From Priors to Projections: Geometry and simplified MIMO demodulation of probabilistic shaping

Abstract

Probabilistic shaping (PS) is a well-known method to achieve improved performance upon a regular quadrature amplitude modulation (QAM) by taking the target constellation and making the distribution of underlying points non-uniform. It has been extensively studied over the years for the additive white Gaussian noise (AWGN) and Rayleigh fading channels. However, the potential of probabilistic shaping in the multiple-input and multiple-output (MIMO) setting needs further investigations. In this paper, we prove that if shaped symbols follow Maxwell-Boltzmann distribution, the optimal maximum a posteriori (MAP) detection is equivalent to the case of uniform constellation with a simple preprocessing step. Our approach has multiple benefits. It enables to utilize the same processing chain for both shaped and unshaped system, which simplifies the receiver architecture. This technique can be applied for both linear MMSE and nonlinear (near-)MAP demapper types. In addition, the complexity of adaptive methods such as sphere decoding can be reduced.

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BibTeX RIS

BibTeX

@misc{ivanov2026from,
  title = {{From Priors to Projections: Geometry and simplified MIMO demodulation of probabilistic shaping}},
  author = {Kirill Ivanov and Wei Yang and Mahmoud Taherzadeh Boroujeni and Jing Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.13492},
  eprint = {2609.13492},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13492},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - From Priors to Projections: Geometry and simplified MIMO demodulation of probabilistic shaping
AU  - Kirill Ivanov
AU  - Wei Yang
AU  - Mahmoud Taherzadeh Boroujeni
AU  - Jing Jiang
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.13492
UR  - https://arxiv.org/abs/2609.13492
AB  - Probabilistic shaping (PS) is a well-known method to achieve improved performance upon a regular quadrature amplitude modulation (QAM) by taking the target constellation and making the distribution of underlying points non-uniform. It has been extensively studied over the years for the additive white Gaussian noise (AWGN) and Rayleigh fading channels. However, the potential of probabilistic shaping in the multiple-input and multiple-output (MIMO) setting needs further investigations. In this paper, we prove that if shaped symbols follow Maxwell-Boltzmann distribution, the optimal maximum a posteriori (MAP) detection is equivalent to the case of uniform constellation with a simple preprocessing step. Our approach has multiple benefits. It enables to utilize the same processing chain for both shaped and unshaped system, which simplifies the receiver architecture. This technique can be applied for both linear MMSE and nonlinear (near-)MAP demapper types. In addition, the complexity of adaptive methods such as sphere decoding can be reduced.
ER  -

Abstract

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