  Many recent works that study the performance of multi-input multi-output
(MIMO) systems in practice assume a Kronecker model where the variances of the
channel entries, upon decomposition on to the transmit and the receive
eigen-bases, admit a separable form. Measurement campaigns, however, show that
the Kronecker model results in poor estimates for capacity. Motivated by these
observations, a channel model that does not impose a separable structure has
been recently proposed and shown to fit the capacity of measured channels
better. In this work, we show that this recently proposed modeling framework
can be viewed as a natural consequence of channel decomposition on to its
canonical coordinates, the transmit and/or the receive eigen-bases. Using tools
from random matrix theory, we then establish the theoretical basis behind the
Kronecker mismatch at the low- and the high-SNR extremes: 1) Sparsity of the
dominant statistical degrees of freedom (DoF) in the true channel at the
low-SNR extreme, and 2) Non-regularity of the sparsity structure (disparities
in the distribution of the DoF across the rows and the columns) at the high-SNR
extreme.
