# Downlink Non-Orthogonal Multiple Access without SIC for Block Fading Channels: An Algebraic Rotation Approach

## TL;DR

This paper introduces a novel algebraic rotation approach for downlink NOMA over block fading channels, enabling full diversity gain without SIC and improving error performance compared to existing schemes.

## Contribution

It proposes a new class of NOMA schemes using algebraic lattices that achieve full diversity with single-user decoding, eliminating the need for SIC.

## Key findings

- Lattice-partition-based schemes attain the largest minimum product distances.
- Proposed schemes outperform benchmark NOMA schemes in simulations.
- Analysis extends to multi-antenna scenarios with similar benefits.

## Abstract

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.