Identification of Generalized Memory Polynomials Using Two-Tone Signals

Abstract

This paper shows that the coefficients of a generalized memory polynomial model of a nonlinear device can be estimated by examining the output when the input is a series of two-tone signals. There are several benefits to using two-tone signals rather than noise-like waveforms for system identification, including the relative ease of generating two-tone signals with a high signal-to-noise ratio and high dynamic range. The two-tone approach described here results in a block upper triangular linear system of equations that can be solved for the unknown coefficients. The block upper triangular structure provides a sufficient condition for the matrix to be nonsingular: if each diagonal submatrix has full column rank, so does the matrix. In addition to showing that certain sets of two-tone signals satisfy this sufficient condition, methods for controlling the condition number are also given. Simulations verify the two-tone estimation method and illustrate the effects of noise and matrix conditioning. Some useful results regarding certain Khatri–Rao products can be found in the proofs.