  Rate-Splitting (RS) has been proposed recently to enhance the performance of
multi-user multiple-input multiple-output (MU-MIMO) systems. In RS, a user
message is split into a common and a private part, where the common part is
decoded by all users, while the private part is decoded only by the intended
user. In this paper, we study RS under a phase-shift keying (PSK) input
alphabet for multi-user multi-antenna system and propose a constructive
interference (CI) exploitation approach to further enhance the sum-rate
achieved by RS under PSK signaling. To that end, new analytical expressions for
the ergodic sum-rate are derived for two precoding techniques of the private
messages, namely, 1) a traditional interference suppression zero-forcing (ZF)
precoding approach, 2) a closed-form CI precoding approach. Our analysis is
presented for perfect channel state information at the transmitter (CSIT), and
is extended to imperfect CSIT knowledge. A novel power allocation strategy,
specifically suited for the finite alphabet setup, is derived and shown to lead
to superior performance for RS over conventional linear precoding not relying
on RS (NoRS). The results in this work validate the significant sum-rate gain
of RS with CI over the conventional RS with ZF and NoRS.
