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

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 $\rho = 10\%$ 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 $\rho = 8\%$, while remaining stable at $\rho = 2\%$ 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 $\rho = 2\%$ to $5.67$~dB at $\rho = 20\%$. 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.