Multivariate statistics applied to assess measurement uncertainty of complex reflection coefficient

In this paper we show an alternative mathematical interpretation of the error propagation law for complex quantities established in supplement 2 of the GUM [1]. We use this interpretation to study VNA's one port reflection measurement which includes several terms that represent complex quantities. We show two different approaches to solve the problem that arises when trying to establish the variance matrix of the sum of two complex quantities. We also give explicit formulae to estimate uncertainty with both approaches.