through a common nonlinear device. In deriving the algorithm, the carrier configuration and the frequency distribution of intermodulation products are both described by polynomials which are related to each other. The frequency distributions of third-order intermodulation products of the various kinds are then obtained with the aid of an FFT algorithm and a numerical method for solving a set of linear equations. When compared to a direct counting procedure, the proposed algorithm has presented a drastic reduction on the required Computational effort. This advantage is particularly important when the number of carriers sharing the nonlinearity is large. In an example with 1366 carriers of three different types sharing the nonlinearity, the CPU time was reduced from 7 h 46 min. down to 52 s.