Tests for assessing multivariate normality and the covariance structure of MIMO data

Measurements taken at the campus of Brigham Young University (BYU) are used to investigate the statistical properties of the indoor MIMO channel. Two statistical tests, Royston´s and Henze-Zirkler´s, are applied to the MIMO data to assess whether the data belongs to a multivariate normal distribution or not. The possibility of modeling the covariance matrix as a Kronecker product of the correlations at the transmitter and receiver are also investigated by deriving a likelihood ratio test. It is found that small MIMO systems such as 2 × 2 can be considered normally distributed and can also be approximated with a Kronecker structure. Larger systems, on the other hand, show evidence of strong non-normality and are not well modeled using a Kronecker product. However, for short measurement segments, these distributions can be used for approximate channel capacity calculations.