Feb 2026· arXiv.org· Vol abs/2602.04083· 0 citations· 55 references
Computer ScienceEngineering
TL;DR
A structure-informed hybrid estimator formulating pilot-limited MIMO channel estimation as low-rank tensor completion from sparse pilot observations is proposed---an underdetermined inverse problem that prior approaches avoid by assuming fully observed tensors.
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.
Accurate channel estimation in frequency-selective multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems requires balancing pilot overhead, reconstruction accuracy, and computational cost. This paper presents a reproducible compressed sensing benchmark for sparse delay-domain channel estimation with reduced pilot observations. Its novelty is not the invention of Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), or Subspace Pursuit (SP), but the construction of a transparent and auditable evaluation protocol in which all estimators operate on the same channel realizations, sensing matrices, pilot budgets, signal-to-noise ratios (SNRs), stopping rules, and Monte Carlo trials. The framework explicitly defines the underdetermined observation model, the per-link 4 × 4 MIMO interpretation, the minimum-norm least-squares (LS) baseline, the identity-prior linear minimum mean-square error (LMMSE) baseline, the oracle-known sparsity assumption, uncertainty reporting, runtime protocol, and the mapping from delay-domain estimates to link- and subcarrier-domain quantities. OMP, CoSaMP, SP, LS, and LMMSE are evaluated for a 128-element delay dictionary, five active taps, sampling ratios from 0.10 to 0.70, SNRs from 0 to 30 dB, and 80 independent trials per operating point. The results show that sparse recovery exploits the assumed delay-domain sparsity more effectively than non-sparse baselines in the underdetermined regime, while pilot density remains a dominant factor in support identification and reconstruction error. The accompanying Python human–machine interface (HMI) produces confidence-aware metrics and publication-ready figures, enabling exact repetition of the benchmark and controlled extension to more realistic channel models. The conclusions are limited to simulation-based algorithmic evidence and define a direct pathway toward standardized-channel, software-defined radio (SDR), and measured radio-frequency (RF) validation.
Juan Inga, Elias Yaacoub, M. Al-Ali et al.· Electronics· 0 citations
Low-complexity channel state information acquisition is crucial for extremely large-scale multiple-input multiple-output (XL-MIMO) systems. However, practical deployments of non-square uniform planar arrays (UPAs) in hybrid-field environments face prohibitive computational complexity and degraded estimation accuracy due to limited elevation angle-of-arrival (AoA) resolution and deteriorated channel sparsity. To tackle these challenges, we propose a low-complexity channel estimation framework. First, an antenna-domain extrapolation scheme synthesizes a virtually enlarged vertical aperture via the spatial correlation among adjacent elements, breaking the elevation resolution limit. The framework then disentangles the parameter coupling by transforming the two-dimensional joint search into two sequential one-dimensional searches. Specifically, elevation AoAs are extracted via an extrapolation-enhanced discrete Fourier transform-Newtonized orthogonal matching pursuit (NOMP) algorithm along the virtually enlarged vertical uniform linear array (ULA), while azimuth AoAs, ranges, and gains are acquired utilizing a discrete fractional Fourier transform-NOMP algorithm along a horizontal ULA. A subspace fitting-driven path matching algorithm pairs these decoupled parameters. To overcome the accuracy bottleneck of the antenna-domain scheme, a correlation-domain extrapolation scheme is further developed by exploiting the structural properties of the spatial correlation matrix to decouple the near-field quadratic and azimuth phase components, yielding a noise-suppressed virtual array. Numerical results validate the effectiveness of the proposed framework.
Yilong Liu, Xi Yang, Binggui Zhou et al.· 0 citations
Accurate channel state information (CSI) is critical for downlink (DL)-multi-user (MU)-multiple-input multiple-output (MIMO) systems, where feedback delays and mobility can degrade precoding performance. To ensure reliable beamforming and interference mitigation, CSI prediction is required. In practical systems, full CSI feedback is often infeasible due to signaling overhead, so transmitters rely on partial CSI reported by the receivers. In this work, we propose a Gaussian mixture model (GMM)-based prediction framework for MIMO-orthogonal frequency-division multiplexing (OFDM) channels under partial feedback using Gram-square-root factorization. To address the high dimensionality, we introduce an efficient parameter reduction technique that exploits structured covariance matrices, significantly lowering complexity without noticeable performance degradation. This reduction is based on the Gram-square-root factorization and remains of interest even when full CSI is available. Simulation results demonstrate that GMMs achieve the highest prediction accuracy and correctly capture the underlying channel subspaces, which is essential for effective MU-precoding. The proposed method outperforms classical baselines such as zero-order hold (ZOH), first-order hold (FOH), and linear minimum mean squared error (LMMSE) predictors, and an advanced neural network (NN)-based predictor. Notably, the parameter-reduced partial CSI GMM achieves performance comparable to that of full CSI prediction, highlighting its ability to efficiently model the channel structure under limited feedback.
Kathrin Klein, Amar Kasibovic, M. Joham et al.· 0 citations
The scalability of modern Massive MIMO systems and prospective 6G networks is fundamentally constrained by the “pilot contamination” effect and the prohibitive overhead of time-frequency resources required for orthogonal pilot transmission. In ultra-dense deployment scenarios, traditional pilot-aided channel estimation methods exhibit a critical degradation in spectral efficiency. The study aims to develop a resource-efficient method for blind channel estimation that is invariant to antenna array topology, with the goal of minimizing signaling overhead and maximizing throughput capacity under conditions of complex spatial correlation. The proposed approach is based on the statistical processing of the sample covariance matrix of received signals utilizing a deep convolutional neural network. In contrast to direct reconstruction techniques, the algorithm employs a residual learning strategy to isolate and mitigate estimation noise arising from finite sample sizes. To resolve the phase ambiguity of the signal subspace, a “virtual pilot” concept (a single reference symbol) is introduced, ensuring that resource overhead approaches zero asymptotically. The study is validated across a wide spectrum of configurations, including linear, rectangular, and circular arrays, as well as distributed antenna systems. Simulation results confirm that the proposed method yields a significant gain in the system’s aggregate spectral efficiency by liberating resources previously allocated to pilot sequences. Despite a marginal degradation in estimation accuracy compared to conventional methods, the algorithm demonstrates high robustness to various spatial correlation profiles and antenna geometries. The proposed method facilitates the realization of massive connectivity scenarios on existing base station hardware architectures, effectively overcoming throughput limitations imposed by the coherence interval length.
Efficient Channel State Information (CSI) feedback is indispensable for frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. Existing compressed sensing (CS) algorithms exploit delay-domain sparsity but suffer from prohibitive iterative latency and discrete grid mismatch. Conversely, deep learning (DL) approaches achieve rapid inference but lack spatial scalability and domain adaptability, failing to generalize to unseen propagation environments, and demand computationally heavy encoders and decoder. In this paper, we propose TAP, a Tap-Assisted Parametric CSI Compression. TAP is a one-shot neural framework that unifies the speed of DL with the mathematical interpretability of CS. TAP replaces iterative pursuit with a lightweight 1D neural network that extracts dominant continuous propagation delays from temporal channel sequences via a differentiable sub-grid interpolation operator. TAP achieves true architecture independence, enabling zero-shot generalization across diverse array geometries and unseen propagation environments. Furthermore, TAP yields a completely decoder-free payload, allowing the BS to reconstruct the channel via a simple inverse fast Fourier transform (IFFT). Extensive evaluations across five 3GPP environments demonstrate that TAP achieves a 3.13 to 12.22 dB channel frequency response normalized mean square error (CFR-NMSE) improvement over CsiNet while shrinking the model footprint by 660 times to under 1 MB. Operating with sub-millisecond latencies, TAP accelerates inference by 2700 times over classical iterative OMP, providing a scalable and deployment-ready solution for next-generation networks.
Minwoo Kim, Hyeonsu Lyu, Sehyun Ryu et al.· 0 citations
Singular value decomposition (SVD) is a core operation in multiple-input multiple-output (MIMO) beamforming, but the cubic complexity of standard SVD routines can lead to a major latency bottleneck as array dimensions scale to extremely large sizes. This paper presents a fully learned neural operator that avoids explicit SVD computation by directly mapping channel matrices to truncated low-rank factors for precoder and combiner design. In contrast to iterative numerical solvers and algorithm-unrolled networks, the proposed structure-aware model, termed SVDNet, produces these factors in a single forward pass at inference, shifting the per-instance decomposition cost to offline training. The model also includes lightweight constraints to enforce basic algebraic properties required by beamforming, such as semi-unitarity of the singular vectors and nonnegative singular values, without invoking matrix factorization kernels. Experiments on extremely large-scale MIMO channels with matrix dimensions up to 512*512 show that the proposed approach achieves spectral efficiency close to exact SVD-based beamforming in single-stream transmission and consistently improves multi-stream sum-rate over representative learned baselines, indicating good scalability for low-latency wireless processing.
Yue Zhang, Yi-Yan Zhang, Rui-Jin Sun et al.· 0 citations
