  This paper considers a low-complexity iterative Linear Minimum Mean Square
Error (LMMSE) multi-user detector for the Multiple-Input and Multiple-Output
system with Non-Orthogonal Multiple Access (MIMO-NOMA), where multiple
single-antenna users simultaneously communicate with a multiple-antenna base
station (BS). While LMMSE being a linear detector has a low complexity, it has
suboptimal performance in multi-user detection scenario due to the mismatch
between LMMSE detection and multi-user decoding. Therefore, in this paper, we
provide the matching conditions between the detector and decoders for
MIMO-NOMA, which are then used to derive the achievable rate of the iterative
detection. We prove that a matched iterative LMMSE detector can achieve (i) the
optimal capacity of symmetric MIMO-NOMA with any number of users, (ii) the
optimal sum capacity of asymmetric MIMO-NOMA with any number of users, (iii)
all the maximal extreme points in the capacity region of asymmetric MIMO-NOMA
with any number of users, (iv) all points in the capacity region of two-user
and three-user asymmetric MIMO-NOMA systems. In addition, a kind of practical
low-complexity error-correcting multiuser code, called irregular
repeat-accumulate code, is designed to match the LMMSE detector. Numerical
results shows that the bit error rate performance of the proposed iterative
LMMSE detection outperforms the state-of-art methods and is within 0.8dB from
the associated capacity limit.
