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

arXiv:2602.04083v3 Announce Type: replace-cross Abstract: 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 ($\rho$); 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 $\rho=2\%$ where CP diverges, while a CP-guided variant becomes best from $\rho\ge 4\%$, reaching $-16.44$~dB at $\rho=8\%$ and $-20.34$~dB at $\rho=20\%$. 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.

Abstract: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 ($\rho$); 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 $\rho=2\%$ where CP diverges, while a CP-guided variant becomes best from $\rho\ge 4\%$, reaching $-16.44$~dB at $\rho=8\%$ and $-20.34$~dB at $\rho=20\%$. 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.

Signal Processing (eess.SP); Artificial Intelligence (cs.AI)

arXiv:2602.04083 [eess.SP]

(or arXiv:2602.04083v3 [eess.SP] for this version)

From: Alexandre Lima Ph.D. [view email] [v1] Tue, 3 Feb 2026 23:38:05 UTC (148 KB) [v2] Mon, 2 Mar 2026 02:57:56 UTC (27,390 KB) [v3] Wed, 19 Aug 2026 13:29:38 UTC (485 KB)

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

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