A complex optimal signal-processing algorithm for frequency-stepped CW data

We derive a complex nonlinear optimal signal-processing algorithm for estimating target ranges from a set of frequency-stepped continuous wave (FSCW) measurements. It is a generalization of a prior optimization algorithm in that the reflection amplitudes are modeled as phasors rather than real-valued scalars. The algorithm solves this nonlinear problem by separating it into its linear and nonlinear parts. The amplitudes of the reflections are first optimized by solving a set of linear equations in the least-squares sense. A performance measure is then calculated and scanned to find its global minimum to yield a set of reflection amplitudes and time-delay estimates. We derive analytical expressions for the performance measure and for the effects of noise in the measurement data. Finally, we present experimental results to demonstrate the performance of our algorithm.