An Exact Analysis on Matrix-Based Precoding for the Common Message in Downlink Rate Splitting Multiple Access

We propose a matrix-based precoding scheme for the common message in downlink rate splitting multiple access (RSMA), where a multi-antenna transmitter serves
$K$
single-antenna users at a time. In the proposed precoding scheme, the matched filtering (MF) precodes the common message, while the private messages are preceded by zero-forcing (ZF). We derive the closed-form expression for the outage probability of the MF/ZF-based RSMA over Rayleigh fading channels. Moreover, we also derive an analytical expression for the ergodic sum rate. In the end, numerical results are presented to validate the correctness of the derived expressions, as well as demonstrate the advantage of our proposed scheme.