High resolution frequency-domain reflectometry by estimation of modulated superimposed complex sinusoids

A nonlinear least-squares-estimation method for time-domain analysis from frequency-domain measurements of a device under test (DUT) is presented. Estimation is based on a parsimonious model that requires a low reflectivity assumption. An extremization algorithm with good global convergence properties is presented for the case of imperfections of small reflectivity modeled as simple lumped frequency-dependent elements. The reflection coefficient at either port of the DUT is modeled as a superposition of modulated complex sinusoids. Through optimization of a sequence of cost functions, the algorithm produces a sequence of fits for models that incorporate an increasing number of imperfections. The method copes with frequency-dependent reflection, and it is shown how prior knowledge can be used to improve the performance of the algorithm. Analysis of experimental data illustrates the potential of the method