Hamiltonian Monte Carlo for Vector Perturbation Precoding in MU-MIMO via Continuous Relaxation
Abstract
Multi-user multiple-input multiple-output (MU-MIMO) is a key technology that improves wireless capacity through multiple antennas. In MU-MIMO downlink precoding, vector perturbation (VP) is a representative nonlinear method that achieves high performance. However, its search for the integer perturbation vector reduces to a closest vector problem, whose complexity grows rapidly as the number of users increases. We propose a method that relaxes the discrete structure of the integer perturbation into a continuous mixture of t-distributions, enabling efficient search via gradient-based Hamiltonian Monte Carlo (HMC). Complexity analysis and numerical experiments demonstrate the effectiveness of the proposed method. Its search complexity scales as O(N^2) in the number of users N. At a symbol error rate of 10^-3, it performs within 2.4 dB of a hypersphere approximation benchmark, which approximates the performance limit of VP. This paper reframes the VP perturbation search as a probabilistic inference problem, providing a general formulation for handling high-dimensional discrete search in a continuous space.
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BibTeX
@misc{hagiwara2026hamiltonian,
title = {{Hamiltonian Monte Carlo for Vector Perturbation Precoding in MU-MIMO via Continuous Relaxation}},
author = {Junichiro Hagiwara and Toshihiko Nishimura and Yasutaka Ogawa and Takeo Ohgane},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23011},
eprint = {2609.23011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23011},
}
RIS
TY - UNPB
TI - Hamiltonian Monte Carlo for Vector Perturbation Precoding in MU-MIMO via Continuous Relaxation
AU - Junichiro Hagiwara
AU - Toshihiko Nishimura
AU - Yasutaka Ogawa
AU - Takeo Ohgane
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.23011
UR - https://arxiv.org/abs/2609.23011
AB - Multi-user multiple-input multiple-output (MU-MIMO) is a key technology that improves wireless capacity through multiple antennas. In MU-MIMO downlink precoding, vector perturbation (VP) is a representative nonlinear method that achieves high performance. However, its search for the integer perturbation vector reduces to a closest vector problem, whose complexity grows rapidly as the number of users increases. We propose a method that relaxes the discrete structure of the integer perturbation into a continuous mixture of t-distributions, enabling efficient search via gradient-based Hamiltonian Monte Carlo (HMC). Complexity analysis and numerical experiments demonstrate the effectiveness of the proposed method. Its search complexity scales as O(N^2) in the number of users N. At a symbol error rate of 10^-3, it performs within 2.4 dB of a hypersphere approximation benchmark, which approximates the performance limit of VP. This paper reframes the VP perturbation search as a probabilistic inference problem, providing a general formulation for handling high-dimensional discrete search in a continuous space.
ER -