An Online Calibration Method Using Hadamard–Fourier Clustering and Neural Network for Large-Scale Phased Arrays
Bibliographic record
Abstract
This article proposes a novel online calibration method based on clustering for large-scale phased array antennas. The proposed clustering method leverages Hadamard and Fourier (HaF) transform features, resulting in increased output power variation (suitable for large phased array calibration), noise robustness, and fewer measurements compared with traditional methods. In addition, it eliminates the need for extra phase measurement instruments, as it relies solely on power measurements. Analytical closed forms are derived to demonstrate the effectiveness of HaF clustering. In this method, the mean phase error (MPhE) in each cluster is determined by a combination of Hadamard features and the extended rotational electrical vector (eREV) field method. Using a trained multilayer perceptron (MLP) neural network and feeding it with each cluster’s MPhEs, the direction of arrival (DOA) error is determined. Subsequently, antenna phase errors are estimated based on the DOA error, and new calibration coefficients are applied to the array. To validate the proposed online calibration method, Monte Carlo simulations and experimental measurements were conducted on a 1024-element modular planar phased array receiver within the frequency range of 18–21 GHz and an angle of elevation range between −70° and 70°. The simulation and experimental results indicate a mean absolute error (MAE) value of approximately 6° for phase error determination and a DOA estimation error of less than 0.1° using the MLP. Furthermore, the array can be calibrated with a maximum calibration error of less than 0.1° within a period of 3 ms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".