  In this paper, Tomlinson-Harashima Precoding (THP) is considered for
multi-user multiple-input single-output (MU-MISO) non-orthogonal multiple
access (NOMA) donwlink. Under the hierarchical structure in which multiple
clusters each with two users are formed and served in the spatial domain and
users in each cluster are served in the power domain, THP is applied to
eliminate the inter-cluster interference (ICI) to the strong users and enlarge
the dimension of the beam design space for mitigation of ICI to weak users as
compared to conventional zero-forcing (ZF) inter-cluster beamforming. With the
enlarged beam design space, two beam design algorithms for THP-aided MISO-NOMA
are proposed. The first is a greedy sequential beam design with user
scheduling, and the second is the joint beam redesign and power allocation. The
two design problems lead to non-convex optimization problems. An efficient
algorithm is proposed to solve the non-convex optimization problems based on
successive convex approximation (SCA). Numerical results show that the proposed
user scheduling and two beam design methods based on THP yield noticeable gain
over existing methods.
