HIGH-RESOLUTION FREQUENCY-DOMAIN REFLECTOMETRY BY ESTIMATION OF MODULATED SUPERIMPOSED COMPLEX SINUSOIDS

By assuming a parametric model for a linear one-port or two-port, the time-domain resolution of a vector network analyzer can be significantly improved with respect to the Rayleigh limit. The measurement problem is formulated as a nonlinear least squares parameter estimation problem involving the extremization of a cost function. An extremization algorithm with good global convergence properties is presented for the case of discontinuities 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 discontinuities.