On Stationarity in the Context of MIMO Fading Channels

Stationarity is investigated in the context of a general multiple-input–multipleoutput (MIMO) fading channel with memory. It is shown that stationary processes behave nicely as one does expect. Concretely, this reports concentrates on three topics with regard to stationarity: firstly it is proven that—under weak conditions on the channel—any stationary channel model will have a capacity-achieving input distribution that is stationary. This statement holds in general and is not restricted to MIMO fading channels. Secondly, it is shown that entropy rate is well-defined also in the context of differential entropy and stationary processes. Moreover, it can be generalized to more complex forms of conditional entropy rates without problems as long as all involved processes are stationary. Again, this are general statements not specific to MIMO fading. Thirdly, in the context of MIMO fading it is shown that the memory of a stationary process fades in a way that one expects.