# Achieve better noise reduction at frequency response function estimation

I have the following problem. I have $$M$$ synchronized, noisy measurements of a MIMO system (2 inputs, 2 outputs) of all inputs and outputs. The inputs are synchronized (no phase shift, coherent measurements) and linear independent, the noise is not synchronized, normally distributed and zero mean. My goal is to estimate the FRF (frequency response function) with phase from my measurements. There are several estimators (H1, H2, Hiv, Hev) suitable for the task. Using the coherency of my measurements, I would expect that simple time averaging (Hev) would give the best result. So:

$$Y(jw) = H(jw) U(jw)$$

$$H(jw) = Y(jw)U(jw)^{-1}$$
where $$Y$$,$$U$$ $$\in$$ $$\mathbb{C^{2x2}}$$, representing one measurement(or the average of all measurements) of both linear independent input signals and corresponding output signals.