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

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.

State-of-Charge Estimation of a Li-Ion Battery using Deep Forward Neural Networks

This article presents two Deep Forward Networks with two and four hidden layers, respectively, that model the drive cycle of a Panasonic 18650PF lithium-ion (Li-ion) battery at a given temperature using the K-fold cross-validation method, in order to estimate the State of Charge (SOC) of the cell. The drive cycle power profile is calculated for an electric truck with a 35kWh battery pack scaled for a single 18650PF cell. We propose a machine learning workflow which is able to fight overfitting when developing deep learning models for SOC estimation. The contribution of this work is to present a methodology of building a Deep Forward Network for a lithium-ion battery and its performance assessment, which follows the best practices in machine learning.