  In this paper, we investigate the downlink precoder design for two-user
power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple
access (NOMA). We propose a novel user-assisted (UA) simultaneous
diagonalization (SD) based MIMO-NOMA scheme that achieves SD of the MIMO
channels of both users through a combination of precoder design and
low-complexity self-interference cancellation at the users, thereby
considerably lowering the overall decoding complexity compared to joint
decoding. The achievable ergodic user rates of the proposed scheme are analyzed
for Rayleigh fading channels based on a finite-size random matrix theory
framework, which is further exploited to develop a statistical power allocation
algorithm. Simulation and numerical results show that the proposed UA-SD
MIMO-NOMA scheme significantly outperforms orthogonal multiple access and a
benchmark precoder design performing SD via generalized singular value
decomposition in terms of the achievable ergodic rate region for most user
rates. The ergodic rate region is further enhanced by a hybrid scheme which
performs time sharing between the proposed UA-SD MIMO-NOMA scheme and
single-user MIMO.
