用张量分解在极少导频下精准估计大规模MIMO信道，提升6G系统性能。
Structure-Informed Estimation for Pilot-Limited MIMO Channels via Tensor Decomposition
- 将稀疏导频下的信道估计建模为低秩张量补全问题，融合张量分解与轻量网络。
- 在10%导频密度下，相比传统方法性能提升7.83~10.88dB，极端稀疏时更稳定。
- 适用于6G宽带系统，尤其适合导频资源受限的场景，兼顾精度与鲁棒性。
宽频带大规模多输入多输出（MIMO）系统中的精确信道状态信息受限于导频开销，这一挑战在迈向6G的高带宽趋势下愈发严峻。本文提出一种结构感知的混合估计算法，将导频受限的MIMO信道估计建模为从稀疏导频观测中进行低秩张量补全——一个此前方法因假设完全观测而回避的欠定逆问题。对比了典型多线性（CP）与托克斯特（Tucker）分解：当信道具有镜面反射特性时，匹配其秩-1参数化的CP表现更优；而在极端导频稀缺情况下，CP出现重尾发散，而Tucker更具数值稳定性。引入轻量级3D U-Net学习低秩结构之外的残差分量，以补偿散射和硬件非理想性。在合成镜面信道上，Tucker补全在10%导频密度（ρ）下相较最小二乘提升10.88 dB、较正交匹配追踪提升7.83 dB；CP在SNR=20 dB时优于Tucker达13.11 dB。在DeepMIMO信道上，混合张量-神经网络（Tensor–NN）估计算法呈现两种模式：在ρ=2%时，基于Tucker的版本保持稳定，而CP版本发散；当ρ≥4%时，基于CP的变体成为最优，在ρ=8%和20%时分别达到-16.44 dB和-20.34 dB的性能。基于Tucker的变体在整个导频范围内优于无约束深度学习，而基于CP的变体在稳定后进一步扩大优势。实证分析证实样本复杂度与信道内在维度（主导路径数）相关，而非张量的环境尺寸。
原文摘要 · Abstract (English)
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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