  This letter rethinks traditional precoding in multi-user wireless
communications with movable antennas (MAs). Utilizing MAs for optimal antenna
positioning, we introduce a sparse optimization (SO)-based approach focusing on
regularized zero-forcing (RZF). This framework targets the optimization of
antenna positions and the precoding matrix to minimize inter-user interference
and transmit power. We propose an off-grid regularized least squares-based
orthogonal matching pursuit (RLS-OMP) method for this purpose. Moreover, we
provide deeper insights into antenna position optimization using RLS-OMP,
viewed from a subspace projection angle. Overall, our proposed flexible
precoding scheme demonstrates a sum rate that exceeds more than twice that of
fixed antenna positions.
