Spatially Correlated MIMO Broadcast Channel with Partially Overlapping Correlation Eigenspaces

The spatially correlated MIMO broadcast channel has grown in importance due to emerging interest in massive MIMO and mm-wave communication, but much about this channel remains unknown. In this paper, we study a two-user MIMO broadcast channel where the spatial correlation matrices corresponding to the two receivers have eigenspaces that are neither identical nor disjoint, but are partially overlapped. Spatially correlated channels occur in e.g. massive MIMO and furthermore different links may credibly have correlation eigenspaces that are neither disjoint nor equal, therefore this problem is practically motivated. This paper develops a new approach for this scenario and calculates the corresponding degrees of freedom. Our technique involves a careful decomposition of the signaling space to allow a combination of pre-beamforming along directions that depend on the relative positioning of the non-overlapping and overlapping components of the eigenspaces, along with the product superposition technique. The ideas are demonstrated with a toy example, are developed in two conditions of varying complexity, and are illuminated by numerical results.