On the Worst-Case Noise in Gaussian MIMO Systems with Proper and with Improper Signaling

From an intuitive point of view, it is to be expected that proper Gaussian noise is the worst-case noise among all possible Gaussian noise signals because a disturbing signal does more harm the higher its differential entropy is. However, formal proofs of such a worst-case noise property can be found in the existing literature only for special cases. In this paper, we provide such proofs for Gaussian MIMO point-to-point channels, for Gaussian MIMO multiple access channels, and for Gaussian MIMO broadcast channels. In each system model, we consider the case of arbitrarily chosen proper complex signaling as well as the case of optimized general complex (proper or improper) signaling. In addition, we comment on the case of Gaussian MIMO interference channels.