On the efficiency loss of the local polynomial method for single experiment MIMO frequency response matrix extraction

The estimation the Frequency Response Matrix (FRM) of multiple-input multiple-output (MIMO) Linear Time-Invariant (LTI) systems is often the first step in analyzing, modeling and controlling the system at hand. Recently, the so-called local-polynomial method (LPM), was developed to extract a nonparametric FRM at all frequency bins out of a single MIMO experiment. This LPM has an efficiency loss when it comes to the variability of the estimated FRM. This paper studies the sources of the efficiency losses in the LPM when using a single experiment to determine the FRM for MEMO systems. A theoretical study of the efficiency shows that a zippered multisine experiment has a low efficiency loss in the LPM when using only a single experiment This is confirmed using simulation results.