Training-Efficient Channel Estimation for the Multiuser Uplink Relying on Generalized Flexible Intelligent Metasurfaces

Abstract

We consider uplink multiuser channel estimation for a generalized flexible intelligent metasurface at the base station, under narrowband far-field propagation and a twin-time-scale mechanical protocol: on the slow time-scale the panel translates rigidly over a planar grid, while on the fast time-scale the surface morphs along its normal direction. From orthogonal multiuser pilots, we show that each user's channel admits a fourth-order canonical polyadic tensor structure. We develop two complementary estimators: alternating least squares factorization followed by paired rotational-invariance wavevector extraction, and a tensor spatial-smoothing multiple signal classification estimator that preserves the multilinear array manifold. Both share a minimum description length front-end for automatic tensor-rank detection. We derive Kruskal identifiability conditions that relate the numbers of elements, morphing states and grid positions to the maximum number of recoverable multipath components, and show that the tensor model reconstructs the channel at panel configurations beyond the training grid. This prediction capability drives a configuration-selective multiuser transmit precoder that searches the entire motion grid without additional pilot overhead. Numerical results confirm the identifiability limits and show that, once the model order is resolved, the configuration search makes the same choice from estimated as from perfect channel state information. The reconfiguration gain over a fixed panel of identical aperture and training budget grows with the user load, and fast morphing proves valuable for conditioning the tensor factorization rather than as a source of beamforming gain.