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

TL;DR

This work addresses the challenge of estimating wideband MIMO channels under pilot scarcity by leveraging a structure-informed approach that combines low-rank tensor completion with neural residual learning. The method exploits the intrinsic multilinear structure of the channel tensor, enabling recovery from sparse pilot observations, and evaluates CP and Tucker decompositions as well as a hybrid Tensor-NN model. Empirical results show 2–12 dB NMSE improvements over baseline methods for synthetic channels and 24–44% additional NMSE reductions on DeepMIMO ray-tracing channels, with sample complexity scaling with the number of dominant paths and subspace dimensions rather than ambient tensor size. The proposed framework offers a scalable, interpretable route to pilot overhead reduction in beyond-5G/6G MIMO systems and provides a foundation for future extensions to time-varying channels and ISAC scenarios.

Abstract

Channel estimation in wideband multiple-input multiple-output (MIMO) systems faces fundamental pilot overhead limitations in high-dimensional beyond-5G and sixth-generation (6G) scenarios. This paper presents a hybrid tensor-neural architecture that formulates pilot-limited channel estimation as low-rank tensor completion from sparse observations -- a fundamentally different setting from prior tensor methods that assume fully observed received signal tensors. A canonical polyadic (CP) baseline implemented via a projection-based scheme (Tucker completion under partial observations) and Tucker decompositions are compared under varying signal-to-noise ratio (SNR) and scattering conditions: CP performs well for specular channels matching the multipath model, while Tucker provides greater robustness under model mismatch. A lightweight three-dimensional (3D) U-Net learns residual components beyond the low-rank structure, bridging algebraic models and realistic propagation effects. Empirical recovery threshold analysis shows that sample complexity scales approximately with intrinsic model dimensionality $L(N_r + N_t + N_f)$ rather than ambient tensor size $N_r N_t N_f$, where $L$ denotes the number of dominant propagation paths. Experiments on synthetic channels demonstrate 10-20\,dB normalized mean-square error (NMSE) improvement over least-squares (LS) and orthogonal matching pursuit (OMP) baselines at 5-10\% pilot density, while evaluations on DeepMIMO ray-tracing channels show 24-44\% additional NMSE reduction over pure tensor-based methods.

Figures (7)

• Figure 1: Tensor--NN framework: low-rank tensor completion produces a coarse estimate, refined by a 3D U-Net that learns residual components.
• Figure 2: NMSE versus pilot ratio for synthetic channels (SNR $= 10$ dB, $L = 5$ paths, Tucker ranks $(4,4,6)$, 500 MC runs). Tucker completion improves over LS by $\sim$2--12 dB across the sweep, exceeding 10 dB for pilot ratios $\ge 0.10$, and it outperforms OMP at all pilot ratios.
• Figure 3: Tucker versus CP as a function of SNR ($\rho= 8\%$, $L = 5$ paths, Tucker ranks $(5,5,6)$, CP rank $R = 5$, 500 MC runs). CP performs better than Tucker at moderate-to-high SNR for specular channels consistent with the multipath model.
• Figure 4: Performance on DeepMIMO ray-tracing channels (ASU_Campus_3p5 scenario, SNR $= 10$ dB) versus pilot ratio. A purely data-driven ResNet baseline is included for reference. Tensor-NN outperforms Tucker and CP and surpasses ResNet for pilot ratios $\rho \ge 0.04$.
• Figure 5: Recovery curves showing NMSE versus pilot ratio $\rho$ for varying number of paths $L$. Higher SNR sharpens the transition and lowers NMSE within the feasible region.