  In this paper, we consider the precoder design for downlink multiple-input
multiple-output (MIMO) rate-splitting multiple access (RSMA) systems. The
proposed scheme with simultaneous diagonalization (SD) decomposes the MIMO
channel matrices of the users into scalar channels via higher-order generalized
singular value decomposition for the common message (CM) and block
diagonalization (BD) for the private messages, thereby enabling low-complexity
element-by-element successive interference cancellation (SIC) and decoding at
the receivers. Furthermore, the proposed SD MIMO-RSMA overcomes a critical
limitation in RSMA systems, whereby the achievable rate of the CM is restricted
by the users with weak effective MIMO channel for the CM, by excluding a subset
of users from decoding the CM. We formulate a non-convex weighted sum rate
(WSR) optimization problem for SD MIMO-RSMA and solve it via successive convex
approximation to obtain a locally optimal solution. Our simulation results
reveal that, for both perfect and imperfect CSI, the proposed SD MIMO-RSMA with
user exclusion outperforms baseline MIMO-RSMA schemes and linear BD precoding.
