  In this paper, we investigate the problem of downlink non-orthogonal multiple
access (NOMA) over block fading channels. For the single antenna case, we
propose a class of NOMA schemes where all the users' signals are mapped into
$n$-dimensional constellations corresponding to the same algebraic lattices
from a number field, allowing every user attains full diversity gain with
single-user decoding, i.e., no successive interference cancellation (SIC). The
minimum product distances of the proposed scheme with arbitrary power
allocation factor are analyzed and their upper bounds are derived. Within the
proposed class of schemes, we also identify a special family of NOMA schemes
based on lattice partitions of the underlying ideal lattices, whose minimum
product distances can be easily controlled. Our analysis shows that among the
proposed schemes, the lattice-partition-based schemes achieve the largest
minimum product distances of the superimposed constellations, which are closely
related to the symbol error rates for receivers with single-user decoding.
Simulation results are presented to verify our analysis and to show the
effectiveness of the proposed schemes as compared to benchmark NOMA schemes.
Extensions of our design to the multi-antenna case are also considered where
similar analysis and results are presented.
