  When the users in a MIMO broadcast channel experience different spatial
transmit correlation matrices, a class of gains is produced that is denoted
transmit correlation diversity. This idea was conceived for channels in which
transmit correlation matrices have mutually exclusive eigenspaces, allowing
non-interfering training and transmission. This paper broadens the scope of
transmit correlation diversity to the case of partially and fully overlapping
eigenspaces and introduces techniques to harvest these generalized gains. For
the two-user MIMO broadcast channel, we derive achievable degrees of freedom
(DoF) and achievable rate regions with/without channel state information at the
receiver (CSIR). When CSIR is available, the proposed achievable DoF region is
tight in some configurations of the number of receive antennas and the channel
correlation ranks. We then extend the DoF results to the $K$-user case by
analyzing the interference graph that characterizes the overlapping structure
of the eigenspaces. Our achievability results employ a combination of product
superposition in the common part of the eigenspaces, and pre-beamforming (rate
splitting) to create multiple data streams in non-overlapping parts of the
eigenspaces. Massive MIMO is a natural example in which spatially correlated
link gains are likely to occur. We study the achievable downlink sum rate for a
frequency-division duplex massive MIMO system under transmit correlation
diversity.
