# On Low Complexity Detection for QAM Isomorphic Constellations

## TL;DR

This paper proposes a low complexity detection method for QAM isomorphic constellations that nearly matches peak-power limited capacity, outperforming standard QAM in efficiency without increasing detection complexity.

## Contribution

It introduces a systematic detection strategy for QAM isomorphic constellations that achieves significant gains and simplifies the detection process.

## Key findings

- Gains larger than 0.6 dB over QAM in peak power limited channels.
- The detection complexity remains unchanged while improving performance.
- Provides a systematic approach for designing low complexity constellations.

## Abstract

Despite of the known gap from the Shannon's capacity, several standards are still employing QAM or star shape constellations, mainly due to the existing low complexity detectors. In this paper, we investigate the low complexity detection for a family of QAM isomorphic constellations. These constellations are known to perform very close to the peak-power limited capacity, outperforming the DVB-S2X standard constellations. The proposed strategy is to first remap the received signals to the QAM constellation using the existing isomorphism and then break the log likelihood ratio computations to two one dimensional PAM constellations. Gains larger than 0.6 dB with respect to QAM can be obtained over the peak power limited channels without any increase in detection complexity. Our scheme also provides a systematic way to design constellations with low complexity one dimensional detectors. Several open problems are discussed at the end of the paper.