Linear Precoding in Parallel MIMO Broadcast Channels: Separable and Inseparable Scenarios

Parallel multiple-input multiple-output (MIMO) broadcast channels are separable from an information theoretic point of view, i.e., the whole capacity region can be achieved with strategies that perform independent encoding and decoding on each carrier subject to a power allocation across carriers. However, recent research has revealed that such a separate transmission can become suboptimal if the transmit strategy is restricted to linear transceivers. The answer to the question whether parallel broadcast channels with linear transceivers are separable or not is a property of the system parameters and the particular channel realization, and judging whether a certain scenario is separable or inseparable is still an open problem for most scenarios. In this paper, we consider some special cases of parallel MIMO broadcast channels and classify them as separable or inseparable, respectively. The insights and the applied proof techniques might be helpful to derive more general classification methods in future research.