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arXiv 2602.04083eess.SPcs.AI
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通过张量分解的结构引导估计以解决受限于试点的MIMO信道

Structure-Informed Estimation for Pilot-Limited MIMO Channels via Tensor Decomposition

Faculty of Exact Sciences and Technology, Pontifical Catholic University of São Paulo (PUC-SP)（精确科学与技术学院，圣保罗天主教大学）

Alexandre Barbosa de Lima

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AI总结：

本文提出一种结合张量分解和深度学习的混合估计器，用于在受限于试点的MIMO信道中实现高精度估计，通过结构引导方法提升低秩补全和残差学习的性能。

摘要：

在宽带多输入多输出（MIMO）系统中，准确的信道状态信息从根本上受到试点开销的限制，这一挑战随着天线数量和带宽向6G扩展而加剧。本文提出了一种结构引导的混合估计器，将受限于试点的MIMO信道估计建模为从稀疏试点观测中进行低秩张量补全——一个严重欠定的逆问题，此前的张量方法通过假设完全观测的接收信号张量来避免。可以张量分解进行比较分析：CP在具有镜面信道的秩一多径结构与CP参数化完全匹配时表现优异，而Tucker在极端试点稀缺的情况下提供更大的数值稳定性，其中CP表现出重尾发散。一个轻量级的3D U-Net学习残差成分，超越主导的低秩结构，补偿扩散散射和硬件非理想性，这些无法仅用代数先验来捕捉。在合成镜面信道上，Tucker补全在试点密度为10%时比最小二乘法提高10.88 dB，在20 dB SNR下，CP比Tucker高出13.11 dB。在DeepMIMO射线追踪信道上，混合估计器在试点密度为8%时超越CP 2.26 dB，超越Tucker 4.80 dB，而在试点密度为2%时保持稳定，此时CP发散；代数结构在全试点密度范围内始终优于无约束深度学习，差距从在试点密度为2%时的1.53 dB增长到在试点密度为20%时的5.67 dB。经验恢复阈值分析确认，样本复杂度与内在信道维度——由主导传播路径的数量决定——而不是与环境张量大小相关。

英文摘要：

Accurate channel state information in wideband MIMO systems is constrained by pilot overhead, a challenge intensifying as bandwidths scale toward 6G. This paper proposes a structure-informed hybrid estimator formulating pilot-limited MIMO channel estimation as low-rank tensor completion from sparse pilot observations---an underdetermined inverse problem that prior approaches avoid by assuming fully observed tensors. Canonical polyadic~(CP) and Tucker decompositions are compared: CP excels for specular channels matching its rank-one parameterization exactly, while Tucker provides numerical stability at extreme pilot scarcity where CP exhibits heavy-tail divergence. A lightweight 3D U-Net learns residual components beyond the low-rank structure, compensating for diffuse scattering and hardware non-idealities. On synthetic specular channels, Tucker completion improves normalized mean-squared error (NMSE) by $10.88$~dB over least squares and $7.83$~dB over orthogonal matching pursuit at $10\%$ pilot density ($ρ$); CP outperforms Tucker by $13.11$~dB at SNR=20~dB. On DeepMIMO channels, the hybrid Tensor--NN estimator has two regimes: Tensor--NN(Tucker) remains stable at $ρ=2\%$ where CP diverges, while a CP-guided variant becomes best from $ρ\ge 4\%$, reaching $-16.44$~dB at $ρ=8\%$ and $-20.34$~dB at $ρ=20\%$. The Tucker-guided variant outperforms unconstrained deep learning across the full pilot range; the CP-guided variant widens this gap once stable. Empirical analysis confirms sample complexity scales with intrinsic channel dimensionality (dominant paths) rather than ambient tensor size.

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