How Far from Kronecker can a MIMO Channel be? Does it Matter?

A common assumption in the design and analysis of many MIMO transmission schemes is the so-called Kronecker model. This model is often a crucial step to obtain mathematically tractable solutions, but has also been criticized for being unrealistic. In this paper, we present a numerical approach to determine a channel whose statistics is as far from being Kronecker as possible, keeping only an assumption of spatial stationarity. As a case study for the relevance of the Kronecker assumption, a numerical analysis is included of the performance of optimal pilot design for Kronecker and non-Kronecker channels. The numerical results indicate that for this particular application, the Kronecker assumption may be used in the algorithm design and provide performance that is close to optimal also for non-Kronecker channels.