  This paper considers a iterative Linear Minimum Mean Square Error (LMMSE)
detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO)
systems with Non-Orthogonal Multiple Access (NOMA). The iterative LMMSE
detection greatly reduces the system computational complexity by departing the
overall processing into many low-complexity distributed calculations. However,
it is generally considered to be sub-optimal and achieves relatively poor
performance. In this paper, we firstly present the matching conditions and area
theorems for the iterative detection of the MIMO-NOMA systems. Based on the
proposed matching conditions and area theorems, the achievable rate region of
the iterative LMMSE detection is analysed. We prove that by properly design the
iterative LMMSE detection, it can achieve (i) the optimal sum capacity of
MU-MIMO systems, (ii) all the maximal extreme points in the capacity region of
MU-MIMO system, and (iii) the whole capacity region of two-user MIMO systems.
