  In this paper, we consider the downlink precoder design for two-user
power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple
access (NOMA) systems. The proposed precoding scheme is based on simultaneous
triangularization and decomposes the MIMO-NOMA channels of the two users into
multiple single-input single-output NOMA channels, assuming low-complexity
self-interference cancellation at the users. In contrast to the precoding
schemes based on simultaneous diagonalization (SD), the proposed scheme avoids
inverting the MIMO channels of the users, thereby enhancing the ergodic rate
performance. Furthermore, we develop a power allocation algorithm based on the
convex-concave procedure, and exploit it to obtain the ergodic achievable rate
region of the proposed MIMO-NOMA scheme. Our results illustrate that the
proposed scheme outperforms baseline precoding schemes based on SD and
orthogonal multiple access for a wide range of user rates and performs close to
the dirty paper coding upper bound. The ergodic rate region can further be
improved by utilizing a hybrid scheme based on time sharing between the
proposed MIMO-NOMA scheme and point-to-point MIMO.
