Spatially Correlated MIMO Broadcast Channel: Analysis of Overlapping Correlation Eigenspaces

Antenna correlation is prevalent in higher frequencies as well as in massive MIMO, thus the study of correlated MIMO broadcast channels is becoming a subject of increasing interest. This paper explores the fundamental limits of such systems, focusing on cases where correlation eigenspaces are neither independent nor identical, so that known beam-space division techniques do not directly apply. We begin by introducing a simple but novel tight outer bound on the degrees of freedom of noncoherent point-to-point MIMO channels under transmit antenna correlation. We then analyze the performance of a two user MEMO broadcast channel when one correlation eigenspace is a subspace of the other. We extend the result to K-user MIMO broadcast channel. Our results show that it is possible to exploit the differences between the correlation structure of transmit antennas towards different receivers to extract degrees of freedom gains out of the system. The extent of these gains are highlighted via several examples.