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

Abstract

Accurate channel state information in wideband multiple-input multiple-output (MIMO) systems is fundamentally constrained by pilot overhead, a challenge that intensifies as antenna counts and bandwidths scale toward 6G. This paper proposes a structure-informed hybrid estimator that formulates pilot-limited MIMO channel estimation as low-rank tensor completion from sparse pilot observations—a severely underdetermined inverse problem that prior tensor approaches avoid by assuming fully observed received signal tensors. Canonical polyadic (CP) and Tucker decompositions are comparatively analyzed: CP excels for specular channels whose rank-one multipath structure matches the CP parameterization exactly, while Tucker provides greater numerical stability at extreme pilot scarcity where CP exhibits heavy-tail divergence. A lightweight 3D U-Net learns residual components beyond the dominant low-rank structure, compensating for diffuse scattering and hardware non-idealities that algebraic priors alone cannot capture. On synthetic specular channels, Tucker completion achieves 10.88 dB NMSE improvement over least squares and 7.83 dB over orthogonal matching pursuit at ρ = 10% pilot density; CP outperforms Tucker by 13.11 dB at SNR=20 dB under the specular multipath model. On DeepMIMO ray-tracing channels, the hybrid estimator surpasses CP by 2.26 dB and Tucker by 4.80 dB at ρ = 8%, while remaining stable at ρ = 2% where CP diverges; algebraic structure consistently outperforms unconstrained deep learning across the full pilot-density range, with a margin growing from 1.53 dB at ρ = 2% to 5.67 dB at ρ = 20%. Empirical recovery threshold analysis confirms that sample complexity scales with intrinsic channel dimensionality—governed by the number of dominant propagation paths—rather than with the ambient tensor size.