Testing for Kronecker Separability in Measured Channels

Kronecker-separable MIMO channels, especially for larger MIMO configurations, are found more often in system simulations than in reality and some good physical explanations for the latter are available. This paper treats testing Kronecker-separability from a statistical perspective. The point raised is that for larger configurations the dimensions of the full correlation matrix become too large (equal to [NMtimesNM], with N number of receivers and M number of transmitters) for reliable estimation with the limited number of realisations normally available. Some examples are given, based on synthetic and measured data.