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 device under test 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