A semi-blind channel estimator required fewer than half as many pilot symbols as a training-based method to reach the same target mean-squared error in one simulated satellite-uplink test. Across signal-to-noise ratios from 5 to 20 decibels, the proposed method also had lower plotted channel-estimation error than expectation-maximization and subspace-based methods. The findings come from mathematical analysis and Monte Carlo simulations, not measured channels, hardware or a field trial.
A second source of information
The method was tested in a single-cell uplink multiple-input, multiple-output model, with an M-antenna base station serving K single-antenna users. The model treats the channel as block-fading across N-symbol coherence blocks: L symbols carry pilots and the remaining N−L symbols carry data. Its regularized least-squares objective combines the pilot-based training information with a blind subspace criterion, allowing the modeled data observations to enter the channel estimate alongside the pilots.
Spiked random matrix theory is used to choose the regularization parameter analytically from the covariance structure. The parameter sets the balance between the training-based and blind parts of the objective. The derivation depends on the paper’s high-dimensional assumptions.
What the theory establishes
The mathematical results concern the behavior of the estimator as system dimensions grow. The appendix states that the mean-squared error converges uniformly over regularization values from 0 to 1. It also reports that a sample-based estimate of the regularization parameter is consistent for the asymptotically optimal value. Within the specified semi-blind estimator family, the proposed estimator is reported to attain the minimum mean-squared error asymptotically.
Those are asymptotic statements, so they are not finite-sample guarantees. The reported minimum applies within the specified semi-blind estimator family, rather than to every possible channel estimator. The analysis reports no finite-sample error bound for the selected parameter.
How the comparisons looked
In one finite-dimensional sweep, the minimum plotted mean-squared error occurred at a regularization value of 0.13, close to the theoretical optimum of 0.1350 and the deterministic Cramer-Rao bound. The normalized mean absolute error, or NMAE, decreased as system dimensions increased. The asymptotic approximation remained accurate across the tested 5 to 20 decibel signal-to-noise range. Exact NMAE values and uncertainty intervals were not tabulated.
The proposed method had lower plotted mean-squared error than the expectation-maximization and subspace-based methods across the tested signal-to-noise range of 5 to 20 decibels. As the number of users increased from 2 to 10, mean-squared error decreased for all three algorithms, while the proposed method remained better than the other two. Under moderate temporal variation, the plots showed lower mean-squared error at higher pilot ratios for all the methods considered. The proposed estimator had the lowest plotted error, and its relative advantage was larger at low pilot overhead.
In system-level simulations using uplink minimum mean-squared-error detection, the proposed estimator had lower plotted bit-error rate and higher achievable sum rate than the training-based estimator over the considered signal-to-noise range. The proposed results approached the reference with perfect channel information as signal-to-noise ratio increased. Exact bit-error-rate and rate values, along with uncertainty intervals, were not reported.
The clearest pilot saving
A target-error experiment used a block length of N=512, a pilot-ratio parameter of alpha=1/2, K=3 users and a signal-to-noise ratio of 15 decibels. In that modeled setting, the semi-blind method required fewer than half as many pilot symbols as the training-based method to reach the same target mean-squared error. The exact pilot lengths were shown graphically, without uncertainty estimates.
Results bounded by the model
The numerical study used the open-source Sionna/OpenNTN framework with 3GPP TR 38.811 non-terrestrial-network models. The default scenario was Dense Urban, with a 2 gigahertz carrier, a satellite altitude of 600 kilometers, an elevation angle of 10 degrees and a vertically polarized 1 by 512 satellite array. Each simulation point was averaged over 1,000 independent Monte Carlo realizations.
The block-fading setup assumes that the channel is approximately constant across the pilot and data observations. Temporal change was explored through a stylized first-order process under moderate variation. The supplied analysis identifies model mismatch, weak spikes, nonorthogonal pilots, other signal constellations and channel changes within a pilot/data block as open questions for the method.
The work is an arXiv preprint version 1, dated 26 August 2026. Its evidence is limited to mathematical derivations under stated asymptotic assumptions and finite simulations of modeled uplink channels. It does not establish performance on measured non-terrestrial-network channels, deployed hardware or field data, or outside the specified channel models, parameter ranges and semi-blind estimator family.
Paper data and sources
Original title: Semi-Blind Channel Estimation for Dynamic NTN Systems via Spiked Random Matrix Theory
Authors: Xue Zhang, Abla Kammoun, Mohamed-Slim Alouini
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text