Three Kinds of Inseparability in Parallel MIMO Broadcast Channels with Linear Transceivers

From an information theoretic point of view, multiple-input multiple-output (MIMO) broadcast channels are separable, i.e., the optimal (capacity achieving) strategy performs encoding and decoding separately on each of the parallel channels (e.g., carriers in multicarrier system). In recent publications, it was shown that this separability can be lost if a restriction to a certain class of transmit strategies (such as linear strategies or zero-forcing strategies) is imposed. In this paper, we categorize the recent results into three different kinds of inseparability, and we discuss the characteristic properties of each kind. Moreover, two new inseparability results that fit into these categories are presented: for the case of linear zero-forcing with time-sharing and for linear transceivers in systems with two users.