# Capacity-Achieving MIMO-NOMA: Iterative LMMSE Detection

## TL;DR

This paper develops a low-complexity iterative LMMSE detector for MIMO-NOMA systems that achieves capacity and outperforms existing methods, enabling efficient multi-user communication with near-capacity performance.

## Contribution

It derives matching conditions for iterative LMMSE detection in MIMO-NOMA, proving capacity achievement for various user configurations and designing a practical coding scheme.

## Key findings

- Achieves capacity in symmetric MIMO-NOMA with any number of users.
- Attains the sum capacity in asymmetric MIMO-NOMA.
- Outperforms state-of-the-art detection methods in BER performance.

## Abstract

This paper considers a low-complexity iterative Linear Minimum Mean Square Error (LMMSE) multi-user detector for the Multiple-Input and Multiple-Output system with Non-Orthogonal Multiple Access (MIMO-NOMA), where multiple single-antenna users simultaneously communicate with a multiple-antenna base station (BS). While LMMSE being a linear detector has a low complexity, it has suboptimal performance in multi-user detection scenario due to the mismatch between LMMSE detection and multi-user decoding. Therefore, in this paper, we provide the matching conditions between the detector and decoders for MIMO-NOMA, which are then used to derive the achievable rate of the iterative detection. We prove that a matched iterative LMMSE detector can achieve (i) the optimal capacity of symmetric MIMO-NOMA with any number of users, (ii) the optimal sum capacity of asymmetric MIMO-NOMA with any number of users, (iii) all the maximal extreme points in the capacity region of asymmetric MIMO-NOMA with any number of users, (iv) all points in the capacity region of two-user and three-user asymmetric MIMO-NOMA systems. In addition, a kind of practical low-complexity error-correcting multiuser code, called irregular repeat-accumulate code, is designed to match the LMMSE detector. Numerical results shows that the bit error rate performance of the proposed iterative LMMSE detection outperforms the state-of-art methods and is within 0.8dB from the associated capacity limit.